Search Results (5,999)

Figure 1
<p>Graph of susceptible against time t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Caputo–Fabrizio case.</p> Full article ">Figure 2
<p>Graph of infected against time t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Caputo–Fabrizio case.</p> Full article ">Figure 3
<p>Graph of recovered against time t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Caputo–Fabrizio case.</p> Full article ">Figure 4
<p>Graph of susceptible with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Riemann–Liouville’s case.</p> Full article ">Figure 5
<p>Graph of infected with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Riemann–Liouville’s case.</p> Full article ">Figure 6
<p>Graph of recovered with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in Riemann–Liouville’s case.</p> Full article ">Figure 7
<p>Graph of susceptible with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in ABC case.</p> Full article ">Figure 8
<p>Graph of infected with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in ABC case.</p> Full article ">Figure 9
<p>Graph of recovered with respect to t, for <math display="inline"><semantics> <mi>τ</mi> </semantics></math> = 0.7 and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> in ABC case.</p> Full article ">Figure 10
<p>Graph of susceptible, infected and recovered class with respect to t, for x=0.15, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> in CF case.</p> Full article ">Figure 11
<p>Graph of susceptible, infected and recovered class with respect to t, for x=0.15, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> in RL case.</p> Full article ">Figure 12
<p>Graph of susceptible, infected and recovered class with respect to t, for x=0.15, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> in ABC case.</p> Full article ">Figure 13
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.01 in CF case.</p> Full article ">Figure 14
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.001 in CF case.</p> Full article ">Figure 15
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.0001 in CF case.</p> Full article ">Figure 16
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.01 in RL case.</p> Full article ">Figure 17
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.001 in RL case.</p> Full article ">Figure 18
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.0001 in RL case.</p> Full article ">Figure 19
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.01 in ABC case.</p> Full article ">Figure 20
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.001 in ABC case.</p> Full article ">Figure 21
<p>Graph of susceptible, infected and recovered class with respect to t, for diffusion coefficient 0.0001 in ABC case.</p> Full article ">Figure 22
<p>Graph of susceptible with CF, RL and ABC derivative for <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math>.</p> Full article ">Figure 23
<p>Graph of infected with CF, RL and ABC derivative for <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math>.</p> Full article ">Figure 24
<p>Graph of recovered with CF, RL and ABC derivative for <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math>.</p> Full article ">

Figure 1
<p>Palladium and copper application, impact on the body, dietary sources and prices, supply, demand, and uses.</p> Full article ">Figure 1 Cont.
<p>Palladium and copper application, impact on the body, dietary sources and prices, supply, demand, and uses.</p> Full article ">Figure 2
<p>(<b>a</b>) Percentage content of elements and (<b>b</b>) comparison of <span class="html-italic">pH_PZC</span> values in/for Lewatit^® VP OC 1065 and Diaion™ CR20 ion exchange resins.</p> Full article ">Figure 3
<p>Low-temperature adsorption/desorption nitrogen isotherm of (<b>a</b>) Diaion™ CR20 and (<b>b</b>) Lewatit^® VP OC 1065 ion exchangers.</p> Full article ">Figure 4
<p>ATR/FT-IR spectra of (<b>a</b>) Diaion™ CR20 and (<b>b</b>) Lewatit^® VP OC 1065 before and after loading with Pd(II) and Cu(II) ions.</p> Full article ">Figure 5
<p>Comparison of M(II) sorption efficiency expressed in <span class="html-italic">q_t</span> values for Diaion™ CR20 (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) and Lewatit^® VP OC 1065 (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>).</p> Full article ">Figure 5 Cont.
<p>Comparison of M(II) sorption efficiency expressed in <span class="html-italic">q_t</span> values for Diaion™ CR20 (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) and Lewatit^® VP OC 1065 (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>).</p> Full article ">Figure 6
<p>Effects of contact time and agitation speed on the Pd(II) adsorption on Diaion™ CR20 (<b>a</b>) and Lewatit^® VP OC 1065 (<b>b</b>).</p> Full article ">Figure 7
<p>Effects of contact time and the initial Pd(II) concentration on Pd(II) adsorption on Diaion™ CR20 (<b>a</b>) and Lewatit^® VP OC 1065 (<b>b</b>).</p> Full article ">Figure 8
<p>Effects of contact time and bead size of ion exchangers (f5 &lt; 0.385 mm; 0.385 mm ≤ f4 &lt; 0.43 mm; 0.43 mm ≤ f3 &lt; 0.6 mm; 0.6 mm ≤ f2 &lt; 0.75 mm; 0.75 mm ≤ f1 &lt; 1.2 mm) on Pd(II) adsorption on Diaion™ CR20 (<b>a</b>,<b>c</b>) and Lewatit^® VP OC 1065 (<b>b</b>,<b>d</b>).</p> Full article ">Figure 9
<p>Effects of contact time and temperature on the Pd(II) adsorption on Diaion™ CR20 (<b>a</b>) and Lewatit^® VP OC 1065 (<b>b</b>).</p> Full article ">Figure 10
<p>Effects of contact time and initial concentration (<b>a</b>), agitation speed (<b>b</b>), bead size of ion exchanger (f5 &lt; 0.385 mm; 0.385 mm ≤ f4 &lt; 0.43 mm; 0.43 mm ≤ f3 &lt; 0.6 mm; 0.6 mm ≤ f2 &lt; 0.75 mm; 0.75 mm ≤ f1 &lt; 1.2 mm), (<b>c</b>) and temperature (<b>d</b>) on Cu(II) adsorption on Diaion™ CR20 from 6 mol/L HCl—10 (<b>a</b>) or 50 mg Cu(II)/L (<b>a</b>–<b>d</b>).</p> Full article ">Figure 11
<p>PFO (<b>a</b>,<b>b</b>), PSO (<b>c</b>,<b>d</b>), and IPD (<b>e</b>,<b>f</b>) plots and fitting of the experimental data of Pd(II) ion adsorption on Diaion™ CR20 (<b>g</b>) and Lewatit^® VP OC 1065 (<b>h</b>).</p> Full article ">Figure 11 Cont.
<p>PFO (<b>a</b>,<b>b</b>), PSO (<b>c</b>,<b>d</b>), and IPD (<b>e</b>,<b>f</b>) plots and fitting of the experimental data of Pd(II) ion adsorption on Diaion™ CR20 (<b>g</b>) and Lewatit^® VP OC 1065 (<b>h</b>).</p> Full article ">Figure 12
<p>Experimental points and fitting of the Langmuir and Freundlich isotherms for Pd(II) (<b>a</b>,<b>c</b>) and Cu(II) (<b>b</b>,<b>d</b>) ion adsorption on the Diaion™ CR20 (<b>a</b>,<b>b</b>) and Lewatit^® VP OC 1065 (<b>c</b>,<b>d</b>).</p> Full article ">Figure 13
<p>Comparison of the breakthrough curves of Pd(II) ion adsorption on Lewatit^® VP OC 1065 (<b>a</b>,<b>c</b>) and Diaion™ CR20 (<b>b</b>,<b>d</b>) from the chloride 0.1–6 mol/L HCl—100 mg Pd(II)/L (<b>a</b>,<b>b</b>) and the chloride-nitrate(V) solutions 0.1–0.9 mol/L HCl—0.9–0.1 mol/L HNO₃—100 mg Pd(II)/L (<b>c</b>,<b>d</b>).</p> Full article ">Figure 13 Cont.
<p>Comparison of the breakthrough curves of Pd(II) ion adsorption on Lewatit^® VP OC 1065 (<b>a</b>,<b>c</b>) and Diaion™ CR20 (<b>b</b>,<b>d</b>) from the chloride 0.1–6 mol/L HCl—100 mg Pd(II)/L (<b>a</b>,<b>b</b>) and the chloride-nitrate(V) solutions 0.1–0.9 mol/L HCl—0.9–0.1 mol/L HNO₃—100 mg Pd(II)/L (<b>c</b>,<b>d</b>).</p> Full article ">Figure 14
<p>Comparison of the adsorption (%<span class="html-italic">S</span>) and desorption (%<span class="html-italic">D</span>) efficiency of Pd(II) ions on/from (<b>a</b>) Diaion™ CR20, (<b>b</b>) Lewatit^® VP OC 1065 ion exchangers in three adsorption–desorption cycles using ammonium hydroxide solutions.</p> Full article ">Figure 15
<p>Effects of simultaneous presence of Pd(II) and Cu(II) ions in the solutions on their sorption yield on the Diaion™ CR20 and Lewatit^® VP OC 1065 ion exchangers from the S (single) and B (bi-component) solutions.</p> Full article ">Figure 16
<p>Diaion™ CR20 (<b>a</b>,<b>c</b>) and Lewatit^® VP OC 1065 (<b>b</b>,<b>d</b>) ion exchange resins beads before the adsorption (<b>a</b>,<b>b</b>) (magnification 5×) and after the Cu(II) and Pd(II) adsorption (<b>c</b>,<b>d</b>) (magnification 2.5×).</p> Full article ">

Figure 1
<p>Influence factors of grasslands carbon sequestration.</p> Full article ">Figure 2
<p>Distribution map of sample provinces (rectangle block).</p> Full article ">Figure 3
<p>Prediction results for Xizang (Tibet) and Qinghai Province.</p> Full article ">Figure 4
<p>Prediction results for Neimongolia–Ningxia-Gansu grassland region.</p> Full article ">Figure 5
<p>Prediction results for Xinjiang grassland region.</p> Full article ">Figure 6
<p>Prediction results for Sichuan and Yunnan Provinces.</p> Full article ">Figure 7
<p>Prediction results for Heilongjiang Province.</p> Full article ">

Figure 1
<p>Representative images of hydrogels: (<b>A</b>) after e-beam irradiation at room temperature (25 °C)<span class="html-italic">;</span> (<b>B</b>); after being stored for 24 h at ambient temperature; (<b>C</b>) cut and immersed in ethanol for 24 h; (<b>D</b>) cut into discs at 15, 10, and 7 mm in diameter.</p> Full article ">Figure 2
<p>The effect of NaAlg concentration, polymer volume, and hydrogel size on the gel fraction.</p> Full article ">Figure 3
<p>The cross-links density of the hydrogel samples.</p> Full article ">Figure 4
<p>Relationship between the amount of polymer solution and swelling degree of hydrogels at different sizes: (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 5
<p>The swelling degree values of the hydrogels based on size: (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 6
<p>The hydrogel samples swelled at equilibrium.</p> Full article ">Figure 7
<p>The first-order swelling kinetics of cross-linked hydrogels: (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 8
<p>The second-order swelling kinetics of cross-linked hydrogels: (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 9
<p>The swelling kinetic curve of the cross-linked hydrogels (ln F vs. ln t): (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 10
<p>The swelling kinetic curve of the cross-linked hydrogels (F vs. t^0.5): (<b>A</b>) for hydrogels with a NaAlg concentration of 0.5% and (<b>B</b>) for hydrogels with a NaAlg concentration of 1%.</p> Full article ">Figure 11
<p>FTIR spectra of (<b>a</b>) native polymers (NaAlg, AA/ and PEO) and (<b>b</b>) I (0.5% NaAlg) and II (1% NaAlg) hydrogels with a diameter of 7 mm.</p> Full article ">Figure 12
<p>SEM images of the (<b>a</b>) I₇_20 mL, (<b>b</b>) I₇_40 mL, (<b>c</b>) II₇_20 mL, and (<b>d</b>) II₇_40 mL hydrogels at 50× magnification. Scale bars indicate 1 mm.</p> Full article ">

Figure 1
<p>Physical structure of PAM (<b>a</b>); diagram of fractional Maxwell model (<b>b</b>).</p> Full article ">Figure 2
<p>Working states of the PAM.</p> Full article ">Figure 3
<p>Hysteresis curve of fractional Maxwell model.</p> Full article ">Figure 4
<p>Hydrological cycle.</p> Full article ">Figure 5
<p>The schematic diagram of the stream to river and river to sea.</p> Full article ">Figure 6
<p>Experimental setup (<b>a</b>); diagram of the apparatus (<b>b</b>): 1—Motor; 2—Compressor; 3—Filter; 4—Air reservoir; 5—Pressure regulator; 6—On–off valve; 7—Pressure gauge; 8—Safety valve; 9—Pressure sensor; 10—PAM; 11—Loadcell; 12—Position sensor; 13—Base; 14—Coupling; 15—Pneumatic cylinder; 16—Proportional valve; 17—NI card 6221; 18—Computer.</p> Full article ">Figure 7
<p>Measured signals versus time: (<b>a</b>) pressure; (<b>b</b>) position.</p> Full article ">Figure 8
<p>Comparison between the experimental and approximate curves.</p> Full article ">Figure 9
<p>Comparison between the simulation and experiment (detailed annotation of the line types is presented in top-left corner panel).</p> Full article ">Figure 10
<p>Convergence of the cost function.</p> Full article ">Figure 11
<p>Comparison of experimented and calculated hysteresis loops with frequency of 3.5 Hz and various force amplitudes: (<b>a</b>) 95 N; (<b>b</b>) 110 N; (<b>c</b>) 122 N; (<b>d</b>) 148 N.</p> Full article ">Figure 12
<p>Comparison of experimented and calculated hysteresis loops with force amplitude of 125 N and various frequencies: (<b>a</b>) 3.5 Hz (<b>b</b>) 4.5 Hz; (<b>c</b>) 7.5 Hz; (<b>d</b>) 8.5 Hz.</p> Full article ">

Figure 1
<p>Topology of LCL grid-tied inverter.</p> Full article ">Figure 2
<p>Amplitude frequency characteristic curves of <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <msub> <mi>u</mi> <mi>j</mi> </msub> <mo>−</mo> <msub> <mi>i</mi> <mrow> <mn>1</mn> <mi>j</mi> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <msub> <mi>u</mi> <mi>j</mi> </msub> <mo>−</mo> <msub> <mi>i</mi> <mrow> <mn>2</mn> <mi>j</mi> </mrow> </msub> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>This amplitude–frequency characteristic curves.</p> Full article ">Figure 4
<p>A diagram of the proposed control strategy.</p> Full article ">Figure 5
<p>The simulation results of the grid current in steady state: (<b>a</b>) the traditional controller; (<b>b</b>) the traditional controller’s THD; (<b>c</b>) the proposed controller; (<b>d</b>) the proposed controller’s THD.</p> Full article ">Figure 6
<p>The simulation results of the grid current with parameter mismatch: (<b>a</b>) the traditional controller; (<b>b</b>) the proposed controller.</p> Full article ">Figure 7
<p>The simulation results of the current command changing the grid current: (<b>a</b>) the traditional controller; (<b>b</b>) the proposed controller.</p> Full article ">Figure 8
<p>The simulation results of the current command changing the grid current: (<b>a</b>) the traditional controller; (<b>b</b>) the proposed controller.</p> Full article ">Figure 9
<p>Simulation results under traditional FOSMC control: (<b>a</b>) grid voltage change; (<b>b</b>) grid current.</p> Full article ">Figure 10
<p>Simulation results under the proposed controller: (<b>a</b>) grid voltage change; (<b>b</b>) grid current.</p> Full article ">Figure 11
<p>dsPACE semi-physical simulation platform.</p> Full article ">Figure 12
<p>The experimental results of the grid current under steady-state conditions: (<b>a</b>) the traditional controller; (<b>b</b>) the proposed controller.</p> Full article ">Figure 13
<p>The experimental results of the grid current under dynamic conditions: (<b>a</b>) the traditional controller; (<b>b</b>) the proposed controller.</p> Full article ">

Figure 1
<p>Plots of <italic>m</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>m</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 1 Cont.
<p>Plots of <italic>m</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>m</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>m</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 2
<p>Plots of <italic>c</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>c</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 2 Cont.
<p>Plots of <italic>c</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>c</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>c</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 3
<p>Plots of <italic>ζ</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ζ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 3 Cont.
<p>Plots of <italic>ζ</italic>_eq1 for <italic>m</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ζ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 4
<p>Plots of <italic>ω</italic>_eqn1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqn1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 4 Cont.
<p>Plots of <italic>ω</italic>_eqn1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqn1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 5
<p>Illustrations of <italic>ω</italic>_eqd1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd1 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.4 (dot), 2.6 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqd1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 5 Cont.
<p>Illustrations of <italic>ω</italic>_eqd1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd1 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.4 (dot), 2.6 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqd1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 6
<p>Illustrations of <italic>γ</italic>_eq1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>γ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>γ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>γ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 6 Cont.
<p>Illustrations of <italic>γ</italic>_eq1 for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>γ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>γ</italic>_eq1 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>γ</italic>_eq1 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 7
<p>Illustrations of |<italic>H</italic>₁(<italic>ω</italic>)| for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₁(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). |<italic>H</italic>₁(<italic>ω</italic>)| for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). |<italic>H</italic>₁(<italic>ω</italic>)| for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). |<italic>H</italic>₁(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 8
<p>Illustrations of <italic>φ</italic>₁(<italic>ω</italic>) for <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₁(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>φ</italic>₁(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash). (<bold>c</bold>). <italic>φ</italic>₁(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>φ</italic>₁(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 9
<p>Illustrations of <italic>x</italic>₁(<italic>t</italic>) for <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₁(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 1.5 (dot), 1.8 (dash). (<bold>b</bold>). <italic>x</italic>₁(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 2.2 (solid), 2.5 (dot), 2.8 (dash).</p> Full article ">Figure 10
<p>Illustrations of <italic>x</italic>₁(<italic>t</italic>) for <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₁(<italic>t</italic>) when for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>b</bold>). <italic>x</italic>₁(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7).</p> Full article ">Figure 11
<p>Plots of <italic>m</italic>_eq2 for <italic>m</italic> = 1 and <italic>c</italic> = 1. (<bold>a</bold>). <italic>m</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 11 Cont.
<p>Plots of <italic>m</italic>_eq2 for <italic>m</italic> = 1 and <italic>c</italic> = 1. (<bold>a</bold>). <italic>m</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>m</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 12
<p>Plots of <italic>c</italic>_eq2 for <italic>c</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 12 Cont.
<p>Plots of <italic>c</italic>_eq2 for <italic>c</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>c</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 13
<p>Plots of <italic>ζ</italic>_eq2 for <italic>m</italic> = 1 and <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 13 Cont.
<p>Plots of <italic>ζ</italic>_eq2 for <italic>m</italic> = 1 and <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ζ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 14
<p>Plots of <italic>ω</italic>_eqn2 for <italic>m</italic> = 1 and <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 14 Cont.
<p>Plots of <italic>ω</italic>_eqn2 for <italic>m</italic> = 1 and <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqn2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 15
<p>Illustrations of <italic>ω</italic>_eqd2 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 15 Cont.
<p>Illustrations of <italic>ω</italic>_eqd2 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>ω</italic>_eqd2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 16
<p>Plots of <italic>γ</italic>_eq2 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 16 Cont.
<p>Plots of <italic>γ</italic>_eq2 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd2 for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>γ</italic>_eq2 when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 17
<p>Plots of |<italic>H</italic>₂(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₂(<italic>ω</italic>)| for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). |<italic>H</italic>₂(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). |<italic>H</italic>₂(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). |<italic>H</italic>₂(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 18
<p>Plots of <italic>φ</italic>₂(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₂(<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>φ</italic>₂(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>c</bold>). <italic>φ</italic>₂(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>d</bold>). <italic>φ</italic>₂(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 19
<p>Plots of <italic>x</italic>₂(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₂(<italic>t</italic>) for <italic>β</italic> = 0.3 (solid), 0.6 (dot), and 0.9 (dash). (<bold>b</bold>). <italic>x</italic>₂(<italic>t</italic>) for <italic>β</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash).</p> Full article ">Figure 20
<p>Plots of <italic>x</italic>₂(<italic>t</italic>) when <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₂(<italic>t</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>b</bold>). <italic>x</italic>₂(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 21
<p>Plots of <italic>m</italic>_eq3 for <italic>m</italic> = 1 and <italic>c</italic> = 1. (<bold>a</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>m</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>m</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>m</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 22
<p>Plots of <italic>c</italic>_eq3 for <italic>m</italic> = 1 and <italic>c</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>c</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>c</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 22 Cont.
<p>Plots of <italic>c</italic>_eq3 for <italic>m</italic> = 1 and <italic>c</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>c</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>c</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>c</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 23
<p>Plots of <italic>ζ</italic>_eq3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>ζ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>ζ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>ζ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 24
<p>Plots of <italic>ω</italic>_eqn3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>ω</italic>_eqn3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>ω</italic>_eqn3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 24 Cont.
<p>Plots of <italic>ω</italic>_eqn3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>ω</italic>_eqn3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>ω</italic>_eqn3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>ω</italic>_eqn3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 25
<p>Plots of <italic>ω</italic>_eqd3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>ω</italic>_eqd3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>ω</italic>_eqd3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 25 Cont.
<p>Plots of <italic>ω</italic>_eqd3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>ω</italic>_eqd3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>ω</italic>_eqd3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>ω</italic>_eqd3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 26
<p>Plots of <italic>γ</italic>_eq3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>γ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>γ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 26 Cont.
<p>Plots of <italic>γ</italic>_eq3 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>γ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>γ</italic>_eq3 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 27
<p>Plots of |<italic>H</italic>₃(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 27 Cont.
<p>Plots of |<italic>H</italic>₃(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.8 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). |<italic>H</italic>₃(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 28
<p>Plots of <italic>φ</italic>₃(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.5 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.5 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.5 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.5 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>φ</italic>₃(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>φ</italic>₃(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 28 Cont.
<p>Plots of <italic>φ</italic>₃(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq3 with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.5 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.5 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.5 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>f</bold>). <italic>φ</italic>₃(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.5 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>g</bold>). <italic>φ</italic>₃(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>φ</italic>₃(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 29
<p>Plots of <italic>x</italic>₃(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>β</italic> = 1, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>b</bold>). <italic>β</italic> = 1, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>c</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>d</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>e</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>f</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>g</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 29 Cont.
<p>Plots of <italic>x</italic>₃(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>β</italic> = 1, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>b</bold>). <italic>β</italic> = 1, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>c</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>d</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>e</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>f</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>g</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 29 Cont.
<p>Plots of <italic>x</italic>₃(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>β</italic> = 1, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>b</bold>). <italic>β</italic> = 1, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>c</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>d</bold>). <italic>β</italic> = 0.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>e</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 1.3 (solid), 1.6 (dot), and 1.9 (dash). (<bold>f</bold>). <italic>β</italic> = 1.5, <italic>α</italic> = 2.3 (solid), 2.6 (dot), and 2.9 (dash). (<bold>g</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>). (<bold>h</bold>). <italic>x</italic>₃(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>β</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 1.7).</p> Full article ">Figure 30
<p>Plots of <italic>c</italic>_eq4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>c</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>c</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>c</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>c</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>c</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.2 (solid), 2.8 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>c</italic>_eq4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 31
<p>Plots of <italic>k</italic>_eq4 for <italic>k</italic> = 1. (<bold>a</bold>). <italic>k</italic>_eq4 when <italic>λ</italic>(<italic>ω</italic>) = 0.3 (solid), 0.6 (dot), 0.9 (dash). (<bold>b</bold>). <italic>k</italic>_eq4 when <italic>λ</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>k</italic>_eq4 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 32
<p>Plots of <italic>ζ</italic>_eq4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ζ</italic>_eq4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 32 Cont.
<p>Plots of <italic>ζ</italic>_eq4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ζ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ζ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ζ</italic>_eq4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 33
<p>Plots of <italic>ω</italic>_eqn4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ω</italic>_eqn4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 33 Cont.
<p>Plots of <italic>ω</italic>_eqn4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.8 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ω</italic>_eqn4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ω</italic>_eqn4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ω</italic>_eqn4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 34
<p>Plots of <italic>ω</italic>_eqd4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 1.7 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 2.5 (solid), 2.7 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ω</italic>_eqd4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 34 Cont.
<p>Plots of <italic>ω</italic>_eqd4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 1.7 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 2.5 (solid), 2.7 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>ω</italic>_eqd4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>ω</italic>_eqd4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>ω</italic>_eqd4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 35
<p>Plots of <italic>γ</italic>_eq4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 1.7 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 2.5 (solid), 2.7 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>γ</italic>_eq4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 35 Cont.
<p>Plots of <italic>γ</italic>_eq4 when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 1.7 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.8 when <italic>α</italic>(<italic>ω</italic>) = 2.5 (solid), 2.7 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>γ</italic>_eq4 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>γ</italic>_eq4 for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>γ</italic>_eq4 when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 36
<p>Plots of |<italic>H</italic>₄(<italic>ω</italic>)| when <italic>m</italic> = 1, <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). |<italic>H</italic>₄(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 37
<p>Plots of <italic>φ</italic>₄(<italic>ω</italic>). (<bold>a</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>φ</italic>₄(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 37 Cont.
<p>Plots of <italic>φ</italic>₄(<italic>ω</italic>). (<bold>a</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot). (<bold>e</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>f</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 and <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7). (<bold>g</bold>). <italic>φ</italic>₄(<italic>ω</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.5 (solid), 2.5 (dot), when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9). (<bold>h</bold>). <italic>φ</italic>₄(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.3, 2.7) and <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 38
<p>Plots of <italic>x</italic>₄(<italic>t</italic>) for <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5. (<bold>e</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 2.5. (<bold>f</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 38 Cont.
<p>Plots of <italic>x</italic>₄(<italic>t</italic>) for <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5. (<bold>e</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 2.5. (<bold>f</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 38 Cont.
<p>Plots of <italic>x</italic>₄(<italic>t</italic>) for <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>x</italic>₄(<italic>t</italic>) when <italic>ω</italic> = 2 and <italic>λ</italic>(<italic>ω</italic>) = 0.5 when <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5. (<bold>d</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 1.5. (<bold>e</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>) and <italic>α</italic>(<italic>ω</italic>) = 2.5. (<bold>f</bold>). <italic>x</italic>₄(<italic>t</italic>) for <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 39
<p>Plots of <italic>c</italic>_eq5 when <italic>k</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 (solid), 0.6 (dot), 0.3 (dash). (<bold>b</bold>). <italic>c</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>c</italic>_eq5 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 40
<p>Plots of <italic>ζ</italic>_eq5 when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 (solid), 0.6 (dot), 0.3 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>ζ</italic>_eq5 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 41
<p>Plots of <italic>ω</italic>_eqn5 when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn5 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 (solid), 0.6 (dot), 0.3 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn5 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>ω</italic>_eqn5 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 42
<p>Plots of <italic>ω</italic>_eqd5 when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd5 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 (solid), 0.6 (dot), 0.3 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd5 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>ω</italic>_eqd5 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 43
<p>Plots of <italic>γ</italic>_eq5 when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.9 (solid), 0.6 (dot), 0.3 (dash). (<bold>b</bold>). <italic>γ</italic>_eq5 for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>γ</italic>_eq5 when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 44
<p>Plots of |<italic>H</italic>₅(<italic>ω</italic>)| when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₅(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.09 (solid), 0.06 (dot), 0.03 (dash). (<bold>b</bold>). |<italic>H</italic>₅(<italic>ω</italic>)| for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). |<italic>H</italic>₅(<italic>ω</italic>)| when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 45
<p>Plots of <italic>φ</italic>₅(<italic>ω</italic>) when <italic>m</italic> = 1 and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₅(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.09 (solid), 0.06 (dot), 0.03 (dash). (<bold>b</bold>). <italic>φ</italic>₅(<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>φ</italic>₅(<italic>ω</italic>) when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 46
<p>Plots of <italic>x</italic>₅(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₅(<italic>t</italic>) for <italic>λ</italic> = 0.9 (solid), <italic>λ</italic> = 0.6 (dot), <italic>λ</italic> = 0.3 (dash). (<bold>b</bold>). <italic>x</italic>₅(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>x</italic>₅(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 46 Cont.
<p>Plots of <italic>x</italic>₅(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₅(<italic>t</italic>) for <italic>λ</italic> = 0.9 (solid), <italic>λ</italic> = 0.6 (dot), <italic>λ</italic> = 0.3 (dash). (<bold>b</bold>). <italic>x</italic>₅(<italic>t</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.5 + 0.4cos(2<italic>ω</italic>). (<bold>c</bold>). <italic>x</italic>₅(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) is a uniformly distributed random function with the range (0.1, 0.9).</p> Full article ">Figure 47
<p>Plots of <italic>c</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash) (negative damping). (<bold>c</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash) (negative damping). (<bold>e</bold>). <italic>c</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>c</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>c</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>c</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 47 Cont.
<p>Plots of <italic>c</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash) (negative damping). (<bold>c</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>c</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash) (negative damping). (<bold>e</bold>). <italic>c</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>c</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>c</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>c</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 48
<p>Plots of <italic>ζ</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ζ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>ζ</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>ζ</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>ζ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 48 Cont.
<p>Plots of <italic>ζ</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ζ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ζ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>ζ</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>ζ</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>ζ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 49
<p>Plots of <italic>ω</italic>_eqn6 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqn6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>ω</italic>_eqn6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>ω</italic>_eqn6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>ω</italic>_eqn6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 49 Cont.
<p>Plots of <italic>ω</italic>_eqn6 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqn6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqn6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>ω</italic>_eqn6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>ω</italic>_eqn6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>ω</italic>_eqn6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 50
<p>Plots of <italic>ω</italic>_eqd6 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd6 with <italic>β</italic>(<italic>ω</italic>) = 0.9 and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>ω</italic>_eqd6 with <italic>β</italic>(<italic>ω</italic>) = 0.9 and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>ω</italic>_eqd6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>ω</italic>_eqd6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>ω</italic>_eqd6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>ω</italic>_eqd6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>ω</italic>_eqd6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>ω</italic>_eqd6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 51
<p>Plots of <italic>γ</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.3 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>γ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.3 and <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>γ</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>γ</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>γ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 51 Cont.
<p>Plots of <italic>γ</italic>_eq6 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>γ</italic>_eq6 with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.3 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>γ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.3 and <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>γ</italic>_eq6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>γ</italic>_eq6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.7 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>γ</italic>_eq6 when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 52
<p>Plots of |<italic>H</italic>₆(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 52 Cont.
<p>Plots of |<italic>H</italic>₆(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). |<italic>H</italic>₆(<italic>ω</italic>)| when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 53
<p>Plots of <italic>φ</italic>₆(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 53 Cont.
<p>Plots of <italic>φ</italic>₆(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>b</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 0.7 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>c</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 1.6 (dot), 1.9 (dash). (<bold>d</bold>). <italic>φ</italic>₆(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>φ</italic>₆(<italic>ω</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 54
<p>Plots of <italic>x</italic>₆(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic> = 1.8, <italic>β</italic> = 1.2, for <italic>λ</italic> = 0.8 (solid), <italic>λ</italic> = 0.5 (dot), <italic>λ</italic> = 0.2 (dash). (<bold>b</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>α</italic> = 1.8, <italic>λ</italic> = 0.8 for <italic>β</italic> = 1.2 (solid), 0.8 (dot), 0.4 (dash). (<bold>c</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>β</italic> = 0.8, <italic>λ</italic> = 0.8 for <italic>α</italic> = 2.2 (solid), <italic>α</italic> = 1.8 (dot), <italic>α</italic> = 1.4 (dash). (<bold>d</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 54 Cont.
<p>Plots of <italic>x</italic>₆(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic> = 1.8, <italic>β</italic> = 1.2, for <italic>λ</italic> = 0.8 (solid), <italic>λ</italic> = 0.5 (dot), <italic>λ</italic> = 0.2 (dash). (<bold>b</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>α</italic> = 1.8, <italic>λ</italic> = 0.8 for <italic>β</italic> = 1.2 (solid), 0.8 (dot), 0.4 (dash). (<bold>c</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>β</italic> = 0.8, <italic>λ</italic> = 0.8 for <italic>α</italic> = 2.2 (solid), <italic>α</italic> = 1.8 (dot), <italic>α</italic> = 1.4 (dash). (<bold>d</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 54 Cont.
<p>Plots of <italic>x</italic>₆(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic> = 1.8, <italic>β</italic> = 1.2, for <italic>λ</italic> = 0.8 (solid), <italic>λ</italic> = 0.5 (dot), <italic>λ</italic> = 0.2 (dash). (<bold>b</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>α</italic> = 1.8, <italic>λ</italic> = 0.8 for <italic>β</italic> = 1.2 (solid), 0.8 (dot), 0.4 (dash). (<bold>c</bold>). <italic>x</italic>₆(<italic>t</italic>) for <italic>β</italic> = 0.8, <italic>λ</italic> = 0.8 for <italic>α</italic> = 2.2 (solid), <italic>α</italic> = 1.8 (dot), <italic>α</italic> = 1.4 (dash). (<bold>d</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.3 and <italic>λ</italic>(<italic>ω</italic>) = 0.2 for <italic>α</italic>(<italic>ω</italic>) = 2.3 (solid), 2.6 (dot), 2.9 (dash). (<bold>e</bold>). when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>β</italic>(<italic>ω</italic>) = 0.7 (solid) and <italic>β</italic>(<italic>ω</italic>) = 1.3 (dot). (<bold>f</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>g</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) and <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot). (<bold>h</bold>). <italic>x</italic>₆(<italic>t</italic>) when <italic>α</italic>(<italic>ω</italic>) = 1.4 + cos(2<italic>ω</italic>), <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>), and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 55
<p>Plots of <italic>c</italic>_eq7 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>c</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.9 (dot), 1.6 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>c</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 0.3 (solid), 0.9 (dot), 1.6 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.9. (<bold>c</bold>). <italic>c</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash). (<bold>d</bold>). <italic>c</italic>_eq7 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) 1.6 (solid), 0.9 (dot), 0.3 (dash).</p> Full article ">Figure 56
<p>Plots of <italic>ζ</italic>_eq7 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>ζ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>ζ</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>ζ</italic>_eq7 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dot). (<bold>e</bold>). <italic>ζ</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 56 Cont.
<p>Plots of <italic>ζ</italic>_eq7 for <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ζ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>ζ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>ζ</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>ζ</italic>_eq7 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dot). (<bold>e</bold>). <italic>ζ</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 57
<p>Plots of <italic>ω</italic>_eqn7 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqn7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>ω</italic>_eqn7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>ω</italic>_eqn6 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>ω</italic>_eqn6 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.8 (solid), 0.2 (dot). (<bold>e</bold>). <italic>ω</italic>_eqn7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 58
<p>Plots of <italic>ω</italic>_eqd7 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>ω</italic>_eqd7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>ω</italic>_eqd7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>ω</italic>_eqd7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>ω</italic>_eqd7 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.8 (dot).</p> Full article ">Figure 59
<p>Plots of <italic>γ</italic>_eq7 for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>γ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.3 (dot) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>γ</italic>_eq7 with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.3 (dot) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>γ</italic>_eq7 when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>γ</italic>_eq7 when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.9 (solid), 0.1 (dot).</p> Full article ">Figure 60
<p>Plots of |<italic>H</italic>₇(<italic>ω</italic>)| for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). |<italic>H</italic>₇(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). |<italic>H</italic>₇(<italic>ω</italic>)| with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). |<italic>H</italic>₇(<italic>ω</italic>)| when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). |<italic>H</italic>₇(<italic>ω</italic>)| when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.3 (dot).</p> Full article ">Figure 61
<p>Plots of <italic>φ</italic>₇(<italic>ω</italic>) for <italic>m</italic> = 1, <italic>c</italic> = 0.2, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>φ</italic>₇(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>φ</italic>₇(<italic>ω</italic>) with <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>φ</italic>₇(<italic>ω</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>d</bold>). <italic>φ</italic>₇(<italic>ω</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 0.1 for <italic>α</italic>(<italic>ω</italic>) = 1.3 (solid), 2.3 (dot).</p> Full article ">Figure 62
<p>Plots of <italic>x</italic>₇(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>x</italic>₇(<italic>t</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>d</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.9, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>e</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.3, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>f</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>g</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.5 (solid), 0.5 (dot). (<bold>h</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 62 Cont.
<p>Plots of <italic>x</italic>₇(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>x</italic>₇(<italic>t</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>d</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.9, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>e</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.3, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>f</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>g</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.5 (solid), 0.5 (dot). (<bold>h</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">Figure 62 Cont.
<p>Plots of <italic>x</italic>₇(<italic>t</italic>) when <italic>ω</italic> = 2, <italic>F</italic>₀ = 1, <italic>θ</italic> = 0, <italic>m</italic> = 1, <italic>c</italic> = 1, and <italic>k</italic> = 1. (<bold>a</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.7. (<bold>b</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.6 (solid), 0.9 (dot), 0.3 (dash) for <italic>λ</italic>(<italic>ω</italic>) = 0.2. (<bold>c</bold>). <italic>x</italic>₇(<italic>t</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.6, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>d</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.9, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>e</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 0.3, <italic>λ</italic>(<italic>ω</italic>) = 0.8 (solid), 0.5 (dot), 0.1 (dash). (<bold>f</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) for <italic>λ</italic>(<italic>ω</italic>) = 0.7 (solid), 0.2 (dot). (<bold>g</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>) for <italic>β</italic>(<italic>ω</italic>) = 1.5 (solid), 0.5 (dot). (<bold>h</bold>). <italic>x</italic>₇(<italic>t</italic>) when <italic>β</italic>(<italic>ω</italic>) = 1.2 + 0.5cos(2<italic>ω</italic>) and <italic>λ</italic>(<italic>ω</italic>) = 0.1 + 0.4cos(2<italic>ω</italic>).</p> Full article ">

Figure 1
<p>The actual state <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and its corresponding estimate for Example 1.</p> Full article ">Figure 2
<p>The actual state <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> and its corresponding estimate for Example 1.</p> Full article ">Figure 3
<p>Actual states <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> and their estimates for Example 2.</p> Full article ">

Figure 1
<p>Parametric representation of the analysed RVE.</p> Full article ">Figure 2
<p>Discretisation meshes used with the FEM and RPIM analyses. (<b>a</b>) A total of 138 nodes and 234 triangular elements. (<b>b</b>) A total of483 nodes and 884 triangular elements. (<b>c</b>) A total of 1785 nodes and 3408 triangular elements. (<b>d</b>) A total of 4005 nodes and 7768 triangular elements. (<b>e</b>) A total of 6993 nodes and 13,664 triangular elements.</p> Full article ">Figure 3
<p>Discretisation convergence study of the following elastic mechanical properties: (<b>a</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>z</mi> </msub> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <msub> <mi>ν</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math>.</p> Full article ">Figure 4
<p>von Mises equivalent stress distribution for the following formulations: FEM-6n (<b>a</b>–<b>c</b>), FEM-3n (<b>d</b>–<b>f</b>), and CRPIM (<b>g</b>–<b>i</b>). The results corresponding to <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>100</mn> </msub> </semantics></math> are shown in (<b>a</b>,<b>d</b>,<b>g</b>), <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>010</mn> </msub> </semantics></math> results are shown in (<b>b</b>,<b>e</b>,<b>h</b>), and <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>001</mn> </msub> </semantics></math> results are shown in (<b>c</b>,<b>f</b>,<b>i</b>).</p> Full article ">Figure 5
<p>von Mises equivalent stress distribution for the following formulations: MRPIM16 (<b>a</b>–<b>c</b>), MRPIM9 (<b>d</b>–<b>f</b>), and MRPIM4 (<b>g</b>–<b>i</b>). The results corresponding to <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>100</mn> </msub> </semantics></math> are shown in (<b>a</b>,<b>d</b>,<b>g</b>), <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>010</mn> </msub> </semantics></math> results are shown in (<b>b</b>,<b>e</b>,<b>h</b>), and <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>001</mn> </msub> </semantics></math> results are shown in (<b>c</b>,<b>f</b>,<b>i</b>).</p> Full article ">Figure 6
<p>von Mises equivalent stress distribution obtained with CRPIM considering a higher-order integration scheme: (<b>a</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>100</mn> </msub> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>010</mn> </msub> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <msub> <mover accent="true"> <mi mathvariant="bold">f</mi> <mo stretchy="false">˜</mo> </mover> <mn>001</mn> </msub> </semantics></math>.</p> Full article ">Figure 7
<p>Overall computational cost of FEM and RPIM formulations.</p> Full article ">Figure 8
<p>Discretisation meshes used with the FEM and RPIM analyses. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>; 5073 nodes and 9839 triangular elements. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.90</mn> </mrow> </semantics></math>; 4807 nodes and 9321 triangular elements. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.85</mn> </mrow> </semantics></math>; 4539 nodes and 8803 triangular elements. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.80</mn> </mrow> </semantics></math>; 4273 nodes and 8285 triangular elements. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math>; 4005 nodes and 7767 triangular elements. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.70</mn> </mrow> </semantics></math>; 3739 nodes and 7249 triangular elements. (<b>g</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.65</mn> </mrow> </semantics></math>; 3472 nodes and 6732 triangular elements. (<b>h</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.60</mn> </mrow> </semantics></math>; 3205 nodes and 6214 triangular elements. (<b>i</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.55</mn> </mrow> </semantics></math>; 2937 nodes and 5696 triangular elements. (<b>j</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.50</mn> </mrow> </semantics></math>; 2671 nodes and 5178 triangular elements.</p> Full article ">Figure 9
<p>Influence of the volume fraction <math display="inline"><semantics> <msub> <mi>v</mi> <mi>f</mi> </msub> </semantics></math> on the homogenised elastic mechanical properties: (<b>a</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>x</mi> </msub> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msub> <mi>E</mi> <mi>y</mi> </msub> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <msub> <mi>ν</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math>.</p> Full article ">Figure 10
<p>Sandwich cantilever beam with aluminium face sheets and PUF core. Three material domains were assumed: aluminium top-face sheet (3), PUF-core (2), and aluminium bottom face sheet (1).</p> Full article ">Figure 11
<p>Variation in the normal stress <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </semantics></math> along the aluminium top face sheet for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 12
<p>Variation in the normal stress <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </semantics></math> along the PUF core for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 13
<p>Variation in the normal stress <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </semantics></math> along the aluminium bottom face sheet for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 14
<p>Variation in the shear stress <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math> along the aluminium top face sheet for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 15
<p>Variation in the shear stress <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math> along the PUF core for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 16
<p>Variation in the shear stress <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math> along the aluminium bottom face sheet for distinct PUF cores. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 17
<p>Sandwich cantilever beam with aluminium face sheets and a functionally graded PUF core. Ten material domains were assumed: aluminium top-face sheet (10), PUF-cores with potential distinct densities (2–9), and aluminium bottom face sheet (1).</p> Full article ">Figure 18
<p>Variation in the normal stress <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </semantics></math> along the beam thickness. (<b>a</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.9</mn> <mo>,</mo> <mn>1.0</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>b</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.9</mn> <mo>,</mo> <mn>1.0</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>c</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.9</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>d</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.9</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>e</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>f</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics></math> m.</p> Full article ">Figure 19
<p>Variatio n in the shear stress <math display="inline"><semantics> <msub> <mi>τ</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </semantics></math> along the beam thickness. (<b>a</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.9</mn> <mo>,</mo> <mn>1.0</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>b</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.9</mn> <mo>,</mo> <mn>1.0</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>c</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.9</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>d</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.9</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>e</b>) FG1 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics></math> m. (<b>f</b>) FG2 beam for <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>∈</mo> <mo>[</mo> <mn>0.0</mn> <mo>,</mo> <mn>0.1</mn> <mo>]</mo> </mrow> </semantics></math> m.</p> Full article ">Figure A1
<p>Integration scheme for the RPIM using a rectangular domain and a regular background integration grid.</p> Full article ">

Figure 1
<p>Graphical exhibition of the bell-shaped soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 2
<p>Graphical exhibition of the compacton soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 3
<p>Graphical exhibition of the anti-compacton soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 4
<p>Graphical exhibition of the singular periodic soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mn>21</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 5
<p>Graphical exhibition of the kink soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 6
<p>Graphical exhibition of the general soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">Figure 7
<p>Graphical exhibition of the singular periodic soliton of the solution <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mn>7</mn> </mrow> </msub> <mfenced separators="|"> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>. (<b>a</b>) 3D figure. (<b>b</b>) 2D figure. (<b>c</b>) Contour plot.</p> Full article ">

Figure 1
<p>Schematic diagram of a horizontal quartz tube reactor used for pyrolysis of SS.</p> Full article ">Figure 2
<p>Schematic diagram of mercury thermal decomposition experimental system.</p> Full article ">Figure 3
<p>Effect of different SS particle sizes on the biochar yield (%) at different pyrolysis temperatures. Standard deviations were all less than ±0.5%.</p> Full article ">Figure 4
<p>Total amount of Fe (<b>A</b>), Zn (<b>B</b>), and Mn (<b>C</b>) in the different particle sizes of sewage sludge at 500, 650, and 800 °C.</p> Full article ">Figure 5
<p>Scanning electron microscope of sludge-derived biochar (S₃ ; <b>A</b>–<b>C</b>) and modified biochar (MS₃ ; <b>D</b>–<b>F</b>) at 500 °C, 650 °C, and 800 °C.</p> Full article ">Figure 6
<p>Structural characterization of sewage sludge, (<b>A</b>) sludge-derived biochar (S₃), and (<b>B</b>) modified sludge–derived biochar (MS₃) for S₃-sized particles at 500, 650, and 800 °C.</p> Full article ">Figure 7
<p>Adsorption of MB over different-sized SS-derived biochar particles produced at 500 °C, pH: 6.5, 30 mg dose. (<b>A</b>) Adsorption kinetics of 10 mg/L of MB along with fit using Pseudo-second-order kinetics model. (<b>B</b>) Effect of initial MB concentration from 10 to 50 mg/L over equilibrium adsorption capacity.</p> Full article ">Figure 8
<p>Equilibrium adsorption capacity with adsorbent dose of S₃: 100–400 µm in 10 mg/L of MB, pH: 6.5.</p> Full article ">Figure 9
<p>Adsorption capacity of methylene blue (<b>A</b>) and mercury (<b>B</b>) with time (C_o (MB): 400 mg/L of MB, pH: 6.5, 500 mg mass dose).</p> Full article ">

Figure 1
<p>LEs of the 8D hyperchaotic system for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Time histories of <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">a</mi> <mo>)</mo> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">b</mi> <mo>)</mo> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> <mo> </mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">d</mi> <mo>)</mo> <mo> </mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math> for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>The 2D phase portraits for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>The 3D phase portraits for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>5</mn> </msub> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>6</mn> </msub> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math>, (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>LEs of the 8D hyperchaotic system for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Time histories of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math> for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>The 2D phase portraits for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>The 3D phase portraits for set of fractional-orders FO₃ at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>5</mn> </msub> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>6</mn> </msub> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math>, (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>The 0–1 Test for Chaos: numerical time series of (<b>left</b>) mean square displacement <math display="inline"><semantics> <mrow> <mo stretchy="false">[</mo> <msub> <mi>M</mi> <mi>i</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">]</mo> </mrow> </semantics></math>, (<b>right</b>) dynamics of translation components <math display="inline"><semantics> <mrow> <mo stretchy="false">[</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">]</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <msub> <mi>x</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>x</mi> <mn>6</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>x</mi> <mn>7</mn> </msub> </semantics></math>.</p> Full article ">

Figure 1
<p><math display="inline"><semantics> <mrow> <msup> <mfenced separators="" open="(" close=")"> <mo>−</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>F</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mfrac> </mstyle> </mfenced> <mi>α</mi> </msup> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </semantics></math>.</p> Full article ">