Free Vibration Analysis of Thick Annular Functionally Graded Plate Integrated with Piezo-Magneto-Electro-Elastic Layers in a Hygrothermal Environment
<p>Configuration and coordinate system of an annular sandwich plate.</p> "> Figure 2
<p>Dimensionless frequency versus radial ratio for different Winkler coefficients.</p> "> Figure 3
<p>Dimensionless frequency versus radial ratio for different Pasternak coefficients.</p> "> Figure 4
<p>Dimensionless frequency versus thickness ratio for different variations in external electric potential.</p> "> Figure 5
<p>Dimensionless frequency versus thickness ratio for different variations in external magnetic potential.</p> "> Figure 6
<p>Dimensionless frequency versus power law index for different variations in radial ratio.</p> "> Figure 7
<p>Dimensionless frequency versus radial ratio for different variations in moisture.</p> "> Figure 8
<p>Dimensionless frequency versus radial ratio for different variations in temperature.</p> "> Figure 9
<p>Dimensionless frequency versus radial ratio for different boundary conditions.</p> ">
Abstract
:1. Introduction
2. Theoretical Basics
3. Governing Equations of the Problem
- Clamped edge:
- Simply supported edge:
- Free edge:
4. Numerical Results
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
- Reddy, J.N.; Romanoff, J.; Antonio Loya, J. nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory. Eur. J. Mech. A Solid 2016, 56, 92–104. [Google Scholar] [CrossRef]
- Sofiyev, A.H.; Deniz, A.; Akcay, I.H.; Yusufoğlu, E.L.Ç.İ.N. The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load. Acta Mech. 2006, 183, 129–144. [Google Scholar] [CrossRef]
- Thai, H.T.; Vo, T. A new sinusoidal shear deformation theory for bending, buckling and vibration of functionally graded plates. Appl. Math. Model. 2013, 37, 3269–3281. [Google Scholar] [CrossRef]
- Jooybar, N.; Malekzadeh, P.; Fiouz, A.; Vaghefi, M. thermal effect on free vibration of functionally graded truncated conical shell panels. Thin Wall Struct. 2016, 103, 45–61. [Google Scholar] [CrossRef]
- Shaban, M.; Alipour, M.M. Semi analytical solution for free vibration of thick FG plates rested on elastic foundation with elastically restrained edge. Acta Mech. Solida. Sin. 2011, 24, 340–354. [Google Scholar] [CrossRef]
- Jodaei, A.; Jalal, M.; Yas, M.H. Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates via SSDQM and comparative modeling by ANN. Math. Comp. Model. 2012, 57, 1408–1425. [Google Scholar] [CrossRef]
- Nateghi, A.; Salamat-talab, M.; Rezapour, J.; Daneshian, B. Size dependent buckling analysis of FG micro beams based on modified couple stress theory. Appl. Math. Model. 2012, 36, 4971–4987. [Google Scholar] [CrossRef]
- Kheirkhah, M.M.; Khalili, S.M.R.; Malekzadeh Fard, K. biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory. Eur. J. Mech. A Solid 2012, 31, 54–66. [Google Scholar] [CrossRef]
- Ghorbanpour Arani, A.; Mosayyebi, M.; Kolahdouzan, F.; Kolahchi, R.; Jamali, M. Refined Zigzag theory for vibration analysis of viscoelasic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers. P I Mech. Eng. G J. Aer. 2017, 231, 2464–2478. [Google Scholar] [CrossRef]
- Allahverdizadeh, A.; Mahjoob, M.J.; Maleki, M.; Nasrollahzadeh, N.; Naei, M.H. Structural modeling, vibration analysis and optimal viscoelastic layer characterization of adaptive sandwich beams with electrorheological fluid core. Mech. Res. Commun. 2013, 51, 15–22. [Google Scholar] [CrossRef]
- Wang, X.; Longfei, L.; Zhou, Y. Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer. Appl. Math. Mech. 2016, 37, 107–120. [Google Scholar] [CrossRef]
- Pandit, M.K.; Singh, B.N.; Sheikh, A.H. Buckling of laminated sandwich plates with soft core based on an improved higher oreder zigzag theory. Thin Wall Struct. 2008, 46, 1183–1191. [Google Scholar] [CrossRef]
- Romanoff, J.; Reddy, J.N. Experimental validation of the modified couple stress Timoshenko beam theory for web-core sandwich panels. Compos. Struct. 2014, 111, 130–137. [Google Scholar] [CrossRef]
- Ranjbaran, A.; Khoshravan, M.R.; Kharazi, M. Buckling analysis of sandwich plate using layerwise theory. J. Mech. Sci. Technol. 2014, 25, 2769–2777. [Google Scholar] [CrossRef]
- Malekzadeh, P.; Afsari, A.; Zahedinejad, P.; Bahadori, R. Three dimensional layerwise finite element free vibration analysis of thick laminated annular plates on elastic foundation. Appl. Math. Model. 2010, 34, 776–790. [Google Scholar] [CrossRef]
- Alipour, M.M.; Shariyat, M. Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory. Aerosp. Sci. Technol. 2014, 32, 235–259. [Google Scholar] [CrossRef]
- Ferreira, A.J.M.; Fasshauer, G.E.; Batra, R.C.; Rodrigues, J.D. Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter. Compos. Struct. 2008, 86, 328–343. [Google Scholar] [CrossRef]
- Alipour, M.M.; Shariyat, M. Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores. Int. J. Mech. Mater. Des. 2017, 13, 125–157. [Google Scholar] [CrossRef]
- Alipour, M.M. Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation. Arch. Civ. Mech. Eng. 2016, 16, 678–694. [Google Scholar] [CrossRef]
- Ansari, R.; Torabi, J.; Faghih Shojaei, M. Buckling and vibration analysis of embedded functionally graded carbon nanotubereinforced composite annular sector plates under thermal loading. Compos. Part B Eng. 2017, 109, 197–213. [Google Scholar] [CrossRef]
- Shi, P.; Dong, C.Y. Vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment. J. Sound Vib. 2012, 331, 3649–3662. [Google Scholar] [CrossRef]
- Malekzadeh, P.; Shahpari, S.A.; Ziaee, H.R. Three-dimensional free vibration of thick functionally graded annular plates in thermal environment. J. Sound Vib. 2010, 329, 425–442. [Google Scholar] [CrossRef]
- Dai, T.; Dai, H.-L. Analysis of a rotating FGMEE circular disk with variable thickness under thermal environment. Appl. Math. Model. 2017, 45, 900–924. [Google Scholar] [CrossRef]
- Jeyaraman, P.; Mahesh, S.; Selvamani, R.; Dimitri, R.; Tornabene, F. Multi thermal waves in a thermo diffusive piezo electric functionally graded rod via refined multi-dual phase-lag model. Curv. Layer. Struct. 2022, 9, 105–115. [Google Scholar] [CrossRef]
- Akbarzadeh, A.H.; Chen, Z.T. Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field. Compos. Struct. 2013, 97, 317–331. [Google Scholar] [CrossRef]
- Lee, C.Y.; Kim, J.H. Hygrothermal postbuckling behavior of functionally graded plates. Compos. Struct. 2013, 95, 278–282. [Google Scholar] [CrossRef]
- Sobhy, M. An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment. Int. J. Mech. Sci. 2016, 110, 62–77. [Google Scholar] [CrossRef]
- Mansouri, M.H.; Shariyat, M. Biaxial thermo-mechani.ical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations. Compos. Part B Eng. 2015, 83, 88–104. [Google Scholar] [CrossRef]
- Ghorbanpour Arani, A.; Kolahchi, R.; Mosayyebi, M.; Jamali, M. Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method. Int. J. Mech. Mater. Des. 2016, 12, 17–38. [Google Scholar] [CrossRef]
- Ke, L.L.; Liu, C.; Wang, Y.S. Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions. Physical E 2015, 66, 93–106. [Google Scholar] [CrossRef]
- Eshraghi, I.; Dag, S.; Soltani, N. Bending and free vibration of FG annular and circular microplates under thermal loading. Compos. Struct. 2016, 137, 196–207. [Google Scholar] [CrossRef]
- Li, Y.S.; Cai, Z.Y.; Shi, S.Y. Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory. Compos. Struct. 2014, 111, 522–529. [Google Scholar] [CrossRef]
- Akbarzadeh, A.H.; Chen, Z.T. Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading. Smart Mater. Struct. 2012, 21, 125013. [Google Scholar] [CrossRef]
- Wang, Y.; Zhang, W. On the thermal buckling and postbuckling responses of temperature-dependent graphene platelets reinforced porous nanocomposite beams. Compos. Struct. 2022, 296, 115880. [Google Scholar] [CrossRef]
- Nie, G.j.; Zhang, Z. Dynamic analysis of multi-directional functionally graded annular plates. Appl. Math Model. 2010, 34, 608–616. [Google Scholar] [CrossRef]
- Arshid, E.; Kiani, A.; Amir, S. Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 2019, 223, 2140–2159. [Google Scholar] [CrossRef]
Properties | |
---|---|
Properties | |
---|---|
Frequencies | Reference | |||||
---|---|---|---|---|---|---|
5 | 7 | 8 | 9 | 10 | ||
Jodaei et al. [6] | 0.081 | 0.08 | 0.0798 | 0.0797 | 0.0796 | |
Nie and Zhang [35] | 0.0798 | 0.0812 | 0.0814 | 0.0802 | 0.0807 | |
Present | 0.0805 | 0.0797 | 0.0795 | 0.0795 | 0.0795 | |
Jodaei et al. [6] | 0.0834 | 0.083 | 0.0827 | 0.0827 | 0.0826 | |
Nie and Zhang [35] | 0.0829 | 0.0843 | 0.0843 | 0.0832 | 0.0837 | |
Present | 0.0828 | 0.0827 | 0.0822 | 0.0822 | 0.0822 | |
Jodaei et al. [6] | 0.0954 | 0.0957 | 0.0953 | 0.0953 | 0.0952 | |
Nie and Zhang [35] | 0.0956 | 0.0969 | 0.0968 | 0.0958 | 0.0961 | |
Present | 0.0948 | 0.0952 | 0.095 | 0.095 | 0.095 |
Grid Points (N) | ||||
---|---|---|---|---|
1 | 5 | 12.4713 | 12.3882 | 12.3046 |
7 | 13.3089 | 13.2251 | 13.1407 | |
8 | 13.3076 | 13.2238 | 13.1394 | |
10 | 13.3076 | 13.2238 | 13.1394 | |
2 | 5 | 12.0093 | 11.9403 | 11.8710 |
7 | 12.7439 | 12.6747 | 12.6051 | |
8 | 12.7437 | 12.6745 | 12.6049 | |
10 | 12.7437 | 12.6745 | 12.6049 | |
3 | 5 | 11.7305 | 11.6691 | 11.6074 |
7 | 12.4071 | 12.3456 | 12.2838 | |
8 | 12.4070 | 12.3455 | 12.2837 | |
10 | 12.4070 | 12.3455 | 12.2837 |
VE | Dimensionless Frequency (ω) | |||
---|---|---|---|---|
Reference | −108 | 2.88 | 3.08 | 3.25 |
0 | 2.85 | 3.06 | 3.23 | |
108 | 2.83 | 3.02 | 3.21 | |
Present | −108 | 2.91 | 3.16 | 3.33 |
0 | 2.94 | 3.16 | 3.31 | |
108 | 2.87 | 3.10 | 3.30 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Kiarasi, F.; Babaei, M.; Asemi, K.; Dimitri, R.; Tornabene, F. Free Vibration Analysis of Thick Annular Functionally Graded Plate Integrated with Piezo-Magneto-Electro-Elastic Layers in a Hygrothermal Environment. Appl. Sci. 2022, 12, 10682. https://doi.org/10.3390/app122010682
Kiarasi F, Babaei M, Asemi K, Dimitri R, Tornabene F. Free Vibration Analysis of Thick Annular Functionally Graded Plate Integrated with Piezo-Magneto-Electro-Elastic Layers in a Hygrothermal Environment. Applied Sciences. 2022; 12(20):10682. https://doi.org/10.3390/app122010682
Chicago/Turabian StyleKiarasi, Faraz, Masoud Babaei, Kamran Asemi, Rossana Dimitri, and Francesco Tornabene. 2022. "Free Vibration Analysis of Thick Annular Functionally Graded Plate Integrated with Piezo-Magneto-Electro-Elastic Layers in a Hygrothermal Environment" Applied Sciences 12, no. 20: 10682. https://doi.org/10.3390/app122010682