CN116011122B - Calculation method for calculating metamaterial sound transmission of periodic special-shaped pipeline - Google Patents

Abstract

The application belongs to the technical field of acoustic metamaterials, and particularly discloses a calculation method for calculating the acoustic transmission of a periodic special-shaped pipeline metamaterial. The calculation method of the periodic special-shaped pipeline metamaterial sound transmission is based on an energy method, and the acoustic impedance at the opening isThe application uses the energy method to determine the correlation between the acoustic impedance of the pipeline and the communication opening (namely the cavity opening) of the special Helmholtz resonant cavity and the acoustic pressure of the opening center point, and can directly calculate the acoustic impedance of the opening by using the acoustic pressure of the opening center point under the condition of knowing the speed of externally applied plane waves, thereby more efficiently and rapidly realizing the calculation of the acoustic transmission of the metamaterial and obtaining the properties such as the transmission loss of the metamaterial.

Description

A computational method for calculating acoustic transmission of metamaterials in periodic shaped pipes

Technical Field

The present invention belongs to the technical field of acoustic metamaterials, and more specifically, relates to a method for calculating acoustic transmission of periodic special-shaped pipe metamaterials.

Background Art

Noise is ubiquitous in production and life. It not only affects the performance and use of equipment, but also causes noise pollution that harms human physical and mental health. Because low-frequency sound waves have strong penetration and dissipate very slowly during propagation, it is difficult to control them. Therefore, the control of low-frequency noise and vibration has always been a hot topic for scholars.

Pipe systems are very common in ship hulls, so being able to design an acoustic duct with good sound absorption characteristics is of great significance to noise control. Because of the simple and adjustable characteristics of the Helmholtz resonance cavity, it is often used in the noise control process of various piping systems. The Helmholtz resonance cavity consists of a cavity connected to a short tube. Generally, its resonant frequency depends only on its geometric dimensions. Through certain simplifications, the resonant frequency of the Helmholtz resonance cavity can be directly calculated. At this resonant frequency, its sound absorption effect is best. Based on the Helmholtz resonance cavity, the researchers have explored various deformations and obtained a variety of special-shaped Helmholtz resonance cavities. This artificial structure designed based on the Helmholtz resonance cavity is also called acoustic metamaterial in the industry.

The research group of the inventor of the present invention has obtained an additional periodic multi-mode coupling-regulated elastic cavity sound-absorbing metamaterial pipeline structure (Chinese patent application number: 202320043849.1, the entire contents of which are incorporated by reference in this application), the additional periodic multi-mode coupling-regulated elastic cavity sound-absorbing metamaterial pipeline structure includes a special-shaped Helmholtz resonance cavity periodically arranged on the outer wall of the pipeline, the special-shaped Helmholtz resonance cavity is a rectangular parallelepiped, and two thin plates (both with structural elasticity and belonging to non-rigid wall surfaces) are respectively arranged on the top surface and the central section, the two thin plates are parallel to each other, and the bottom of the special-shaped Helmholtz resonance cavity is connected to the outer wall of the pipeline through an opening. The additional periodic multi-mode coupling-regulated elastic cavity sound-absorbing metamaterial pipeline structure, by adding multiple local resonance cavities to the pipeline, can significantly attenuate sound waves in certain frequency ranges (corresponding to the appearance of multiple peaks on the transmission loss curve), especially in the low-frequency region (the frequency is often not more than 250Hz), so as to achieve low-frequency sound absorption of the pipeline, thereby effectively controlling or even absorbing low-frequency noise.

Although the existing technology has conducted many studies on the sound absorption structure of the Helmholtz resonant cavity, further research is still needed on how to calculate the transmission loss during the sound wave transmission process and simplify the calculation process. In the existing technology, technicians often use the finite element method for simulation. Although the simulation results are highly reliable, the calculation process of the finite element method is often time-consuming and inefficient. Another more common theoretical derivation method is the electroacoustic analogy method, but this method has low accuracy and cannot capture all the sound absorption peaks, and the effect is not good.

Summary of the invention

In view of the above defects or improvement needs of the prior art, the purpose of the present invention is to provide a calculation method for calculating the acoustic transmission of periodic shaped pipe metamaterials. For the periodic shaped pipe metamaterial design obtained by the inventor in the previous study, the correlation between the acoustic impedance at the opening (i.e., the cavity opening) connecting the pipe and the shaped Helmholtz resonant cavity and the sound pressure at the center of the opening is clarified by using the energy method. Under the condition of known external plane wave velocity, the acoustic impedance at the opening can be directly calculated by the sound pressure at the center of the opening, so as to more efficiently and quickly realize the calculation of the acoustic transmission of the metamaterial and obtain the transmission loss and other properties of the metamaterial. The results obtained by the calculation method of the present invention have a high degree of matching with the results obtained by the prior finite element method, and have good reliability and correctness. In particular, the present invention can better calculate the acoustic impedance Z _EH , the sound intensity transmission coefficient t _I , and the transmission loss TL under different sound wave frequency conditions by optimally controlling the number of truncated terms of the cavity and the thin plate in the energy method. The low-frequency calculation results corresponding to the calculation method of the present invention are almost identical to the simulation results of the finite element method, and the number of low-frequency sound absorption peaks of the pipeline can be calculated quickly and accurately, which can provide guidance for the application of pipelines in low-frequency sound absorption and other sound transmission applications in engineering.

To achieve the above object, according to one aspect of the present invention, a calculation method for calculating the acoustic transmission of a periodic shaped pipe metamaterial is provided. The periodic shaped pipe metamaterial includes a shaped Helmholtz resonance cavity periodically arranged on the outer wall of the pipe, wherein the pipe is in the shape of a rectangular parallelepiped, and two ports of the pipe are located on the same horizontal line, one on the left and one on the right, and the shaped Helmholtz resonance cavity is located above the pipe, and a plane wave with a velocity v is horizontally input from one port of the pipe; the shaped Helmholtz resonance cavity is in the shape of a rectangular parallelepiped, and two elastic thin plates are respectively arranged on the top surface and the horizontal center section of the rectangular parallelepiped, and the two thin plates are parallel to each other and are arranged horizontally, and the bottom of the shaped Helmholtz resonance cavity is connected to the outer wall of the pipe through an opening, and the opening is completely covered by the shaped Helmholtz resonance cavity; the opening is a square, the sides of the square are parallel to the sides of the thin plate, and the center of the opening and the center points of the two thin plates are located on the same vertical line; it is characterized in that the calculation method for the acoustic transmission of the periodic shaped pipe metamaterial is based on the energy method, and the acoustic impedance Z _EH at the opening is:

Wherein, P ₁ (opening center point, t) represents the sound pressure at the opening center point varying with time t, and v is the velocity of the plane wave.

As a further preferred embodiment of the present invention, the sound intensity transmission coefficient _tI at both ends of the pipeline is:

Wherein, S is the cross-sectional area of the pipe, and S _b is the cross-sectional area of the opening;

R _b is the real part corresponding to Z _EH , X _b is the imaginary part corresponding to Z _EH ; ρ ₀ is the density of the fluid in the special-shaped Helmholtz resonance cavity, and c ₀ is the sound velocity of the fluid in the special-shaped Helmholtz resonance cavity.

As a further preferred embodiment of the present invention, the transmission loss TL at both ends of the pipeline is:

TL＝101g(1/t _I ).

As a further preferred embodiment of the present invention, for any elastic thin plate, one side of the elastic thin plate is parallel to the axial direction of the pipeline, which is recorded as the x direction; the other side is perpendicular to the axial direction of the pipeline, which is recorded as the y direction; then, a three-dimensional rectangular coordinate system is established with the x direction as the X-axis direction and the y direction as the Y-axis direction, and the XOY plane of the three-dimensional rectangular coordinate system is set horizontally;

In the thin plate displacement expression based on the three-dimensional Fourier series, the number of truncated terms in the X-axis direction corresponding to each thin plate is an integer ≥6, and the number of truncated terms in the Y-axis direction is an integer ≥6; in the cavity sound pressure expression based on the three-dimensional Fourier series, the number of truncated terms in the X-axis direction corresponding to each cavity in the special-shaped Helmholtz resonance cavity is an integer ≥10, the number of truncated terms in the Y-axis direction is an integer ≥10, and the number of truncated terms in the Z-axis direction is an integer ≥10.

As a further preference of the present invention, in the thin plate displacement expression based on the three-dimensional Fourier series, the number of truncated terms in the X-axis direction corresponding to each thin plate is an integer ≥15, and the number of truncated terms in the Y-axis direction is an integer ≥15; in the cavity sound pressure expression based on the three-dimensional Fourier series, the number of truncated terms in the X-axis direction corresponding to each cavity in the special-shaped Helmholtz resonance cavity is an integer ≥13, the number of truncated terms in the Y-axis direction is an integer ≥13, and the number of truncated terms in the Z-axis direction is an integer ≥13.

As a further preferred embodiment of the present invention, the acoustic impedance Z _EH , the sound intensity transmission coefficient t _I , and the transmission loss TL all correspond to a sound wave frequency ≤ 250 Hz.

As a further preferred embodiment of the present invention, the elastic thin plates are all aluminum thin plates.

Through the above technical scheme conceived by the present invention, compared with the prior art, the present invention clarifies the correlation between the acoustic impedance at the opening connecting the pipeline and the special-shaped Helmholtz resonant cavity (i.e., the cavity opening) and the sound pressure at the center point of the opening by using the energy method. Under the condition of known external plane wave velocity, the sound pressure at the center point of the opening can be used to directly calculate the acoustic impedance at the opening, thereby realizing the calculation of metamaterial acoustic transmission more efficiently and quickly, and obtaining the transmission loss and other properties of the metamaterial.

The energy method is a method known in the prior art, but the energy method is often used in the prior art to calculate the coupling between a complete plate and a complete cavity. The periodic special-shaped pipe metamaterial targeted by the present invention has a multi-mode coupling-regulated opening for connecting the elastic cavity and the pipe, which destroys the integrity of the cavity. In view of this, the present invention targets the opening (i.e., the cavity opening) where the pipe connects the special-shaped Helmholtz resonant cavity, and calculates the energy at the opening, that is, calculates the energy at the opening by adjusting the speed of the sound wave transmitted into the elastic cavity through the pipe, thereby calculating the external input energy of the system.

The results obtained by the calculation method of the present invention have a high degree of match with the results obtained by the prior finite element method, and have good reliability and correctness. However, unlike the finite element method, which is time-consuming and inefficient, the calculation method of the present invention can achieve calculations more efficiently, and the calculation speed is 30% faster than that of the finite element method (as shown in the examples below).

The present invention can better calculate the acoustic impedance Z _EH , the sound intensity transmission coefficient t _I , and the transmission loss TL under different sound wave frequency conditions by optimally controlling the number of truncated items of the cavity and the thin plate in the energy method. As analyzed in detail in the embodiments below, when the number of truncated items in the X-axis direction corresponding to each thin plate is an integer ≥6, and the number of truncated items in the Y-axis direction is an integer ≥6 (that is, when p≥6, q≥6), in the low-frequency range, the calculation result of the transmission loss based on the present invention has tended to be stable and convergence has been achieved; when the number of truncated items in the X-axis direction corresponding to each cavity in the heteromorphic Helmholtz resonance cavity is an integer ≥10, the number of truncated items in the Y-axis direction is an integer ≥10, and the number of truncated items in the Z-axis direction is an integer ≥10 (that is, when m _x , _my , m _z , n _x , _ny , _nz are all greater than or equal to 10), in the low-frequency range, the calculation result of the transmission loss has tended to be stable and convergence has been achieved. The low-frequency calculation results corresponding to the calculation method of the present invention are almost identical to the simulation results of the finite element method. Of course, in order to better realize the calculation of the full frequency band, it is preferred to set p≥15, q≥15, and _mx , _my , _mz , _nx , _ny , and _nz to be greater than or equal to 13.

The low-frequency (sound wave frequency ≤ 250 Hz) calculation results corresponding to the calculation method of the present invention are almost identical to the simulation results of the finite element method, and the number of low-frequency sound absorption peaks of the pipeline can be quickly and accurately calculated, which can provide guidance for the application of pipelines in low-frequency sound absorption and other sound transmission applications in engineering. By calculating the cavity acoustic impedance Z _EH , the present invention can quickly determine the influence of the special-shaped Helmholtz resonance cavity on the sound waves propagating in the pipeline, thereby quantifying the magnitude of the Helmholtz resonance cavity's absorption effect on the pipeline sound waves, and further comparing the sound absorption performance of other existing special-shaped Helmholtz resonance cavities, which can help researchers determine which Helmholtz resonance cavity has a better effect.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a unit cell of a special-shaped local resonance-type pipeline metamaterial in the present invention.

FIG. 2 is a calculation result of different plate truncation terms (ie, truncation terms) based on the method of the present invention.

FIG. 3 is a calculation result of the number of truncation items of different cavities based on the method of the present invention.

FIG4 is a comparison diagram of the theoretical values calculated by the method of the present invention and the simulation results obtained by the finite element method in the embodiment; the legend “theory” in the figure corresponds to the method of the present invention, and the legend “simulation” corresponds to the finite element method.

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

The periodic shaped pipe metamaterial on which the present invention is based is a metamaterial obtained by periodically adding a shaped local resonance cavity to the side of an acoustic pipe. Similar to the previous research results "A kind of additional periodic multi-mode coupling regulation elastic cavity sound absorption metamaterial pipe structure" (Chinese patent application number: 202320043849.1), the periodic shaped pipe metamaterial on which the present invention is based includes a shaped Helmholtz resonance cavity periodically arranged on the outer wall of the pipe, and the shaped Helmholtz resonance cavity is a rectangular parallelepiped, and the top surface and the center section are respectively provided with two thin plates (both have structural elasticity and belong to non-rigid wall surfaces, that is, elastic plates), the two thin plates are parallel to each other, and the bottom of the shaped Helmholtz resonance cavity is connected to the outer wall of the pipe through an opening, and the center of the opening and the center points of the two thin plates are located on the same straight line.

The following is an introduction to a cell of a periodic metamaterial (the complete periodic structure is to extend the cell along the axial direction of the pipe to form a long pipe and several special-shaped Helmholtz resonant cavities located on the long pipe):

As shown in Figure 1, the special-shaped Helmholtz resonance cavity is a rectangular Helmholtz resonance cavity with a size of L _x ×L _y ×L _z and an elastic thin plate on the top, with a thin plate structure inserted inside (so that the Helmholtz resonance cavity is divided into two sub-cavities by the thin plate, respectively recorded as cavity 1 and cavity 2), and the bottom of the Helmholtz resonance cavity is connected to the outer wall of the pipe through the neck opening. The size of the top thin plate is L _x ×L _y , the thickness is h ₁ , the Young's modulus is E ₁ , the Poisson's ratio is μ ₁ , and the density is ρ _1. The distance between the center plane of the internal thin plate and the upper bottom is From the neck The dimensions are L _x ×L _y , the thickness is h ₂ , the Young's modulus is E ₂ , the Poisson's ratio is μ ₂ , and the density is ρ ₂ . The neck opening is a square with a side length of r _n , the channel cross section is a _d ×b _d , and the cell length is L. The specific parameters are shown in Table 1:

Table 1 Geometric parameters of the unit cell of the shaped local resonance channel metamaterial

Note: m ₁ =ρ ₁ ×h ₁ , m ₂ =ρ ₂ ×h ₂

The energy method is used to derive the cavity acoustic impedance Z _EH of the unit cell of the shaped local resonance pipe metamaterial. The flat plate 1 and flat plate 2 in FIG1 correspond to panel ₁ and panel ₂ respectively in the formula deduction in the following text, and the cavity 1 and cavity 2 correspond to cavity ₁ and cavity ₂ respectively in the formula deduction in the following text. The derivation process is as follows:

The sound pressure p in the cavity satisfies the wave equation:

The boundary conditions are:

Among them, ▽ is the Laplace operator, w is the bending displacement of the plate, p is the sound pressure in the cavity, n represents the external normal direction of the cavity surface, and v represents the particle velocity at the neck connection.

According to the modal superposition principle, in order to meet the acoustic boundary conditions of the wall, the sound pressure in cavity 1 can be expressed by a three-dimensional improved Fourier series:

Wherein, λ _mx = m _x π/L _x , λ _my = m _y π/L _y , λ _mz = m _z π/(L _z /2), m _x , my _y , m _z represent the number of truncated terms in the x, y, and z directions of cavity 1, respectively. For cavity 1, because its top is an elastic plate and its bottom is connected to the pipe, similar to the prior art, the sound pressure expression in cavity 1 contains two auxiliary functions: ξ _1z = L _z ζ _z (ζ _z -1) ² /2 and ξ _2z = L _z ζ _z ² (ζ _z -1)/2, where ζ _z = (zL _z /2)/(L _z /2).

Write the above sound pressure expression in matrix form:

P ₁ (x, y, z) = A ^T Q _xyz (4)

The Lagrangian function of cavity 1 can be expressed as:

in, represents the total potential energy of cavity 1, represents the total kinetic energy of particle vibration in cavity 1, represents the work done by the bending vibration of the plate 1 on the medium in the cavity 1, and W _c&v represents the work done by the external velocity v. The external velocity is the external acceleration applied to the air medium in the pipeline in a direction parallel to the axial direction of the pipeline.

For cavity 1, the total potential energy for:

Total Kinetic Energy for:

The work done by the bending vibration of plate 1 on the medium in cavity 1 is:

In the formula represents the displacement of plate 1.

The work done by the external velocity v is:

Similar to cavity 1, the sound pressure _P2 in cavity 2 is expressed as:

in _nx , _ny , and _nz represent the number of truncation items of cavity 2 in the x, y, and z directions, respectively.

In order to satisfy the continuity of the vibration velocity of the cavity 2 and the elastic plate 1 as well as the coupling surface of the elastic plate 2, similar to the prior art, two auxiliary functions are added to the sound pressure expression of the cavity 2: ξ _1Lz ＝L _z ζ _z '(ζ _z '-1) ² /2 and ξ _2Lz ＝L _z ζ _z ' ² (ζ _z '-1)/2. Among them, ζ _z '＝z/(L _z /2).

The sound pressure in cavity 2 can be written in matrix form as follows:

P ₂ (x, y, z) = D ^T R _xyz (11)

The Lagrangian function of cavity 2 is:

Among them, U _Cavity2 and Represent the total potential energy and total kinetic energy in cavity 2 respectively. and They represent the work done by plate 1 and plate 2 on cavity 2 respectively.

For cavity 2, the total potential energy and total kinetic energy They are:

and

The work done by plate 1 and plate 2 on cavity 2 is:

and

in, and represent the displacements of plate 1 and plate 2 respectively.

As the boundary of the closed cavity, the vibration equations of elastic plate 1 and plate 2 are:

Their elastic boundaries can be expressed as follows (the boundary conditions of plate 1 and plate 2 are exactly the same, and the boundary conditions do not change with time):

At x = 0,

At x = L _x ,

At y = 0,

At y = _Ly , in, and Represent the vibration displacement of plate 1 and plate 2, corresponding to w(x,y) in formula (19) to formula (22); _m1 and _m2 represent the surface density of plate 1 and plate 2, respectively; _D1 and _D2 represent the bending stiffness of plate 1 and plate 2, respectively, corresponding to D in formula (19) to formula (22); μ represents Poisson's ratio; _kx0 and _Kx0 represent the stiffness of the spring and torsion spring at x=0, respectively (the definition of the spring and torsion spring stiffness at other boundaries is similar). Both elastic plates are simply supported boundary conditions, the spring stiffness can be set to be large enough, and the torsion spring stiffness can be set to be small enough. The specific values can be set with reference to the conventional settings of the prior art.

Based on thin plate theory, ignoring the effects of rotational inertia and lateral shear deformation, the displacement of plate 1 can be expressed in the form of a modified Fourier series:

Among them, p and q represent the number of truncation items of plate 1 in the x and y directions respectively.

The displacement of plate 1 can be written in matrix form:

The Lagrangian function of plate 1 can be expressed as:

in, represents the total potential energy generated by the lateral deformation of plate 1, represents the total kinetic energy of plate 1; and They represent the work done on plate 1 by the acoustic pressure _p1 in cavity 1 and the acoustic pressure _p2 in cavity 2. According to the continuity conditions of the coupled surface acoustic pressure and particle velocity, we can obtain:

Potential energy of plate 1 and kinetic energy It can be written as:

The work done by cavity 1 and cavity 2 on plate 1 is:

and

Similar to plate 1, the displacement of plate 2 is:

Write the above formula in matrix form:

w _Panel2 = C ^T Ψ _xy (35)

The Lagrangian function of plate 2 is:

in, and represent the total potential energy and total kinetic energy of plate 2 respectively. It represents the work done by the sound pressure in cavity 2 on plate 2.

For each term in the Lagrangian function of Plate 2, we have:

Combining equations (5), (12), (27) and (36), the Rayleigh-Leeds method is used to differentiate the unknown Fourier coefficients, thereby obtaining the linear equations of the coupled system.

For formula (5), the derivative of the unknown Fourier coefficients is:

Each term in equation (40) can be written in matrix form:

Then equation (40) becomes:

For formula (12), the derivative of the unknown Fourier coefficients is:

Each term in equation (46) can be written in matrix form:

Then equation (46) becomes:

Λ ₂ D-Ω ₂ D-Φ ₂ B-Γ ₂ C＝0 (51)

For formula (27), the derivative of the unknown Fourier coefficients is:

Each term in equation (52) can be written in matrix form:

Then equation (52) becomes: Λ ₃ B-Ω ₃ B+Φ ₃ A+Θ ₃ D＝0 (57)

For formula (36), the derivative of the unknown Fourier coefficients is:

Each term in equation (58) can be written in matrix form:

Then equation (58) becomes: Λ ₄ C-Ω ₄ C+Θ ₄ D＝0(62)

Combining formulas (45), (51), (57) and (62), the acoustic pressure P ₁ of cavity 1 can be calculated, and thus the acoustic impedance of the cavity mouth can be calculated as:

Wherein, P ₁ (L _x /2,L _y /2,0,t) represents the sound pressure at the middle point of the multi-local resonance cavity opening (ie, the coordinate point (L _x /2,L _y /2,0)) (the sound pressure will change with time t).

The additional shaped local resonance type pipe metamaterial can be regarded as an acoustic pipe with the shaped local resonance cavity as a side branch. Assume that the cross-sectional area of the main pipe is S, and the cross-sectional area of the side branch pipe (i.e., the multi-local resonance elastic cavity opening) is S _b . According to the calculation result of formula (63), the acoustic impedance Z _EH of the side branch pipe opening (i.e., the multi-local resonance elastic cavity opening) is expressed as Z _EH =R _b +jX _b , where R _b is the real part of the acoustic impedance Z _EH , and X _b is the imaginary part of the acoustic impedance Z _EH . The sound intensity transmission coefficient at both ends of the pipe is:

Then the transmission loss of the additional shaped local resonance pipe metamaterial can be obtained (i.e., the transmission loss at both ends of the pipe):

TL＝10lg(1/t _I ) (65)

Adjust the number of plate truncation items and cavity truncation items, and the calculation results of different numbers of plate truncation items are shown in Figure 2, and the calculation results of different numbers of cavity truncation items are shown in Figure 3. It is not difficult to see from Figure 2 that when p≥6 and q≥6, the calculation results of transmission loss have tended to be stable and converged in the low-frequency range; it is not difficult to see from Figure 3 that when _mx , _my , _mz , _nx , _ny , and _nz are all greater than or equal to 10, the calculation results of transmission loss have tended to be stable and converged in the low-frequency range.

Considering the whole frequency band, it is preferred to set p≥15, q≥15, and _mx , _my , _mz , _nx , _ny , and _nz to be greater than or equal to 13. In the following embodiment 1, the settings adopted are that p and q are both equal to 15, and _mx , _my , _mz , _nx , _ny , and _nz are all equal to 13.

Example 1

According to Table 2, a unit cell of a shaped local resonance type pipeline metamaterial is set, wherein flat plate 1 and flat plate 2 are respectively made of aluminum plates, and cavity 1 and cavity 2 are filled with air. Organic glass plate materials are used to form the tube wall and the four side walls of the Helmholtz resonance cavity (thus satisfying the rigid wall acoustic boundary conditions), and the external acceleration v=1m/s. The method of the present invention is used to calculate the acoustic transmission of the periodic shaped pipeline metamaterial, and the variation of the transmission loss with the frequency is obtained. At the same time, the finite element method is used to calculate the acoustic transmission of the periodic shaped pipeline metamaterial for comparative verification, and the results are shown in Figure 4. The calculation method proposed by the present invention is 30% faster than the finite element method. Taking this embodiment as an example, using the same computer (the configuration of the computer is shown in Table 3 below), the calculation of the method of the present invention takes about 40 minutes, and the finite element simulation calculation takes about 1 hour.

Table 2 Geometric parameters of the unit cell of the heterogeneous local resonance channel metamaterial

Table 3 Computer configuration used in Example 1

CPU Intel(R)Core(TM)i9-10900K CPU@3.70GHz 3.70GHz Memory 64GB harddisk 1TB Display 21.5 inches operating system Windows 10 Professional 64-bit The operating environment of the method of the present invention Matlab2018a (or above) version Finite element simulation software COMSOL Multiphysics version 6.0 (or above)

As shown in Figure 4, the method of the present invention has a good match with the finite element method, which proves the reliability and correctness of the calculation method of the present invention. Especially in the low-frequency region (frequency does not exceed 250Hz), the results of the method of the present invention and the finite element method are almost consistent and highly matched. It can be seen that the calculation method of the present invention can accurately calculate the sound transmission characteristics of the pipeline, especially can accurately capture the number of low-frequency sound absorption peaks of the pipeline, and provide guidance for the application of pipelines in low-frequency sound absorption and other sound transmission applications in engineering.

At the same time, it can be seen from Figure 4 that the "an additional periodic multi-mode coupling-regulated elastic cavity sound-absorbing metamaterial pipeline structure" developed by our research group has multiple sound absorption peaks at low frequencies, which once again confirms the low-frequency sound absorption of the pipeline.

It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A calculation method for calculating metamaterial sound transmission of a periodic special-shaped pipeline comprises the following steps ofThe periodic special-shaped pipeline metamaterial comprises a special-shaped Helmholtz resonant cavity which is periodically arranged on the outer wall of a pipeline, wherein the pipeline is cuboid, two ports of the pipeline are left and right and are positioned on the same horizontal line, the special-shaped Helmholtz resonant cavity is positioned above the pipeline, and plane waves with the speed v are horizontally input from one port of the pipeline; the special-shaped Helmholtz resonant cavity is cuboid, 2 elastic thin plates are respectively arranged on the top surface and the horizontal central section of the cuboid, the two thin plates are parallel to each other and are horizontally arranged, the bottom of the special-shaped Helmholtz resonant cavity is communicated with the outer wall of the pipeline through an opening, and the opening is completely covered by the special-shaped Helmholtz resonant cavity; the opening is square, the sides of the square are parallel to the sides of the thin plates, and the center of the opening and the three points of the center points of the two thin plates are positioned on the same vertical straight line; the method is characterized in that the calculation method of the periodic special-shaped pipeline metamaterial sound transmission is based on an energy method, and the acoustic impedance Z at the opening part _EH The method comprises the following steps:

wherein P is ₁ (opening center point, t) represents sound pressure at the opening center point as a function of time t, v being the velocity of the plane wave.

2. The method for calculating the acoustic transmission of the periodically profiled conduit metamaterial according to claim 1, wherein the sound intensity transmission coefficient t at both ends of the conduit _I The method comprises the following steps:

s is the sectional area of the pipeline;

R _b is Z _EH The corresponding real part, X _b Is Z _EH A corresponding imaginary part; ρ ₀ For the density of the fluid in the profiled Helmholtz resonator, c ₀ Is the sound velocity of the fluid in the profiled Helmholtz resonator.

3. The method for calculating the acoustic transmission of the periodically profiled conduit metamaterial according to claim 2, wherein the transmission loss TL at both ends of the conduit is:

TL＝10lg(1/t _I )。

4. a method of calculating periodic profiled conduit metamaterial acoustic transmissions as claimed in any one of claims 1 to 3, wherein for any one of the elastomeric sheets one edge of the elastomeric sheet is parallel to the conduit axial direction, denoted as x-direction; the other side is perpendicular to the axial direction of the pipeline and is marked as the y direction; then, taking the X direction as the X axis direction and the Y direction as the Y axis direction, establishing a three-dimensional space rectangular coordinate system, wherein the XOY plane of the three-dimensional space rectangular coordinate system is horizontally arranged;

in the sheet displacement expression based on the three-dimensional Fourier series, the number of truncated items in the X-axis direction corresponding to each sheet is an integer more than or equal to 6, and the number of truncated items in the Y-axis direction is an integer more than or equal to 6; in the cavity sound pressure expression based on the three-dimensional Fourier series, the number of truncated items in the X-axis direction corresponding to each cavity in the special-shaped Helmholtz resonant cavity is an integer not less than 10, the number of truncated items in the Y-axis direction is an integer not less than 10, and the number of truncated items in the Z-axis direction is an integer not less than 10.

5. The method for calculating the acoustic transmission of the periodically-shaped pipeline metamaterial according to claim 4, wherein in the sheet displacement expression based on the three-dimensional Fourier series, the number of truncated terms in the X-axis direction corresponding to each sheet is an integer not less than 15, and the number of truncated terms in the Y-axis direction is an integer not less than 15; in the cavity sound pressure expression based on the three-dimensional Fourier series, the number of truncated items in the X-axis direction corresponding to each cavity in the special-shaped Helmholtz resonant cavity is an integer more than or equal to 13, the number of truncated items in the Y-axis direction is an integer more than or equal to 13, and the number of truncated items in the Z-axis direction is an integer more than or equal to 13.

6. A computing cycle special-shaped pipeline superfilter as claimed in any one of claims 1-3A method for calculating acoustic transmission of a material, characterized by acoustic impedance Z _EH Sound intensity transmission coefficient t _I The sound wave frequency corresponding to the transmission loss TL is less than or equal to 250Hz.

7. A method of calculating the acoustic transmission of a periodically profiled conduit metamaterial according to any one of claims 1 to 3, wherein the resilient sheets are all aluminium sheets.