CN116259381A - A Calculation Method for Insertion Loss of Multilayer Coupled Plate Acoustic Metamaterials - Google Patents

Abstract

The invention discloses an insertion loss calculation method of a multilayer coupling plate type acoustic metamaterial, which comprises the following steps of: constructing an acoustic transmission loss calculation model of a multilayer coupling plate type acoustic metamaterial and homogeneous steel plate composite structure; and using an acoustic wave equation as input in an incident sound field, constructing a force balance equation, and setting a periodic boundary condition and a sound-solid coupling condition. And obtaining parameters and static heat permeability coefficients of fiber layers with different densities, converting the fiber layers into equivalent fluid domains, and calculating to obtain the sound pressure of an incident surface and the transmission sound pressure of a transmission sound field. The acoustic power and the transmission coefficient are calculated from the sound pressure, and the acoustic transmission loss is calculated from the transmission coefficient. The difference value of the acoustic transmission loss of the multilayer coupling plate type acoustic metamaterial and the acoustic transmission loss of the homogeneous steel plate composite structure is the insertion loss of the material. The invention uses the insertion loss to express the sound insulation performance of the acoustic metamaterial, and can consider the influence of the coupling of the metamaterial and the existing structure on the sound insulation performance, thereby being more fit for practical application.

Description

A method for calculating the insertion loss of multi-layer coupled plate-type acoustic metamaterials

Technical Field

The present invention relates to the research and development field of sound insulation materials, and in particular to a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial.

Background Art

The wavelength of medium and low frequency (100Hz ~ 1000Hz) noise is longer and has strong penetration, so the attenuation of medium and low frequency noise has always been an important goal of noise control. From the mass law, it can be seen that in order to achieve better sound insulation performance, it is often necessary to use a larger mass of sound insulation materials, which does not meet the requirements of lightweight development. The main advantage of acoustic metamaterials is that they do not need to increase a lot of mass and show good sound insulation performance in the low and medium frequency bands. Therefore, acoustic metamaterials have great potential in noise control. The excellent sound insulation performance of acoustic metamaterials comes from the structural configuration rather than the material properties. Typical membrane acoustic metamaterials attach mass and elastic membranes to a rigid frame to establish local resonance or anti-resonance as the working frequency.

However, the disadvantage of membrane metamaterials is that they need to pre-apply tension to the elastic membrane, which will lead to additional time and cost, limiting the engineering application of membrane metamaterials. In order to solve the tension problem, the concept of plate-type acoustic metamaterials was introduced. Membrane and plate-type acoustic metamaterials have similar sound insulation mechanisms. Subsequently, in order to meet engineering applications, three basic structures, namely, membrane or plate-type acoustic metamaterials with mass addition, massless addition and constrained structure, were proposed one after another. Plate-type acoustic metamaterials are more likely to be used in practice because of their simple structure, no need to pre-apply tension, and easy large-scale production. Limited by the local resonance mechanism, membrane or plate-type acoustic metamaterials usually have a narrow operating frequency band. In order to control noise in a wider frequency band, expanding the operating frequency bandwidth has become an important research topic.

Due to the requirement for lightweight materials and the complex material installation surface, sound insulation materials are usually traditional materials such as multi-layer fibers, damping layers, and porous blankets. They are characterized by excellent sound insulation performance in the high-frequency range, but insufficient sound insulation in the medium and low-frequency range. Multi-layer coupling of acoustic metamaterials with traditional acoustic materials can obviously enhance the sound insulation performance of traditional materials in the medium and low-frequency range. Therefore, multi-layer coupled plate-type acoustic metamaterials are a solution for effective sound insulation in the full frequency band. However, the existing technology cannot measure the sound insulation performance of multi-layer coupled plate-type acoustic metamaterials, which is not conducive to the application of multi-layer coupled plate-type acoustic metamaterials.

China's invention patent CN115186554A discloses "an acoustic metamaterial structure design optimization method based on joint simulation". This method can be used for the study of single-layer metamaterial structures and can optimize and improve the structure of metamaterials according to actual sound insulation needs. However, in actual use scenarios, metamaterials usually form composite structures with other solid materials, porous materials, etc. This method cannot take into account the coupling phenomenon existing in the composite structure.

Summary of the invention

The technical problem to be solved by the present invention is to propose a method for calculating the insertion loss of a multilayer coupled plate-type acoustic metamaterial, which takes into account the structure of the metamaterial, the fiber distribution, and the influence of the metamaterial on the insertion loss when used in combination with a metal structure, and can quickly and accurately analyze and predict the sound insulation performance of the acoustic metamaterial.

In order to achieve the purpose of the present invention, the present invention provides a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial, comprising the following steps:

①. Obtain the structural dimension parameters and material parameters of the multi-layer coupled plate-type acoustic metamaterial. The multi-layer coupled plate-type acoustic metamaterial includes two layers of fiber material and metamaterial layer with different densities.

②. Construct a calculation model for the acoustic transmission loss of a composite structure of a multi-layer coupled plate-type acoustic metamaterial and a homogeneous steel plate. A three-dimensional model is constructed based on the size of the smallest periodic unit of the metamaterial layer. The entire acoustic transmission loss calculation model includes the perfect matching layers at both ends, the incident sound field, the transmitted sound field, the homogeneous steel plate, and the multi-layer coupled plate-type acoustic metamaterial.

③ Use the acoustic wave equation as input in the incident sound field;

④. Establish the mechanical equilibrium equation; in each air domain, the pressure distribution conforms to the Helmholtz equation:

为梯度算子，ρ₀为空气密度，c₀为声音在空气中的传播速度。in

is the gradient operator, ρ ₀ is the air density, and c ₀ is the speed of sound propagation in air.

In the solid domain, the stress distribution conforms to Newton's second law:

Where _ρs represents the material density, u represents the displacement vector in three directions, _σc represents the stress tensor, which conforms to Hooke's law for linear elastic materials. C is the constant matrix of the material, which can be obtained according to the elastic modulus and Poisson's ratio of the material for linear elastic materials, and ε is the strain matrix;

⑤. Apply Floquet periodic boundary conditions to the computational model. This condition indicates that in a periodically distributed structure, the field values of the relative boundary surfaces differ by only one phase, so as to characterize large-scale periodically distributed multi-layer coupled plate-type acoustic metamaterials.

⑥ Set a 1mm air layer between the fiber and the solid to avoid rigid contact between the fiber and the solid. Define the acoustic-solid coupling conditions at the contact surface between the air and the metamaterial and the homogeneous steel plate to ensure the displacement continuity and force continuity of the coupling surface:

Where n represents the direction cosine of the normal line outside the coupling plane, a represents the acceleration vector of the structure, and F represents the pressure vector of the structure;

⑦⑦. Obtain the density ρ _d , porosity φ, tortuosity factor τ, flow resistivity σ, viscous characteristic length Λ, thermal characteristic length Λ′ and static thermal permeability k′ ₀ of fiber layers with different densities respectively. Use the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model to characterize the fiber layer. Convert the fiber layer into an equivalent fluid domain through the effective mass density ρ _c and the effective bulk modulus K _c. Calculate the equivalent sound velocity c _c through the effective mass density ρ _c and the effective bulk modulus K _c. Calculate the sound pressure distribution of the fiber layer based on the effective mass density ρ _c and the equivalent sound velocity c _c .

The effective mass density ρ _c is expressed as:

The effective bulk modulus _Kc is expressed as:

Where μ is the dynamic viscosity of air, γ is the specific heat of air, _P0 is the atmospheric pressure, β is the thermal conductivity of air, _Cp is the constant pressure heat capacity of air, and the equivalent sound speed _cc can be calculated by the effective mass density _ρc and the effective bulk modulus _Kc :

Substituting the effective mass density ρ _c and the equivalent sound velocity c _c into the Helmholtz equation in ④, the sound pressure distribution of the fiber layer can be calculated;

⑧. Mesh the three-dimensional model, set the analysis frequency and frequency step, calculate the sound pressure P _in of the incident surface and the transmitted sound pressure P _out through finite element software, obtain the incident sound power W _in and the transmitted sound power W _out based on the sound pressure P _in and the transmitted sound pressure P _out of the incident surface, obtain the transmission coefficient based on the incident sound power W _in and the transmitted sound power W _out , and calculate the sound transmission loss STL of the structure according to the obtained transmission coefficient;

⑨. The established calculation model is used to calculate the acoustic transmission loss STL ₁ of the composite structure of the multilayer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the acoustic transmission loss STL ₂ of the single-layer steel plate. The insertion loss IL of the multilayer coupled plate-type acoustic metamaterial is the difference between STL ₁ and STL ₂ .

Furthermore, the metamaterial includes a film, a frame and an additional mass. The structural size parameters that need to be obtained include the side length of the periodic unit of the metamaterial layer, the radius of the additional mass, the radius of the film and the thickness of various materials. The material parameters that need to be obtained include the elastic modulus, density and Poisson's ratio of the frame, film and additional mass.

Furthermore, in step ③, the incident sound wave _pin is expressed as:

Where k _x , _ky and k _z are the wave number components of the sound wave in each direction, i represents the imaginary unit, and x, y, z represent the coordinate symbols in the three-dimensional coordinate system;

为方位角，k为波数，ω为角频率，c₀为空气声速。Where θ is the incident angle of the sound wave,

is the azimuth angle, k is the wave number, ω is the angular frequency, and c ₀ is the air sound speed.

Furthermore, in step ⑧, the three-dimensional model is meshed using hexahedral elements, the maximum size of the mesh does not exceed one fifth of the minimum wavelength of the calculated frequency, and the number of mesh layers of the perfectly matched layer is not less than 8. The analysis frequency is set to 200-1500 Hz, and the frequency step is 10 Hz.

Furthermore, in step ⑧, the expressions of incident sound power W _in and transmitted sound power W _out are:

Where S _in and S _out represent the incident surface and the transmission surface respectively. The transmission coefficient t is expressed as:

Calculate the sound transmission loss STL of the structure based on the transmission coefficient:

STL＝-10log ₁₀ t (11)

Furthermore, in step ⑨, the established calculation model is used to calculate the acoustic transmission loss STL ₁ of the composite structure of the multilayer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the acoustic transmission loss STL ₂ of the single-layer steel plate, and the insertion loss IL of the multilayer coupled plate-type acoustic metamaterial is the difference between STL ₁ and STL ₂ .

Compared with the prior art, the present invention has at least the following advantages:

1) The present invention uses the JCA-L acoustic model to characterize the fiber material, fully considering the influence of the fiber material on the sound insulation performance of the metamaterial, and increasing the calculation accuracy.

2) The present invention uses the smallest periodic unit of the metamaterial layer for modeling and applies Floquet periodic boundaries to the model, which can greatly speed up the calculation speed.

3) The present invention uses insertion loss to represent the sound insulation performance of the acoustic metamaterial, which can take into account the influence of the coupling between the metamaterial and the existing structure on the sound insulation performance, and is more suitable for practical applications.

4) The present invention can analyze acoustic metamaterials of different structural sizes by using simulation means, and is applicable to situations where sound waves are incident at different angles, which can effectively reduce the number of experiments and provide a basis for the structural design of acoustic metamaterials.

5) The method of the present invention involves the coupling between metamaterials, fiber materials and solid materials, takes into account the influence of the coupling phenomenon on the sound insulation performance of metamaterials, is closer to the actual application scenarios of metamaterials, and the results obtained are more accurate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for calculating insertion loss of a multi-layer coupled plate-type acoustic metamaterial provided by an embodiment of the present invention.

FIG. 2 is a structural diagram of a multi-layer coupled plate-type acoustic metamaterial in the present invention.

FIG. 3 is a diagram of a finite element model for calculating sound transmission loss in the present invention.

FIG. 4 is a schematic diagram of the calculation results of the insertion loss in the present invention.

DETAILED DESCRIPTION

The present invention is further described in detail below with reference to the accompanying drawings.

As shown in FIG1 , a method for calculating the insertion loss of a multilayer coupled plate-type acoustic metamaterial provided by the present invention comprises the following steps:

Step 1: Obtain the structural size parameters and material parameters of the multi-layer coupled plate-type acoustic metamaterial.

The multilayer coupled plate-type acoustic metamaterial includes a periodically distributed metamaterial layer and two fiber material layers with different densities. The metamaterial layer includes a film, a frame and an additional mass. The structural size parameters that need to be obtained include: the side length of the periodic unit of the metamaterial layer, the radius of the additional mass, the film radius and the thickness of various materials (film, frame, additional mass and two fiber material layers with different densities); the material parameters that need to be obtained include the elastic modulus, density and Poisson's ratio of materials such as the frame, film and additional mass.

In some embodiments of the present invention, as shown in Figure 2, the film is a PET film, the frame is a PP plastic frame, and the additional mass is an aluminum block. The film is attached to the frame, and the aluminum block is located at the center of the film.

Step 2: Construct a calculation model for the acoustic transmission loss of a composite structure of a multi-layer coupled plate-type acoustic metamaterial and a homogeneous steel plate. A three-dimensional model is constructed with the size of the smallest periodic unit of the metamaterial layer. The entire acoustic transmission loss calculation model includes the perfect matching layers at both ends, the incident sound field, the transmitted sound field, the homogeneous steel plate, and the multi-layer coupled plate-type acoustic metamaterial. The perfect matching layer is a completely sound-absorbing boundary that can prevent multiple reflections of sound waves.

In some embodiments of the present invention, the established acoustic transmission loss calculation model is a finite element model as shown in FIG3 , wherein the outermost layers at both ends are perfectly matched layers, and from the perfect matching layer on the left to the perfect matching layer on the right, there are the incident sound field, the homogeneous steel plate, the multi-layer coupled plate-type acoustic metamaterial, and the transmitted sound field, respectively. An air gap is left between the homogeneous steel plate and the multi-layer coupled plate-type acoustic metamaterial, and an air gap is also left between the two fiber material layers and the metamaterial layer in the multi-layer coupled plate-type acoustic metamaterial.

Step 3: Using the acoustic wave equation as input in the incident sound field, the incident sound wave p _in can be expressed as:

where k _x , _ky and k _z are the wave number components of the sound wave in each direction respectively.

为方位角，声波方向如图3所示，可通过改变入射角及方位角的大小从而改变声波的入射方向。k为波数，ω为角频率，c₀为空气声速；i表示虚部单位，x、y、z表示三维坐标系中的坐标符号。θ is the incident angle of the sound wave,

is the azimuth angle, and the direction of the sound wave is shown in Figure 3. The incident direction of the sound wave can be changed by changing the incident angle and the azimuth angle. k is the wave number, ω is the angular frequency, c ₀ is the air speed of sound; i represents the imaginary unit, and x, y, and z represent the coordinate symbols in the three-dimensional coordinate system.

Among them, using the acoustic wave equation as the input of the acoustic transmission loss calculation model can facilitate the calculation of different situations of metamaterial insertion loss when the incident wave is at different angles.

Step 4: Establish the mechanical equilibrium equation. In each air domain, the pressure distribution conforms to the Helmholtz equation:

为梯度算子，ρ₀为空气密度，c₀为声音在空气中的传播速度，p表示声压。in

is the gradient operator, ρ ₀ is the air density, c ₀ is the speed of sound propagation in the air, and p represents the sound pressure.

In the solid domain, the stress distribution conforms to Newton's second law:

Where _ρs represents the material density, u represents the displacement vector in three directions, _σc represents the stress tensor, which conforms to Hooke's law for linear elastic materials. The constant matrix of C material can be obtained according to the elastic modulus and Poisson's ratio of the material, and ε is the strain matrix;

Step 5: Apply Floquet periodic boundary conditions to the computational model to characterize large-scale periodically distributed multi-layer coupled plate-type acoustic metamaterials.

Among them, applying Floquet periodic boundary conditions to the calculation model can use a smaller model to represent the complete structure and speed up the calculation.

In some embodiments of the present invention, as shown in FIG3 , the entire model is surrounded by Floquet periodic boundary conditions, and the two opposite boundary surfaces are the source surface and the target surface, and the field values of the source surface and the target surface differ by only a phase.

Step 6: As shown in Figure 3, set a 1 mm air layer between the fiber and the solid to avoid rigid contact between the fiber and the solid. Define the acoustic-solid coupling conditions at the contact surface between the air and the metamaterial and the homogeneous steel plate to ensure the displacement continuity and force continuity of the coupling surface:

Where n represents the direction cosine of the normal line outside the coupling plane, a represents the acceleration vector of the structure, and F represents the pressure vector of the structure;

Step 7: Obtain the density ρ _d , porosity φ, tortuosity factor τ, flow resistivity σ, viscous characteristic length Λ, thermal characteristic length Λ′ and static thermal permeability k′ ₀ of fiber layers with different densities respectively, characterize the fiber layer using the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model, and transform the fiber layer into an equivalent fluid domain by calculating the effective mass density ρ _c and the effective bulk modulus K _c .

The effective mass density ρ _c is expressed as:

The effective bulk modulus _Kc is expressed as:

Where μ is the dynamic viscosity of air, γ is the specific heat of air, _P0 is the atmospheric pressure, β is the thermal conductivity of air, _Cp is the constant pressure heat capacity of air, and the equivalent sound speed _cc can be calculated by the effective mass density _ρc and the effective bulk modulus _Kc :

Substituting the effective mass density ρ _c and the equivalent sound velocity c _c into the Helmholtz equation in ④, the sound pressure distribution of the fiber layer can be calculated;

Step 8. Use hexahedral units to mesh the three-dimensional model. The maximum size of the mesh should not exceed one-fifth of the minimum wavelength of the calculated frequency, and the number of mesh layers of the perfectly matched layer should not be less than 8. Set the analysis frequency to 200-1500Hz and the frequency step to 10Hz. Use finite element software to calculate the incident surface sound pressure P _in and the transmitted sound pressure P _out , and then obtain the incident sound power W _in and the transmitted sound power W _out :

Where S _in and S _out represent the incident surface and the transmission surface respectively. The transmission coefficient t is expressed as:

Calculate the sound transmission loss STL of the structure based on the transmission coefficient:

STL＝-10log ₁₀ t (11)

In this step, the sound pressure distribution obtained by finite element calculation is integrated to calculate the sound power of the incident surface and the transmission surface, and then the sound transmission loss of the structure is obtained.

Step 9: Calculate the acoustic transmission loss STL ₁ of the composite structure of the multilayer coupled plate-type acoustic metamaterial and the homogeneous steel plate using the above steps. Remove the multilayer coupled plate-type acoustic metamaterial from the model and only calculate the acoustic transmission loss STL ₂ of the single-layer steel plate. The insertion loss IL of the multilayer coupled plate-type acoustic metamaterial is the difference between STL ₁ and STL ₂ .

In some embodiments of the present invention, the insertion loss results obtained by using the method are shown in FIG. 4 , which illustrates the effectiveness of the method of the present invention.

The present invention takes into account the STL of the combined structure of the metamaterial and the homogeneous steel plate, and more accurately simulates the coupling between the metamaterial and the existing structure during actual use.

The aforementioned embodiments of the present invention provide an effective method for calculating the sound insulation performance of a multi-layer coupled plate-type acoustic metamaterial, which can meet the application requirements of the acoustic metamaterial and facilitate the targeted design of a sound insulation solution.

The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial, characterized in that it comprises the following steps: ①, obtaining structural size parameters and material parameters of a multi-layer coupled plate-type acoustic metamaterial, wherein the multi-layer coupled plate-type acoustic metamaterial comprises a periodically distributed metamaterial layer and two fiber material layers with different densities; ②②, construct a calculation model for the acoustic transmission loss of a composite structure of a multi-layer coupled plate-type acoustic metamaterial and a homogeneous steel plate, and construct a three-dimensional model based on the size of the smallest periodic unit of the metamaterial layer. The entire acoustic transmission loss calculation model includes the perfect matching layers at both ends, the incident sound field, the transmitted sound field, the homogeneous steel plate, and the multi-layer coupled plate-type acoustic metamaterial region; ③③, using the acoustic wave equation as input in the incident sound field; ④. Establish mechanical equilibrium equation; ⑤. Apply periodic boundary conditions to the acoustic transmission loss calculation model; ⑥ Set an air layer between the fiber and the solid to avoid rigid contact between the fiber and the solid, define the acoustic-solid coupling conditions at the contact surface between the air and the metamaterial and the homogeneous steel plate to ensure the displacement continuity and force continuity of the coupling surface: ⑦. Obtain the density ρ _d , porosity φ, tortuosity factor τ, flow resistivity σ, viscous characteristic length Λ, thermal characteristic length Λ′ and static thermal permeability k′ ₀ of fiber layers with different densities respectively. Use the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model to characterize the fiber layer. Convert the fiber layer into an equivalent fluid domain through the effective mass density ρ _c and the effective bulk modulus K _c. Calculate the equivalent sound velocity c _c through the effective mass density ρ _c and the effective bulk modulus K _c. Calculate the sound pressure distribution of the fiber layer based on the effective mass density ρ _c and the equivalent sound velocity c _c . ⑧. Mesh the three-dimensional model, set the analysis frequency and frequency step, calculate the sound pressure P _in of the incident surface and the transmitted sound pressure P _out through finite element software, obtain the incident sound power W _in and the transmitted sound power W _out based on the sound pressure P _in and the transmitted sound pressure P _out of the incident surface, obtain the transmission coefficient based on the incident sound power W _in and the transmitted sound power W _out , and calculate the sound transmission loss STL of the structure according to the obtained transmission coefficient; ⑨. The established calculation model is used to calculate the acoustic transmission loss of the composite structure of the acoustic metamaterial and the homogeneous steel plate and the acoustic transmission loss of the single-layer steel plate. The difference between the two calculated acoustic transmission losses is used as the insertion loss of the acoustic metamaterial. 2. According to claim 1, a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial is characterized in that the metamaterial layer includes a film, a frame and an additional mass, and the structural size parameters that need to be obtained include: the side length of the periodic unit of the metamaterial layer, the radius of the additional mass, the film radius and the thickness of various different materials; the material parameters that need to be obtained include the elastic modulus, density and Poisson's ratio of the frame, film and additional mass. 3. The method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, characterized in that in step ③, the incident sound wave _pin is expressed as:

Where k _x , _ky and k _z are the wave number components of the sound wave in each direction, i represents the imaginary unit, and x, y, z represent the coordinate symbols in the three-dimensional coordinate system;

Where θ is the incident angle of the sound wave,

is the azimuth angle, k is the wave number, ω is the angular frequency, and c ₀ is the air sound speed. 4. The method for calculating insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, characterized in that, in step ④, in each air domain, the pressure distribution conforms to the Helmholtz equation:

in

is the gradient operator, ρ ₀ is the air density, c ₀ is the air sound speed, and p represents the sound pressure; In the solid domain, the stress distribution conforms to Newton's second law:

Where _ρs represents the material density, u represents the displacement vectors in three directions, _σc represents the stress tensor, the material constant matrix, and ε is the strain matrix. 5. The method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1 is characterized in that, in step ⑤, the Floquet periodic boundary condition represents that in a structure with a periodic distribution, the field values of the relative boundary surfaces differ by only one phase, so as to characterize a multi-layer coupled plate-type acoustic metamaterial with a large periodic distribution. 6. The method for calculating insertion loss of a multilayer coupled plate-type acoustic metamaterial according to claim 1, characterized in that in step ⑥, the acoustic-solid coupling condition is

Where n represents the direction cosine of the out-of-plane normal of the coupling, a represents the acceleration vector of the structure, and F represents the pressure vector on the structure. 7. The method for calculating insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, characterized in that in step 7, the effective mass density ρ _c is expressed as:

The effective bulk modulus _Kc is expressed as:

Where μ is the dynamic viscosity of air, γ is the specific heat of air, P ₀ is the atmospheric pressure, β is the thermal conductivity of air, and C _p is the constant pressure heat capacity of air; The equivalent sound speed c _c is calculated by the effective mass density ρ _c and the effective bulk modulus K _c :

8. The method for calculating insertion loss of a multilayer coupled plate-type acoustic metamaterial according to claim 1, characterized in that in step ⑧, the expressions of incident acoustic power W _in and transmitted acoustic power W _out are:

Wherein, S _in and S _out represent the incident surface and the transmission surface respectively; The transmission coefficient t is obtained as:

Calculate the sound transmission loss STL of the structure based on the transmission coefficient: STL = -10log ₁₀ t (11). 9. The method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1 is characterized in that, in step ⑧, the three-dimensional model is divided into grids using hexahedral units, the maximum size of the grid does not exceed one-fifth of the minimum wavelength of the calculated frequency, and the number of grid layers of the perfect matching layer is not less than 8 layers. 10. The method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, characterized in that in step ⑨, the acoustic transmission loss STL ₁ of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the acoustic transmission loss STL ₂ of the single-layer steel plate are calculated respectively by using the established calculation model, and the insertion loss IL of the multi-layer coupled plate-type acoustic metamaterial is the difference between STL ₁ and STL ₂ .

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