Calculation method for insertion loss of a multi-layer coupled plate-type acoustic metamaterial

Abstract

The present invention discloses a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial, including: constructing a sound transmission loss calculation model for a composite structure of a multi-layer coupled plate-type acoustic metamaterial and a homogeneous steel plate; using the acoustic wave equation as input in the incident sound field, constructing a force balance equation, and setting periodic boundary conditions and acoustic-solid coupling conditions. Obtain different density fiber layer parameters and static thermal permeability coefficients, convert the fiber layer into an equivalent fluid domain, and calculate the sound pressure on the incident surface and the transmitted sound pressure of the transmitted sound field. Calculate the sound power and transmission coefficient according to the sound pressure, and calculate the sound transmission loss from the transmission coefficient. The difference between the sound transmission loss of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the sound transmission loss of a single-layer steel plate is the insertion loss of the material. The present invention uses the insertion loss to represent the sound insulation performance of the acoustic metamaterial, can consider the influence of the coupling between the metamaterial and the existing structure on the sound insulation performance, and is more suitable for practical applications.

Description

Technical Field

[0001] The present invention relates to the research and development field of sound insulation materials, and particularly to a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial. Background Art

[0002] The wavelengths of mid-low frequency (100 Hz - 1000 Hz) noises are relatively long and the penetration power is strong. Therefore, the attenuation of mid-low frequency noises has always been an important goal of noise control. According to the mass law, in order to achieve better sound insulation performance, sound insulation materials with a relatively large mass are often required, which does not meet the requirements of lightweight development. The main advantage of acoustic metamaterials is that they do not need to increase a large amount of mass and exhibit good sound insulation performance in the low and mid-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. A typical membrane-type acoustic metamaterial attaches a mass and an elastic membrane to a rigid frame to establish local resonance or anti-resonance as the working frequency.

[0003] However, the disadvantage of the membrane-type metamaterial is that a pre-tension force needs to be applied to the elastic membrane in advance, which will lead to an increase in additional time and cost and limit the engineering application of the membrane-type metamaterial. To solve the problem of the pre-tension force, the concept of plate-type acoustic metamaterials was introduced, and the membrane-type and plate-type acoustic metamaterials have similar sound insulation mechanisms. Subsequently, to meet the engineering applications, three basic structures, namely mass-added, massless-added, and restricted-structure membrane or plate-type acoustic metamaterials, were successively proposed. The plate-type acoustic metamaterial is more likely to be applied in practice because of its simple structure, no need to apply a pre-tension force in advance, and easy large-scale production. Limited by the local resonance mechanism, the membrane or plate-type acoustic metamaterial usually has a relatively narrow working frequency band. In order to control noises in a wider frequency band, expanding the working frequency bandwidth has become an important research topic.

[0004] Due to the requirements for material lightweight and the complex material installation surface, sound insulation materials are usually traditional materials such as multi-layer fibers, damping layers, and porous blankets. Their characteristics are excellent sound insulation performance in the high-frequency range, but insufficient sound insulation in the mid-low frequency range. Coupling acoustic metamaterials with traditional acoustic materials in multiple layers can obviously enhance the sound insulation performance of traditional materials in the mid-low frequency range. Therefore, the multi-layer coupled plate-type acoustic metamaterial is a solution for effective sound insulation in the full frequency band. However, in the prior art, the sound insulation performance of the multi-layer coupled plate-type acoustic metamaterial cannot be measured, which is not conducive to the application of the multi-layer coupled plate-type acoustic metamaterial.

[0005] The Chinese invention patent CN115186554A discloses "a method for optimizing the design of acoustic metamaterial structures based on co - simulation". This method can be used for the research of single - layer metamaterial structures and can optimize and improve the structure of the metamaterial according to actual sound insulation requirements. However, in actual use scenarios, metamaterials usually form composite structures with other solid materials, porous materials, etc., and this method cannot take into account the coupling phenomena existing in the composite structures. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: to propose a calculation method for the insertion loss of a multi - layer coupled plate - type acoustic metamaterial, which considers the structure of the metamaterial, the fiber distribution, and the influence 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.

[0007] To achieve the object of the present invention, a calculation method for the insertion loss of a multi - layer coupled plate - type acoustic metamaterial provided by the present invention includes the following steps:

[0008] 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 fiber materials with different densities and a metamaterial layer.

[0009] ②. Construct a sound transmission loss calculation model for the composite structure of the 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 sound transmission loss calculation model includes regions such as perfect matching layers at both ends, incident sound fields, transmitted sound fields, homogeneous steel plates, and multi - layer coupled plate - type acoustic metamaterials;

[0010] ③. Use the acoustic wave equation as the input in the incident sound field;

[0011] ④. Establish a mechanical equilibrium equation; in each air domain, the pressure distribution conforms to the Helmholtz equation:

[0012]

[0013] where is the gradient operator, ρ0 is the air density, and c0 is the sound propagation speed in air.

[0014] In the solid domain, its stress distribution conforms to Newton's second law:

[0015]

[0016] where ρ s represents the material density, u represents the displacement vector in three directions, and σ cdenotes the stress tensor, which follows Hooke's law for linearly elastic materials. The constant matrix of material C can be obtained based on the elastic modulus and Poisson's ratio of the material for linearly elastic materials, and ε is the strain matrix;

[0017] ⑤. Apply the Floquet periodic boundary condition to the computational model. This condition indicates that in a structure with a periodic distribution, the field values on the opposite boundary surfaces only differ by a phase, in order to characterize a large-scale periodically distributed multi-layer coupled plate-type acoustic metamaterial;

[0018] ⑥. 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 condition at the contact surfaces of the air with the metamaterial and the homogeneous steel plate to ensure the displacement continuity and force continuity of the coupling surface:

[0019]

[0020]

[0021] where n represents the direction cosine of the outer normal of the coupling surface, a represents the acceleration vector of the structure, and F represents the pressure vector acting on the structure;

[0022] 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 different density fiber layers respectively. Use the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model to characterize the fiber layer. Through the effective mass density ρ c and the effective bulk modulus K c transform the fiber layer into an equivalent fluid domain. Calculate the equivalent sound speed c c through the effective mass density ρ c and the effective bulk modulus K c , and calculate the sound pressure distribution of the fiber layer based on the effective mass density ρ c and the equivalent sound speed c c ;

[0023] The effective mass density ρ c is expressed as:

[0024]

[0025] The effective bulk modulus K c is expressed as:

[0026]

[0027] where μ is the dynamic viscosity of air, γ is the specific heat ratio of air, P0 is the atmospheric pressure, β is the thermal conductivity of air, Cp is the constant pressure heat capacity of air, and through the effective mass density ρ c and the effective bulk modulus K c the equivalent sound speed c can be calculated c as follows:

[0028]

[0029] Substitute the effective mass density ρ c and the equivalent sound speed c c into the Helmholtz equation in ④, and the sound pressure distribution of the fiber layer can be calculated;

[0030] ⑧. Mesh the three-dimensional model, set the analysis frequency and frequency step size, and calculate the sound pressure P in on the incident surface and the transmitted sound pressure P out through the finite element software. Based on the sound pressure P in on the incident surface and the transmitted sound pressure P out the incident sound power W in and the transmitted sound power W out are obtained. Based on the incident sound power W in and the transmitted sound power W out the transmission coefficient is obtained, and the sound transmission loss STL of the structure is calculated according to the obtained transmission coefficient;

[0031] ⑨. Use the established calculation model to calculate the sound transmission loss STL1 of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the sound transmission loss STL2 of the single-layer steel plate respectively. The insertion loss IL of the multi-layer coupled plate-type acoustic metamaterial is the difference between STL1 and STL2.

[0032] Furthermore, the metamaterial includes a thin film, a frame, and an additional mass. The structural size parameters to be obtained are the side length of the periodic unit of the metamaterial layer, the radius of the additional mass, the radius of the thin film, and the thicknesses of various different materials. The material parameters to be obtained are the elastic modulus, density, and Poisson's ratio of the materials such as the frame, the thin film, and the additional mass.

[0033] Furthermore, in step ③, the incident sound wave p in is expressed as:

[0034]

[0035] where k x , k y and k z are the wave number components of the sound wave in each direction respectively, i represents the imaginary unit, and x, y, and z represent the coordinate symbols in the three-dimensional coordinate system;

[0036]

[0037] In the formula, θ is the incident angle of the sound wave, is the azimuth angle, k is the wave number, ω is the angular frequency, and c0 is the speed of sound in air.

[0038] 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 layers. The analysis frequency is set to 200 - 1500 Hz, and the frequency step is 10 Hz.

[0039] Furthermore, in step ⑧, the incident sound power W in and the transmitted sound power W out are expressed as

[0040]

[0041] where S in and S out represent the incident surface and the transmitted surface respectively. The transmission coefficient t is expressed as:

[0042]

[0043] The sound transmission loss STL of the structure is calculated according to the transmission coefficient:

[0044] STL = -10log 10 t (11)

[0045] Furthermore, in step ⑨, the sound transmission loss STL1 of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the sound transmission loss STL2 of the single-layer steel plate are calculated respectively using the established calculation model. The insertion loss IL of the multi-layer coupled plate-type acoustic metamaterial is the difference between STL1 and STL2.

[0046] Compared with the prior art, the present invention has at least the following advantages:

[0047] 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 improving the calculation accuracy.

[0048] 2) The present invention models with the minimum periodic unit of the metamaterial layer and applies the Floquet periodic boundary to the model, which can greatly accelerate the calculation speed.

[0049] 3) The present invention uses the insertion loss to represent the sound insulation performance of the acoustic metamaterial, which can consider the influence of the coupling between the metamaterial and the existing structure on the sound insulation performance and is more suitable for practical applications.

[0050] 4) The present invention can analyze acoustic metamaterials with different structural dimensions by using simulation means, and is applicable to the case 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.

[0051] 5) The method of the present invention involves the coupling situation among 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 scenario of metamaterials, and the obtained results are more accurate. Description of the Drawings

[0052] Figure 1 is a flowchart of a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial provided by an embodiment of the present invention.

[0053] Figure 2 is a structural diagram of a multi-layer coupled plate-type acoustic metamaterial in the present invention.

[0054] Figure 3 is a finite element model diagram for calculating the sound transmission loss in the present invention.

[0055] Figure 4 is a schematic diagram of the calculation result of the insertion loss in the present invention. Detailed Embodiments

[0056] The present invention will be further described in detail below in conjunction with the embodiments of the drawings.

[0057] As Figure 1 shown, a method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial provided by the present invention includes the following steps:

[0058] Step 1, obtain the structural dimension parameters and material parameters of the multi-layer coupled plate-type acoustic metamaterial.

[0059] The multi-layer coupled plate-type acoustic metamaterial includes a periodically distributed metamaterial layer and two fiber material layers with different densities. The metamaterial layer includes a thin film, a frame and an additional mass. The structural dimension parameters 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 thin film, and the thicknesses of various different materials (thin film, frame, additional mass and two fiber material layers with different densities); the material parameters to be obtained include the elastic modulus, density and Poisson's ratio of materials such as the frame, thin film and additional mass.

[0060] In some embodiments of the present invention, as Figure 2 shown, the thin film is a PET thin film, the frame is a PP plastic frame, and the additional mass is an aluminum block. The thin film is attached to the frame, and the aluminum block is located at the center of the thin film.

[0061] Step 2: Construct a sound transmission loss calculation model for 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 sound transmission loss calculation model includes regions such as perfectly matched layers at both ends, an incident sound field, a transmitted sound field, a homogeneous steel plate, and a multi-layer coupled plate-type acoustic metamaterial. The perfectly matched layer is a perfectly absorbing boundary that can prevent multiple reflections of sound waves.

[0062] In some embodiments of the present invention, the established sound transmission loss calculation model is a finite element model as shown in Figure 3 . Among them, the outermost layers at both ends are perfectly matched layers. From the left perfectly matched layer to the right perfectly matched layer, there are, in sequence, an incident sound field, a homogeneous steel plate, a multi-layer coupled plate-type acoustic metamaterial, and a transmitted sound field. There is an air gap between the homogeneous steel plate and the multi-layer coupled plate-type acoustic metamaterial, and there is also an air gap between the two fiber material layers and the metamaterial layer in the multi-layer coupled plate-type acoustic metamaterial.

[0063] Step 3: Use the acoustic wave equation as the input in the incident sound field. The incident sound wave p in can be expressed as:

[0064]

[0065] where k x , k y and k z are respectively the wave number components of the sound wave in each direction.

[0066]

[0067] θ is the incident angle of the sound wave, is the azimuth angle, and the sound wave direction is as shown in Figure 3 . The incident direction of the sound wave can be changed by changing the magnitudes of the incident angle and the azimuth angle. k is the wave number, ω is the angular frequency, c0 is the speed of sound in air; i represents the imaginary unit, and x, y, z represent the coordinate symbols in the three-dimensional coordinate system.

[0068] Among them, using the acoustic wave equation as the input of the sound transmission loss calculation model can facilitate the calculation of different situations of the insertion loss of the metamaterial under the condition of incident waves at different angles.

[0069] Step 4: Establish a mechanical equilibrium equation. In each air domain, the pressure distribution conforms to the Helmholtz equation:

[0070]

[0071] where is the gradient operator, ρ0 is the air density, c0 is the speed of sound propagation in air, and p represents the sound pressure.

[0072] In the solid domain, the stress distribution conforms to Newton's second law:

[0073]

[0074] where ρ s represents the material density, u represents the displacement vector in three directions, and σ c represents the stress tensor. For linearly elastic materials, it conforms to Hooke's law. The constant matrix of material C can be obtained based on the elastic modulus and Poisson's ratio of the material, and ε is the strain matrix;

[0075] Step 5: Apply the Floquet periodic boundary condition to the computational model to characterize the large-scale periodically distributed multi-layer coupled plate-type acoustic metamaterials.

[0076] Among them, applying the Floquet periodic boundary condition to the computational model can characterize the complete structure with a smaller-sized model and accelerate the calculation speed.

[0077] In some embodiments of the present invention, as Figure 3 shown, the four sides of the entire model are all set as Floquet periodic boundary conditions. The two opposite side surfaces are respectively the source surface and the target surface, and the field values of the source surface and the target surface only differ by a phase.

[0078] Step 6: As 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 condition 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:

[0079]

[0080] In the formula, n represents the direction cosine of the outer normal of the coupling surface, a represents the acceleration vector of the structure, and F represents the pressure vector exerted on the structure;

[0081] Step 7: Respectively 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 different density fiber layers, use the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model to characterize the fiber layer, and convert the fiber layer into an equivalent fluid domain by calculating the effective mass density ρ c and the effective bulk modulus K c

[0082] The effective mass density ρ c is expressed as:

[0083] ​

[0084] Effective bulk modulus K c It is expressed as:

[0085]

[0086] where μ is the dynamic viscosity of air, γ is the specific heat ratio of air, P0 is the atmospheric pressure, β is the thermal conductivity of air, C p is the constant-pressure heat capacity of air, and the equivalent sound speed c can be calculated through the effective mass density ρ c and the effective bulk modulus K c as: c For:

[0087]

[0088] Substitute the effective mass density ρ c and the equivalent sound speed c c into the Helmholtz equation in ④, and the sound pressure distribution of the fiber layer can be calculated;

[0089] Step 8: Use hexahedral elements to mesh the three-dimensional model. 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 layers. Set the analysis frequency to 200 - 1500 Hz, the frequency step to 10 Hz, and calculate the incident sound pressure P in and the transmitted sound pressure P out on the incident surface through the finite element software, and then obtain the incident sound power W in and the transmitted sound power W out :

[0090]

[0091] where S in and S out represent the incident surface and the transmitted surface respectively. The transmission coefficient t is expressed as:

[0092]

[0093] Calculate the sound transmission loss STL of the structure according to the transmission coefficient:

[0094] STL = -10log 10 t (11)

[0095] In this step, the sound power on the incident surface and the transmitted surface is calculated by integrating the sound pressure distribution obtained by finite element calculation, and then the sound transmission loss of the structure is obtained.

[0096] Step 9: Calculate the sound transmission loss STL1 of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate using the above steps. Remove the multi-layer coupled plate-type acoustic metamaterial from the model and only calculate the sound transmission loss STL2 of the single-layer steel plate. The insertion loss IL of the multi-layer coupled plate-type acoustic metamaterial is the difference between STL1 and STL2.

[0097] In some embodiments of the present invention, the insertion loss results obtained by the above method are as Figure 4 shown, demonstrating the effectiveness of the method of the present invention.

[0098] The present invention takes into account the STL of the composite structure of the metamaterial and the homogeneous steel plate, and more accurately simulates the coupling situation between the metamaterial and the existing structure during actual use.

[0099] The foregoing embodiments of the present invention provide an effective method for calculating the sound insulation performance of the multi-layer coupled plate-type acoustic metamaterial, which can meet the application requirements of the acoustic metamaterial and facilitate the targeted design of the sound insulation scheme.

[0100] 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 can 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 broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the insertion loss of a multi-layer coupled plate-type acoustic metamaterial, characterized in that, It includes 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 periodically distributed metamaterial layers and two fiber material layers with different densities; ②. Construct a sound transmission loss calculation model for the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate. Build a three-dimensional model based on the size of the minimum periodic unit of the metamaterial layer. The entire sound transmission loss calculation model includes perfect matching layers at both ends, an incident sound field, a transmitted sound field, a homogeneous steel plate, and a multi-layer coupled plate-type acoustic metamaterial region; ③. Use the acoustic wave equation as the input in the incident sound field; ④. Establish a mechanical equilibrium equation; ⑤. Apply periodic boundary conditions to the sound 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 surfaces of the air with the metamaterial and the homogeneous steel plate to ensure the displacement continuity and force continuity of the coupling surface: ⑦. Obtain the densities ρ of different density fiber layers respectively d , porosity φ, tortuosity factor τ, flow resistivity σ, viscous characteristic length Λ, thermal characteristic length Λ′, and static thermal permeability k′0, and use the Johnson-Champoux-Allard-Lafarge (JCA-L) acoustic model to characterize the fiber layer. Through the effective mass density ρ c and effective bulk modulus K c convert the fiber layer into an equivalent fluid domain. Through the effective mass density ρ c and effective bulk modulus K c calculate the equivalent sound speed c c , and based on the effective mass density ρ c and equivalent sound speed c c calculate the sound pressure distribution of the fiber layer; ⑧. Mesh the three-dimensional model, set the analysis frequency and frequency step size, and calculate the sound pressure \(P\) of the incident surface through finite element software. in and the transmitted sound pressure \(P\) out . Based on the sound pressure \(P\) of the incident surface in and the transmitted sound pressure \(P\) out , obtain the incident sound power \(W\) in and the transmitted sound power \(W\) out . Based on the incident sound power \(W\) in and the transmitted sound power \(W\) out , obtain the transmission coefficient, and calculate the sound transmission loss STL of the structure according to the obtained transmission coefficient. ⑨. Use the established calculation model to calculate the sound transmission loss of the composite structure of the acoustic metamaterial and the homogeneous steel plate and the sound transmission loss of the single-layer steel plate respectively. The difference between the two calculated sound transmission losses is used as the insertion loss of the acoustic metamaterial.

2. The insertion loss calculation method of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, characterized in that The metamaterial layer includes a thin film, a frame, and an additional mass. The required structural dimension parameters 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 thin film, and the thicknesses of various different materials; the required material parameters include the elastic modulus, density, and Poisson's ratio of the frame, thin film, and additional mass.

3. The insertion loss calculation method of a multi-layer coupled plate type acoustic metamaterial according to claim 1, characterized in that In step ③, the incident sound wave p in is expressed as: where k x , k y and k z are respectively the wave number components of the sound wave in each direction, i represents the imaginary unit, and x, y, and 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 c0 is the speed of sound in air.

4. The insertion loss calculation method of the 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: where is the gradient operator, ρ0 is the air density, c0 is the speed of sound in air, and p represents the sound pressure; In the solid domain, its stress distribution conforms to Newton's second law: where ρ s represents the material density, u represents the displacement vector in three directions, and σ c represents the stress tensor, the constant matrix of the material, and ε is the strain matrix.

5. The insertion loss calculation method of the multi-layer coupled plate type acoustic metamaterial according to claim 1, characterized in that In step ⑤, the Floquet periodic boundary condition means that in a structure with periodic distribution, the field values of its opposite boundary surfaces only differ by a phase to characterize the large-scale periodically distributed multi-layer coupled plate-type acoustic metamaterial.

6. The insertion loss calculation method of the multi-layer 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 outer normal of the coupling surface, a represents the acceleration vector of the structure, and F represents the pressure vector acting on the structure.

7. The insertion loss calculation method of the 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: Effective bulk modulus K c Is expressed as: where μ is the dynamic viscosity of air, γ is the specific heat ratio of air, P0 is the atmospheric pressure, β is the thermal conductivity of air, and C p is the constant-pressure heat capacity of air; through the effective mass density ρ c and the effective bulk modulus K c the equivalent sound velocity c is calculated c as follows: 。 8. The insertion loss calculation method of the multi-layer coupled plate type acoustic metamaterial according to claim 1, characterized in that, In step ⑧, the expression for the incident sound power W in and the transmitted sound power W out is Among them, 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 according to the transmission coefficient; STL = -10 log 10 t (11).

9. The insertion loss calculation method of the multi-layer coupled plate type acoustic metamaterial according to claim 1, characterized in that, In step ⑧, use hexahedral elements to divide the mesh of the three-dimensional model. 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 perfect matching layer is not less than 8 layers.

10. The insertion loss calculation method of a multi-layer coupled plate-type acoustic metamaterial according to claim 1, wherein In step ⑨, use the established calculation model to calculate the sound transmission loss STL1 of the composite structure of the multi-layer coupled plate-type acoustic metamaterial and the homogeneous steel plate and the sound transmission loss STL2 of the single-layer steel plate respectively. The insertion loss IL of the multi-layer coupled plate-type acoustic metamaterial is the difference between STL1 and STL2.

Images