Analytical method for sound insulation characteristics of thin film acoustic metamaterials

Abstract

This invention relates to the field of thin-film acoustic metamaterials, and particularly to an analytical method for the sound insulation properties of thin-film acoustic metamaterials. The method includes: establishing a physical model of the thin-film acoustic metamaterial, and using continuous transverse and torsional springs around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial; obtaining the vibration displacement of the thin-film acoustic metamaterial based on the Rayleigh-Ritz method and using Gaussian functions as basis functions; establishing an acoustic-vibration coupling model of the thin-film acoustic metamaterial under external force excitation based on the vibration displacement and Hamilton's principle; and establishing a sound insulation analysis model of the thin-film acoustic metamaterial under vertical plane wave excitation based on the acoustic-vibration coupling model and the plane wave equation. The sound insulation analysis model of this invention can accurately predict the sound insulation properties of the thin-film acoustic metamaterial under arbitrary boundary conditions such as fixed support, simply supported, and free.

Description

Technical Field

[0001] This invention relates to the field of thin-film acoustic metamaterials technology, and in particular to a method for analyzing the sound insulation properties of thin-film acoustic metamaterials. Background Technology

[0002] Thin-film acoustic metamaterials are artificially designed "subwavelength" scale materials with negative equivalent mass characteristics. Due to their light weight, small size, and strong designability, they have gradually become a research hotspot for solving noise problems.

[0003] Current theoretical research on thin-film acoustic metamaterials mostly focuses on boundary conditions such as fixed and simply supported boundaries. Since the boundary conditions of metamaterials have a significant impact on their sound insulation performance, and in practical applications of acoustic metamaterials, not only classical boundary conditions such as fixed and simply supported boundaries exist, but general elastic constraints are more consistent with actual application conditions. Therefore, it is necessary to establish a theoretical model for the unit cell structure of thin-film acoustic metamaterials under general elastic constraints to explore their sound insulation mechanism under general boundary conditions. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for analyzing the sound insulation properties of thin-film acoustic metamaterials.

[0005] This invention employs the following technical solution: a method for analyzing the sound insulation properties of thin-film acoustic metamaterials, the method comprising:

[0006] A physical model of a thin-film acoustic metamaterial is established, and continuous transverse and torsional springs are used around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial.

[0007] The vibration displacement of the thin-film acoustic metamaterial is obtained based on the Rayleigh-Ritz method and using the Gaussian function as the basis function.

[0008] Based on the vibration displacement and Hamilton's principle, an acoustic-vibration coupling model of thin-film acoustic metamaterials under external force excitation is established.

[0009] Based on the acoustic-vibration coupling model and combined with the plane wave equation, a sound insulation analysis model of thin-film acoustic metamaterials under vertical plane wave excitation is established.

[0010] An analytical method for the sound insulation properties of thin-film acoustic metamaterials according to an embodiment of the present invention is provided. This method establishes a physical model of the thin-film acoustic metamaterial, then uses continuous transverse and torsional springs to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial. Based on the Rayleigh-Ritz method and Hamilton's principle, combined with the plane wave equation, a sound insulation analysis model of the thin-film acoustic metamaterial under vertical plane wave excitation is established. The resulting sound insulation analysis model can accurately predict the sound insulation properties of the thin-film acoustic metamaterial under any boundary conditions, including fixed, simply supported, and free conditions. It is no longer limited to a single boundary condition and has strong adaptability to boundary conditions, enabling it to be used to analyze the sound insulation properties of thin-film acoustic metamaterials in practical application scenarios.

[0011] Furthermore, the steps of establishing a physical model of the thin-film acoustic metamaterial and simulating the general elastic constraint boundary conditions of the thin-film acoustic metamaterial by using continuous transverse and torsional springs around the physical model specifically include:

[0012] A physical model of a thin-film acoustic metamaterial is established, the physical model including a rectangular thin film and a rectangular mass block located at the upper center of the rectangular thin film;

[0013] A three-dimensional coordinate system is established with the center point of the lower end of the rectangular film as the origin, wherein the width, length, and thickness of the rectangular film are L, ... x L y and h m The width, length, and thickness of the rectangular mass block are l, ... x l y and h mass ;

[0014] A series of transverse and torsional springs are used around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial, and the stiffness of the b-th transverse spring is set to k. b The stiffness of the b-th torsion spring is K. b When k b →∞ and K b →∞ indicates a fixed boundary condition, when k b →0 and K b →0 indicates a free boundary condition, when k b →∞ and K b →0 indicates a simply supported boundary condition, where b∈(x0,x1,y0,y1).

[0015] Furthermore, the steps for obtaining the vibration displacement of thin-film acoustic metamaterials based on the Rayleigh-Ritz method and using Gaussian functions as basis functions specifically include:

[0016] According to the Rayleigh-Ritz method, the vibrational displacement w of the thin-film acoustic metamaterial is expressed as:

[0017]

[0018] Wherein, the vibration displacement w is the vibration displacement in the z-direction, and a i (t) represents the i-th time-dependent term in the vibration displacement, where t is the time. Let a be the i-th basis function, and a and They respectively represent elements a i (t) and Column vectors;

[0019] Will Represented as:

[0020]

[0021] in, Let represent the Kroc inner product, where α is a column vector of m basis functions along the x-direction and β is a column vector of n basis functions along the y-direction, using Gaussian functions as basis functions, i.e.:

[0022]

[0023]

[0024]

[0025]

[0026] in, Let be the i-th Gaussian function in the x-direction. Let be the i-th Gaussian function in the y-direction, where j and p are both scaling factors of the Gaussian function, and q i Let r be the translation factor of the i-th Gaussian function in the x-direction. i Let be the translation factor of the i-th Gaussian function in the y-direction, then It contains mn elements.

[0027] Furthermore, based on the dimensions of the rectangular film, the stretching factor and translation factor are defined as follows:

[0028]

[0029]

[0030] Here, ceil represents the ceil function, and floor represents the floor function.

[0031] Furthermore, the steps for establishing an acoustic-vibration coupling model of the thin-film acoustic metamaterial under external force excitation based on the vibration displacement and Hamilton's principle specifically include:

[0032] Calculate the total kinetic energy E and total potential energy Q of the thin-film acoustic metamaterial based on Hamilton's principle.

[0033] The total mass matrix of a thin-film acoustic metamaterial is defined as M based on its total kinetic energy E, and the total stiffness matrix of a thin-film acoustic metamaterial is defined as G based on its total potential energy Q.

[0034] Under external excitation, the Lagrangian function of the thin-film acoustic metamaterial is:

[0035] R = E - Q + W ext

[0036] Among them, W ext W is the work done by the external force f(t) on the thin-film acoustic metamaterial. ext The calculation formula is:

[0037]

[0038] Where F(t) is the external force f(t) with multiple degrees of freedom;

[0039] Based on the Euler-Lagrange equations, the forced vibration equations of thin-film acoustic metamaterials under external force excitation under general elastically constrained boundary conditions are obtained:

[0040]

[0041] The Euler-Lagrange equations are:

[0042]

[0043] Based on the forced vibration equation, the acoustic-vibration coupling model of the thin-film acoustic metamaterial under external force excitation is obtained:

[0044] (G-ω 2 M)a=F(t)

[0045] Where ω represents the characteristic frequency in multiple degrees of freedom, and the column vector a of the thin-film acoustic metamaterial under external force f(t) excitation is calculated according to the acoustic-vibration coupling model.

[0046] Furthermore, the specific steps for defining the total mass matrix M of a thin-film acoustic metamaterial based on its total kinetic energy E include:

[0047] Calculate the kinetic energy of the rectangular mass block and the kinetic energy of the rectangular film, respectively. The kinetic energy E of the rectangular mass block is... kmass and the kinetic energy E of the rectangular thin film km for:

[0048]

[0049]

[0050] The kinetic energy E of the rectangular mass block kmass The kinetic energy E of the rectangular thin film km The summation yields the total kinetic energy E of the thin-film acoustic metamaterial:

[0051]

[0052] Where, ρ mass Let ρ be the density of the rectangular mass block. m The density of the rectangular film;

[0053] make Where M is the total mass matrix of the thin-film acoustic metamaterial.

[0054] Furthermore, the steps for defining the total stiffness matrix G of the thin-film acoustic metamaterial based on its total potential energy Q specifically include:

[0055] Calculate the potential energy of the rectangular film, the potential energy of the rectangular mass block, and the potential energy stored in the boundary spring, which includes the transverse spring and the torsional spring.

[0056] Wherein, the potential energy Q of the rectangular thin film pm for:

[0057]

[0058] Among them, D m This represents the bending stiffness of the rectangular film. S m V represents the Young's modulus of the rectangular thin film. m This represents the Poisson's ratio of the rectangular thin film;

[0059] The potential energy Q of the rectangular mass block pmass for:

[0060]

[0061]

[0062] Among them, D mass This represents the bending stiffness of the rectangular mass block. S mass Let v represent the Young's modulus of the rectangular mass block. mass This represents the Poisson's ratio of the rectangular mass block;

[0063] The potential energy Q of the boundary spring edgs for:

[0064]

[0065]

[0066] The total potential energy Q of the thin-film acoustic metamaterial is obtained by adding the potential energy of the rectangular thin film, the potential energy of the rectangular mass block, and the potential energy of the boundary spring.

[0067]

[0068]

[0069] Among them, G pm Let G be the stiffness matrix of the rectangular thin film. pmass Let G be the stiffness matrix of the rectangular mass block. edgs Let G be the stiffness matrix of the boundary spring, and G be the total stiffness matrix of the thin-film acoustic metamaterial.

[0070] Furthermore, the steps for establishing a sound insulation analysis model of thin-film acoustic metamaterials under vertical plane wave excitation, based on the aforementioned acoustic-vibration coupling model and combined with the plane wave equation, specifically include:

[0071] A plane wave excitation with perpendicular incidence is applied to a thin-film acoustic metamaterial, and the incident sound pressure is S. in Acoustic pressure excitation S on the surface of thin-film acoustic metamaterials b The incident sound pressure S in Twice that of the plane wave excitation on the thin-film acoustic metamaterial, the work W is... p,ext for:

[0072]

[0073] Among them, F b External force under perpendicular excitation of a plane wave;

[0074] Based on W p,ext The column vector a of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained by using the aforementioned acoustic-vibration coupling model, and the vibration displacement of the surface of the thin-film acoustic metamaterial at this time is obtained.

[0075] Transmitted sound pressure S on the surface of thin-film acoustic metamaterials ts for:

[0076] S ts =ρ f c f v f

[0077] Where, ρ f Let v be the fluid density near the thin-film acoustic metamaterial, c be the sound velocity of the fluid near the thin-film acoustic metamaterial, and v be the velocity of sound in the fluid near the thin-film acoustic metamaterial. fThe amplitude of the surface vibration velocity of the thin-film acoustic metamaterial;

[0078] The average transmitted sound pressure on the surface of the thin-film acoustic metamaterial is obtained by averaging the surface vibration velocity.

[0079]

[0080] The sound pressure transmission coefficient of a thin-film acoustic metamaterial structure is defined by the ratio of the transmitted sound pressure to the incident sound pressure:

[0081]

[0082] Then, the sound insulation of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained:

[0083] TL = 20log 10 (1 / T p dB

[0084] Wherein, TL is the sound insulation analysis model. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a flowchart illustrating the analytical method for the sound insulation properties of thin-film acoustic metamaterials according to the present invention;

[0087] Figure 2 for Figure 1 A top view of the physical model of the thin-film acoustic metamaterial in step S1;

[0088] Figure 3 for Figure 1 A side view of the physical model of the thin-film acoustic metamaterial in step S1;

[0089] Figure 4 A schematic diagram of the physical model of the thin-film acoustic metamaterial used to verify this invention;

[0090] Figure 5 A schematic diagram of the acoustic-structure interaction (FEA) model of the thin-film acoustic metamaterial used to verify this invention.

[0091] Figure 6 A schematic diagram of a thin-film acoustic metamaterial structure with the same area used for verification of this invention;

[0092] Figure 7 Simulation results of sound insulation curves for square and circular thin-film acoustic metamaterials with the same area when verifying this invention;

[0093] Figure 8 A schematic diagram of the four-sensor standing wave tube test system built for the verification of this invention;

[0094] Figure 9 A schematic diagram of the experimental testing platform built for verifying this invention;

[0095] Figure 10 (a) is a schematic diagram of a thin-film acoustic metamaterial test specimen during the verification of this invention;

[0096] Figure 10 (b) is a schematic diagram of the installation of the thin-film acoustic metamaterial during the verification of the present invention;

[0097] Figure 11 Simulation diagram showing the impact of the scaling factor on the sound insulation prediction of the analytical sound insulation model;

[0098] Figure 12 A comparison chart of the sound insulation curves of the FEA method, the standing wave tube test method, and the thin-film acoustic metamaterials obtained by the present invention;

[0099] Figure 13 (a) Comparison of the sound insulation curves of the thin-film acoustic metamaterial obtained by the FEA method and the present invention when the boundary is a simple boundary;

[0100] Figure 13 (b) Comparison of the sound insulation curves of the FEA method and the thin-film acoustic metamaterials obtained by the present invention when the boundary is free. Detailed Implementation

[0101] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0102] In the description of the embodiments of the present invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0103] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0104] In the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of the present invention according to the specific circumstances.

[0105] Reference Figures 1 to 3 According to one embodiment of the present invention, a method for analyzing the sound insulation properties of thin-film acoustic metamaterials includes:

[0106] S1: Establish a physical model of the thin-film acoustic metamaterial, and use continuous transverse springs and torsional springs around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial.

[0107] Furthermore, the steps of establishing a physical model of the thin-film acoustic metamaterial and simulating the general elastic constraint boundary conditions of the thin-film acoustic metamaterial by using continuous transverse and torsional springs around the physical model specifically include:

[0108] A physical model of a thin-film acoustic metamaterial is established, which includes a rectangular thin film and a rectangular mass block located at the center of the upper end of the rectangular thin film.

[0109] A three-dimensional coordinate system is established with the center point of the lower end of the rectangular film as the origin, where the width, length, and thickness of the rectangular film are L, ... x L y and h m The width, length, and thickness of the rectangular mass block are l, ... x l y and h mass ;

[0110] A series of transverse and torsional springs are used around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial, and the stiffness of the b-th transverse spring is set to k. b The stiffness of the b-th torsion spring is K. b When k b →∞ and Kb →∞ indicates a fixed boundary condition, when k b →0 and K b →0 indicates a free boundary condition, when k b →∞ and K b →0 indicates a simply supported boundary condition, where b∈(x0,x1,y0,y1).

[0111] S2: The vibration displacement of the thin-film acoustic metamaterial is obtained based on the Rayleigh-Ritz method and using the Gaussian function as the basis function; In this embodiment, the Rayleigh-Ritz method is well known to those skilled in the art, so it will not be described in detail here;

[0112] Furthermore, the steps for obtaining the vibration displacement of thin-film acoustic metamaterials based on the Rayleigh-Ritz method and using Gaussian functions as basis functions specifically include:

[0113] According to the Rayleigh-Ritz method, the vibrational displacement w of the thin-film acoustic metamaterial is expressed as:

[0114]

[0115] Wherein, the vibration displacement w is the vibration displacement in the z-direction, and a i (t) represents the i-th time-dependent term in the vibration displacement, where t is the time. Let a be the i-th basis function, and a and They respectively represent elements a i (t) and Column vectors;

[0116] Will Represented as:

[0117]

[0118] in, Let represent the Kroc inner product, where α is a column vector of m basis functions along the x-direction and β is a column vector of n basis functions along the y-direction, using Gaussian functions as basis functions, i.e.:

[0119]

[0120]

[0121]

[0122]

[0123] in, Let be the i-th Gaussian function in the x-direction. Let be the i-th Gaussian function in the y-direction, where j and p are both scaling factors of the Gaussian function, and qi Let r be the translation factor of the i-th Gaussian function in the x-direction. i Let be the translation factor of the i-th Gaussian function in the y-direction, then It contains mn elements.

[0124] Furthermore, based on the dimensions of the rectangular thin film, the stretching factor and translation factor are defined as follows:

[0125]

[0126]

[0127] Here, ceil represents the ceil function, and floor represents the floor function.

[0128] S3: Based on vibration displacement and Hamilton's principle, establish an acoustic-vibration coupling model of thin-film acoustic metamaterials under external force excitation; in this embodiment, Hamilton's principle is well known to those skilled in the art, so it will not be described in detail here.

[0129] Furthermore, the specific steps for establishing an acoustic-vibration coupling model of thin-film acoustic metamaterials under external force excitation based on vibration displacement and Hamilton's principle include:

[0130] Calculate the total kinetic energy E and total potential energy Q of the thin-film acoustic metamaterial based on Hamilton's principle.

[0131] The total mass matrix of a thin-film acoustic metamaterial is defined as M based on its total kinetic energy E, and the total stiffness matrix of a thin-film acoustic metamaterial is defined as G based on its total potential energy Q.

[0132] Under external excitation, the Lagrangian function of the thin-film acoustic metamaterial is:

[0133] R = E - Q + W ext

[0134] Among them, W ext W is the work done by the external force f(t) on the thin-film acoustic metamaterial. ext The calculation formula is:

[0135]

[0136] Where F(t) is the external force f(t) with multiple degrees of freedom;

[0137] Based on the Euler-Lagrange equations, the forced vibration equations of thin-film acoustic metamaterials under external force excitation under general elastically constrained boundary conditions are obtained:

[0138]

[0139] The Euler-Lagrange equations are:

[0140]

[0141] Based on the forced vibration equation, the acoustic-vibration coupling model of the thin-film acoustic metamaterial under external force excitation is obtained:

[0142] (G-ω 2 M)a=F(t)

[0143] Where ω represents the characteristic frequency in multiple degrees of freedom, and the column vector a of the thin-film acoustic metamaterial under external force f(t) excitation is calculated according to the acoustic-vibration coupling model.

[0144] Furthermore, the specific steps for defining the total mass matrix M of a thin-film acoustic metamaterial based on its total kinetic energy E include:

[0145] Calculate the kinetic energy of the rectangular mass block and the rectangular thin film respectively. The kinetic energy E of the rectangular mass block is... kmass and the kinetic energy E of the rectangular thin film km for:

[0146]

[0147]

[0148] The kinetic energy E of the rectangular mass block kmass With the kinetic energy E of the rectangular thin film km The summation yields the total kinetic energy E of the thin-film acoustic metamaterial:

[0149]

[0150] Where, ρ mass Let ρ be the density of the rectangular mass block. m The density of the rectangular thin film;

[0151] make Where M is the total mass matrix of the thin-film acoustic metamaterial.

[0152] Furthermore, the steps for defining the total stiffness matrix G of the thin-film acoustic metamaterial based on its total potential energy Q specifically include:

[0153] Calculate the potential energy of the rectangular thin film, the potential energy of the rectangular mass block, and the potential energy stored in the boundary springs, which include transverse springs and torsional springs.

[0154] Among them, the potential energy Q of the rectangular thin film pm for:

[0155]

[0156] Among them, D m This represents the bending stiffness of a rectangular thin film. S m V represents the Young's modulus of a rectangular thin film. m The Poisson's ratio represents that of a rectangular thin film.

[0157] The potential energy Q of the rectangular mass block pmass for:

[0158]

[0159] Among them, D mass This represents the bending stiffness of the rectangular mass block. S mass Let v represent the Young's modulus of the rectangular mass block. mass This represents the Poisson's ratio of the rectangular mass block.

[0160] The potential energy Q of the boundary spring edgs for:

[0161]

[0162]

[0163] The total potential energy Q of the thin-film acoustic metamaterial is obtained by adding the potential energy of the rectangular thin film, the potential energy of the rectangular mass block, and the potential energy of the boundary spring.

[0164]

[0165]

[0166] Among them, G pm G is the stiffness matrix of the rectangular thin film. pmass Let G be the stiffness matrix of the rectangular mass block. edgs Let G be the stiffness matrix of the boundary spring, and G be the overall stiffness matrix of the thin-film acoustic metamaterial.

[0167] S4: Based on the acoustic-vibration coupling model and combined with the plane wave equation, establish a sound insulation analysis model for thin-film acoustic metamaterials under vertical plane wave excitation;

[0168] Furthermore, based on the acoustic-vibration coupling model and combined with the plane wave equation, the specific steps for establishing a sound insulation analysis model of thin-film acoustic metamaterials under vertical plane wave excitation include:

[0169] A plane wave excitation with perpendicular incidence is applied to a thin-film acoustic metamaterial, and the incident sound pressure is S. in Acoustic pressure excitation S on the surface of thin-film acoustic metamaterials b The incident sound pressure S in Twice that of the plane wave excitation on the thin-film acoustic metamaterial, the work W is...p,ext for:

[0170]

[0171] Among them, F b External force under perpendicular excitation of a plane wave;

[0172] Based on W p,ext The column vector a of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained by using the acoustic-vibration coupling model, and the vibration displacement of the surface of the thin-film acoustic metamaterial at this time is obtained.

[0173] Transmitted sound pressure S on the surface of thin-film acoustic metamaterials ts for:

[0174] S ts =ρ f c f v f

[0175] Where, ρ f Let v be the fluid density near the thin-film acoustic metamaterial, c be the sound velocity of the fluid near the thin-film acoustic metamaterial, and v be the velocity of sound in the fluid near the thin-film acoustic metamaterial. f The amplitude of the surface vibration velocity of the thin-film acoustic metamaterial;

[0176] The average transmitted sound pressure on the surface of the thin-film acoustic metamaterial is obtained by averaging the surface vibration velocity.

[0177]

[0178] The sound pressure transmission coefficient of a thin-film acoustic metamaterial structure is defined by the ratio of the transmitted sound pressure to the incident sound pressure:

[0179]

[0180] Then, the sound insulation of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained:

[0181] TL = 20log 10 (1 / T p dB

[0182] Wherein, TL is the sound insulation analysis model.

[0183] Reference Figures 4 to 13 A square HDPE film and a square aluminum block are selected to form a composition as follows: Figure 4 The thin-film acoustic metamaterial structure shown was used to study and verify the sound insulation analysis model:

[0184] The specific structural parameters of the thin-film acoustic metamaterial are shown in Table 1, and the material parameters are shown in Table 2.

[0185] Table 1 Structural parameters of thin-film acoustic metamaterials

[0186] Film side length L 26 <![CDATA[Thin film thickness h m > 0.3 Mass block side length l 8 <![CDATA[Mass block thickness h mass > 2

[0187] Table 2 Material parameters of components of thin-film acoustic metamaterials

[0188] film HDPE 960 0.1 0.36 mass block aluminum 2700 70 0.33

[0189] Establishing such a commercial acoustic software COMSOL Figure 5 The acoustic-structure coupling model shown includes a thin-film acoustic metamaterial and two acoustic cavities, one on the left and one on the right.

[0190] The two acoustic cavities in the model are 26mm×26mm×50mm in size and are given the properties of air material. The end faces of the two acoustic cavities are set as plane wave radiation boundary conditions, with one end set as an incident pressure field with an amplitude of 1Pa and the other boundary set as hard acoustic field boundaries. The solution frequency range is selected as 100Hz-1600Hz, the step size is 10Hz, and the mesh size is 0.45mm. The sound insulation curves of the thin film acoustic metamaterial under different boundary conditions are obtained by setting the constraints around the unit cell of the thin film acoustic metamaterial as fixed, simply supported, or free.

[0191] To facilitate subsequent experimental verification based on standing wave tubes, and due to limitations in experimental conditions, only circular acoustic metamaterials can be tested. Therefore, it is necessary to investigate the difference in sound insulation properties between square and circular thin-film acoustic metamaterials under fixed-boundary conditions. To match the diameter of the standing wave tube (d = 29 mm), FEA models of circular and square thin-film acoustic metamaterials with equal area are established, such as... Figure 6 As shown, the sound insulation curves of the two are obtained by solving the problem. Figure 7 As shown.

[0192] Depend on Figure 7 It can be seen that the simulation results of the sound insulation curves of square and circular thin-film acoustic metamaterials with the same area are very similar. This is because both have the same film area and the same regular symmetrical structure, resulting in similar vibration characteristics and thus similar sound insulation curves. To further verify the design using a standing wave tube, a circular acoustic metamaterial sample was used to verify the established analytical model for the sound insulation of the square thin-film acoustic metamaterial. An experimental test platform was built based on a four-sensor standing wave tube, and the accuracy of the analytical model under fixed-boundary conditions was verified from the perspective of the sound insulation curve using the standing wave tube test method. A schematic diagram of the test platform is shown below. Figure 8 As shown.

[0193] Based on the above schematic diagram, the following can be constructed: Figure 9The experimental platform shown has a specimen diameter of 29 mm. The thin-film acoustic metamaterial consists of a 0.3 mm thick HDPE film, and the central mass block is an 8 mm × 8 mm × 2 mm aluminum block. The film and the mass block are bonded together with 402 glue. The actual experimental specimen is shown below. Figure 10 As shown in (a), the sample is mounted on the standing wave tube, and the fixed boundary is achieved by clamping the source tube and the receiver tube. The mounting method is as follows: Figure 10 As shown in (b).

[0194] The fixed boundary of the theoretical model can be set to k b &K b =10 12 To simulate this, the choice of scaling factors j and p affects the solution accuracy of the model. Therefore, it is necessary to analyze the convergence of the scaling factors. According to the definition of the scaling factor, the minimum value of j and p is 9. Substituting j = p = 9, 10, and 11 into the sound insulation analysis model, we obtain the sound insulation curves under the three schemes as follows: Figure 11 As shown.

[0195] Depend on Figure 11 It can be seen that as the scaling factor increases, the predicted sound insulation curves differ, but the overall trend is consistent. Furthermore, when the scaling factor increases from 10 to 11, the sound insulation curve remains essentially unchanged, especially at the sound insulation peak, where the two curves are highly consistent. However, when j = p = 9, 10, and 11, the calculation time for the sound insulation analysis model is 50.3 min, 89.6 min, and 310.5 min, respectively; therefore, the subsequent sound insulation analysis model will use the j = p = 10 scheme.

[0196] First, the accuracy of the sound insulation analysis model is verified from the perspective of the sound insulation curve, and the comparison results are as follows: Figure 12 As shown, the results indicate that the overall trends of the sound insulation curves of the thin-film acoustic metamaterials obtained by the three methods are highly consistent. The thin-film acoustic metamaterials produce a distinct sound insulation peak and two sound insulation valleys in the calculated frequency band. The established sound insulation analysis model can predict the sound insulation curve of the thin-film acoustic metamaterials relatively accurately.

[0197] To ensure the applicability of the sound insulation analysis model under general boundary conditions, this invention also verifies the accuracy of the sound insulation analysis model using two classic boundary conditions: simply supported and free. Verification is performed by analyzing the sound insulation curves using the FEA method. Specifically, the boundary conditions of the FEA model are changed to simply supported or free boundaries and solved in COMSOL. The simply supported boundary in the sound insulation analysis model can be set as k... b =10 12 ,K b =0 can be used to simulate, while the free boundary can be represented by k. b &K b=0 to simulate, and the scaling factor is selected according to the scheme of j=p=10. The sound insulation curves of simply supported boundary and free boundary obtained by the FEA method and the analytical method of the sound insulation analysis model of this invention are as follows. Figure 13 (a) and such Figure 13 As shown in (b).

[0198] Depend on Figure 12 It can be seen that the sound insulation prediction values ​​of thin-film acoustic metamaterials obtained by the two methods under simply supported and free boundary conditions differ at the sound insulation peaks and valleys, but the differences are not significant, and the two are highly consistent in the overall sound insulation trend.

[0199] In summary, the analytical method for the sound insulation characteristics of thin-film acoustic metamaterials according to an embodiment of the present invention establishes a physical model of the thin-film acoustic metamaterial, then uses continuous transverse and torsional springs to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial, and then, based on the Rayleigh-Ritz method and Hamilton's principle, combined with the plane wave equation, establishes a sound insulation analysis model of the thin-film acoustic metamaterial under vertical plane wave excitation. The obtained sound insulation analysis model can accurately predict the sound insulation characteristics of the thin-film acoustic metamaterial under any boundary conditions such as fixed support, simply supported, and free, and is no longer limited to a single boundary condition. It has strong boundary condition adaptability and can be used to analyze the sound insulation characteristics of thin-film acoustic metamaterials in practical application scenarios.

[0200] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0201] Without causing conflict, those skilled in the art can freely combine and use the above-mentioned additional technical features.

[0202] 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 within the protection scope of the present invention.

Claims

1. An analytical method for the sound insulation properties of thin film acoustic metamaterials, characterized by, The method includes: A physical model of a thin-film acoustic metamaterial is established, and continuous transverse and torsional springs are used around the physical model to simulate the general elastic constraint boundary conditions of the thin-film acoustic metamaterial. The vibration displacement of the thin-film acoustic metamaterial is obtained based on the Rayleigh-Ritz method and using the Gaussian function as the basis function. Based on the vibration displacement and Hamilton's principle, an acoustic-vibration coupling model of thin-film acoustic metamaterials under external force excitation is established. Based on the acoustic-vibration coupling model and combined with the plane wave equation, a sound insulation analysis model of thin-film acoustic metamaterials under vertical plane wave excitation is established. The steps of establishing a physical model of a thin-film acoustic metamaterial and simulating the general elastic constraint boundary conditions of the thin-film acoustic metamaterial by using continuous transverse and torsional springs around the physical model specifically include: A physical model of a thin-film acoustic metamaterial is established, the physical model including a rectangular thin film and a rectangular mass block located at the upper center of the rectangular thin film; A three-dimensional coordinate system is established with the center point of the lower end of the rectangular film as the origin, wherein the width, length, and thickness of the rectangular film are respectively... , and The width, length, and thickness of the rectangular mass block are respectively... , and ; Continuous transverse and torsional springs are used around the physical model to simulate the general elastic constraint boundary conditions of thin-film acoustic metamaterials, and the first... The stiffness of the aforementioned transverse spring is , No. The stiffness of the aforementioned torsion spring is ,when and When represents the fixed-support boundary condition, when and When represents the free boundary condition, when and When represents a simply supported boundary condition, where ; The specific steps for obtaining the vibration displacement of thin-film acoustic metamaterials based on the Rayleigh-Ritz method and using Gaussian functions as basis functions include: According to the Rayleigh-Ritz method, the vibration displacement of thin-film acoustic metamaterials is... Represented as: Among them, vibration displacement The vibration displacement is in the z-direction. The time-dependent displacement in the vibration item, For time, For the first basis functions and They respectively represent elements and Column vectors; will be described below. is represented by: wherein denotes the Krohn inner product, is a column vector consisting of m basis functions in the direction, is a column vector consisting of n basis functions in the direction, using Gaussian functions as basis functions, i.e. in, Let be the i-th Gaussian function in the x-direction. Let be the i-th Gaussian function in the y-direction. and All are scaling factors of the Gaussian function. Let be the translation factor of the i-th Gaussian function in the x-direction. Let be the translation factor of the i-th Gaussian function in the y-direction, then It contains mn elements; The specific steps for establishing an acoustic-vibration coupling model of thin-film acoustic metamaterials under external force excitation based on the vibration displacement and Hamiltonian principle include: Calculate the total kinetic energy of thin-film acoustic metamaterials based on Hamilton's principle. and total potential energy ; Total kinetic energy based on thin-film acoustic metamaterials Define the total mass matrix of thin-film acoustic metamaterials as follows: Total potential energy based on thin-film acoustic metamaterials Define the overall stiffness matrix of the thin-film acoustic metamaterial as follows: ; Under external excitation, the Lagrangian function of the thin-film acoustic metamaterial is: in, external force Work done on thin-film acoustic metamaterials. The calculation formula is: wherein external force ; Based on the Euler-Lagrange equations, the forced vibration equations of thin-film acoustic metamaterials under external force excitation under general elastically constrained boundary conditions are obtained: The Euler-Lagrange equations are: Based on the forced vibration equation, the acoustic-vibration coupling model of the thin-film acoustic metamaterial under external force excitation is obtained: in, This represents the characteristic frequency in multiple degrees of freedom, and the acoustic-vibration coupling model is used to calculate the effect of external force on the thin-film acoustic metamaterial. Column vectors under excitation ; Based on the aforementioned acoustic-vibration coupling model and combined with the plane wave equation, the specific steps for establishing a sound insulation analysis model of thin-film acoustic metamaterials under vertical plane wave excitation include: A plane wave excitation with perpendicular incidence is applied to a thin-film acoustic metamaterial, and the incident sound pressure is assumed to be... Acoustic pressure excitation on the surface of thin-film acoustic metamaterials Incident sound pressure Twice that, the work done by plane wave excitation on the thin-film acoustic metamaterial. for: in, External force under perpendicular excitation of a plane wave; based on The column vector of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained by solving the aforementioned acoustic-vibration coupling model. And obtain the vibration displacement of the surface of the thin-film acoustic metamaterial at this time; Transmission acoustic pressure of a thin film acoustic metamaterial surface is: wherein, is the fluid density near the thin film acoustic metamaterial, is the fluid sound speed near the thin film acoustic metamaterial, is the surface vibration velocity amplitude of the thin film acoustic metamaterial; averaging the surface vibration velocity of the thin film acoustic metamaterial to obtain the average transmitted sound pressure of the surface of the thin film acoustic metamaterial : The sound pressure transmission coefficient of a thin-film acoustic metamaterial structure is defined by the ratio of the transmitted sound pressure to the incident sound pressure: Then, the sound insulation of the thin-film acoustic metamaterial under perpendicular plane wave excitation is obtained: wherein is the sound insulation analysis model.

2. The method for analyzing the sound insulation properties of thin-film acoustic metamaterials according to claim 1, characterized in that, Based on the dimensions of the rectangular film, the stretching factor and translation factor are defined as follows: wherein represents function, represents function.

3. The method for analyzing the sound insulation properties of thin-film acoustic metamaterials according to claim 1, characterized in that, Total kinetic energy based on thin-film acoustic metamaterials Define the total mass matrix of thin-film acoustic metamaterials as follows: The specific steps include: Calculate the kinetic energy of the rectangular mass block and the kinetic energy of the rectangular film, respectively. and the kinetic energy of the rectangular thin film for: The kinetic energy of the rectangular mass block Kinetic energy of the rectangular thin film The summation yields the total kinetic energy of the thin-film acoustic metamaterial. : wherein, is the density of the rectangular mass, is the density of the rectangular thin film; Let where, is the total mass matrix of the thin film acoustic metamaterial.

4. The method of claim 1, wherein, Total potential energy based on thin-film acoustic metamaterials Define the overall stiffness matrix of the thin-film acoustic metamaterial as follows: The specific steps include: Calculate the potential energy of the rectangular film, the potential energy of the rectangular mass block, and the potential energy stored in the boundary spring, which includes the transverse spring and the torsional spring. Among them, the potential energy of the rectangular thin film for: in, This represents the bending stiffness of the rectangular film. , This represents the Young's modulus of the rectangular film. This represents the Poisson's ratio of the rectangular thin film; The potential energy of the rectangular mass is: = in, This represents the bending stiffness of the rectangular mass block. , This represents the Young's modulus of the rectangular mass block. This represents the Poisson's ratio of the rectangular mass block; The potential energy of the boundary spring is: The total potential energy of the thin-film acoustic metamaterial is obtained by adding the potential energy of the rectangular film, the potential energy of the rectangular mass block, and the potential energy of the boundary spring. : ； in, Let be the stiffness matrix of the rectangular thin film. Let be the stiffness matrix of the rectangular mass block. Here is the stiffness matrix of the boundary spring. represents the overall stiffness matrix of the thin-film acoustic metamaterial.

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