A method and system for obtaining acoustic properties of multi-layer composite structure rubber

Abstract

The present invention provides a method and system for obtaining the acoustic performance of a multi-layer composite structure rubber, which belongs to the field of underwater sound absorbing materials. The method first measures the physical parameters of each layer of rubber in the multi-layer composite structure rubber, then uses the physical parameters to obtain the basic acoustic parameters at a set frequency point, and finally uses the basic acoustic parameters and a transfer matrix to obtain the acoustic performance parameters of the multi-layer composite structure rubber at the set frequency point; the acoustic performance parameters include: sound pressure reflection coefficient, sound pressure transmission coefficient, and sound absorption coefficient. The present invention improves the accuracy of obtaining the sound absorption coefficient, and is suitable for different sound wave incident conditions and different transmission media.

Description

Technical Field

[0001] The invention belongs to the field of underwater sound absorbing materials, and in particular relates to a method and a system for obtaining the acoustic performance of multi-layer composite structure rubber. Background Art

[0002] Because rubber materials have good viscoelasticity, when sound waves act on them, the stress-strain hysteresis behavior of the rubber polymer chain segments can consume the energy of the sound waves. And because the acoustic impedance of rubber is similar to that of water, it is not easy for sound waves to produce strong reflection when they are shot from water to rubber. Therefore, rubber is widely used in the field of underwater sound absorbing materials.

[0003] In order to enhance the sound absorption performance of underwater sound absorbing materials, a periodically arranged cavity structure is usually provided inside the material. Although such a structure greatly enhances its sound absorption performance at low frequencies, as the water depth increases, the water pressure causes the cavity structure to deform and the sound absorption performance will be seriously reduced.

[0004] Uniform rubber materials can be approximately regarded as volume incompressible materials, so they have good pressure resistance. However, when the material thickness is limited, the sound absorption performance of uniform rubber materials is severely limited. Multilayer composite structure rubber produces an acoustic impedance gradient by adjusting the gradient distribution of the dynamic modulus of each layer of material, so that the energy of the sound wave incident into it is gradually consumed. This is a means to improve the sound absorption performance of rubber materials without setting a cavity structure.

[0005] The transfer matrix method in multilayer media is a common research method for studying the sound absorption mechanism of multilayer composite structures. Most of the current research uses the classical transfer matrix, as shown in the following formula, which uses the interface sound pressure P and the particle normal vibration velocity u as the transfer parameters between the layered interfaces, where k is the medium wave number, l is the medium thickness, and c is the medium sound velocity.

[0006]

[0007] However, the classical transfer matrix has the following shortcomings:

[0008] 1. It does not have the function of calculating the sound pressure transmission coefficient;

[0009] 2. It can only calculate the condition where the sound wave enters the material vertically, but cannot calculate the condition where the sound wave enters the material obliquely;

[0010] 3. The dynamic modulus of rubber acoustic materials is not considered: the classical transfer matrix assumes that the modulus of the material does not change with the frequency of the sound wave, which is inconsistent with the test data. It regards the modulus of the material as a fixed value and obtains the acoustic performance parameters at all frequencies with only one calculation, resulting in poor simulation results.

[0011] 4. When the transmission surface of the rubber is two different media, air and water, the solution formula is different, and the operation of working condition conversion is very complicated.

[0012] In summary, the accuracy of the sound absorption coefficient obtained by the existing method is not high and it cannot be applied to different sound wave incident conditions. Therefore, it is urgent to study a method that can obtain the acoustic properties of multi-layer composite structural rubber in order to overcome the above shortcomings. Summary of the invention

[0013] The purpose of the present invention is to solve the above-mentioned problems existing in the prior art, to provide a method and system for obtaining the acoustic properties of multi-layer composite structural rubber, to improve the accuracy of the average relative error of the sound absorption coefficient, and to be applicable to different sound wave incident conditions and different transmission surface media.

[0014] The present invention is achieved through the following technical solutions:

[0015] In a first aspect of the present invention, a method for obtaining acoustic properties of a multi-layer composite structure rubber is provided, wherein the method first measures the physical parameters of each layer of rubber in the multi-layer composite structure rubber, then obtains basic acoustic parameters at a set frequency point using the physical parameters, and finally obtains acoustic performance parameters of the multi-layer composite structure rubber at the set frequency point using the basic acoustic parameters and a transfer matrix;

[0016] The acoustic performance parameters include: sound pressure reflection coefficient, sound pressure transmission coefficient, and sound absorption coefficient.

[0017] A further improvement of the present invention is:

[0018] The multi-layer composite structure rubber comprises n layers of rubber, which are the first layer, the second layer, and the nth layer from bottom to top;

[0019] The incident medium above the nth layer of rubber and the transmission medium below the first layer of rubber are both fluids;

[0020] The incident medium is the n+1th layer, and the transmission medium is the 0th layer.

[0021] A further improvement of the present invention is:

[0022] The method comprises:

[0023] (1) Measuring the dynamic modulus, density ρ and thickness d of each layer of rubber in the multi-layer composite structure rubber, setting the frequency point f, the incident angle of the sound wave, and the transmission medium; the dynamic modulus includes: storage modulus E′ and loss factor tanδ;

[0024] (2) Obtain the basic acoustic parameters of each layer of rubber: longitudinal wave velocity V p , shear wave velocity V s, longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ;

[0025] (3) Obtaining the longitudinal wave and transverse wave incident angles of each layer of rubber, as well as the wave numbers of the longitudinal wave and transverse wave in the x-direction and z-direction;

[0026] (4) obtaining the transfer matrix of each layer of rubber, and obtaining the total matrix using the transfer matrix of each layer of rubber;

[0027] (5) Use the total matrix to obtain the sound pressure reflection coefficient, sound pressure transmission coefficient and sound absorption coefficient.

[0028] Preferably, the operation in step (2) includes:

[0029] The basic acoustic parameters of each layer of rubber are calculated using the following formula:

[0030]

[0031]

[0032] μ=ρV s 2 ,

[0033] Where v is Poisson's ratio, using a typical value for rubber, and j is an imaginary unit.

[0034] Preferably, the operation of step (3) includes:

[0035] The longitudinal wave incident angle θ of each layer of rubber is calculated using the following formula: i With the shear wave incident angle γ i , and the wave number k of the longitudinal wave in the x and z directions vpx , k vpz , the wave number k of the shear wave in the z direction vsz :

[0036]

[0037]

[0038] k vpz =k vp cosθ i , k vsz =k vs cosγ i , k vpx =k vp sinθ i

[0039] Here, i represents the i-th layer of medium.

[0040] Preferably, the operation of step (4) includes:

[0041] For each layer of rubber, the matrix I of the upper interface of the layer of rubber is calculated using the following formula: upi :

[0042]

[0043] in z up is the z-axis coordinate of the interface on the layer of medium;

[0044] The matrix I of the lower interface of the rubber layer is calculated using the following formula: downi :

[0045]

[0046] in z down is the z-axis coordinate of the lower interface of the rubber layer;

[0047] The transfer matrix M of the rubber layer is calculated using the following formula: n :

[0048] M i =I upi / I downi , i=1,2......n;

[0049] The total matrix F is calculated using the following formula:

[0050] F=M n *M n-1 *…*M1,F are 4×4 matrices.

[0051] Preferably, the operation of step (5) includes:

[0052] The sound pressure reflection coefficient R is calculated using the following formula:

[0053]

[0054] The sound pressure transmission coefficient T is calculated using the following formula:

[0055]

[0056] The sound absorption coefficient αl is calculated using the following formula:

[0057] αl=1-R 2 -T 2

[0058] Among them, Z n+1is the characteristic impedance of the incident medium, and Z0 is the characteristic impedance of the transmission medium, which can be calculated using the following formula:

[0059] Z0=ρ0V p0 / cosθ0

[0060] Among them, C rc =F rc -F 4c *F r1 / F 41 , F rc Represents the element in the rth row and cth column of the total matrix F.

[0061] A further improvement of the present invention is:

[0062] Setting multiple frequency points, performing the operations from step (1) to step (5) at each frequency point in turn, obtaining the acoustic performance parameters at each frequency point, and storing the acoustic performance parameters at all frequency points;

[0063] Then, a reflection coefficient graph is plotted with frequency as the horizontal axis and reflection coefficient as the vertical axis; a transmission coefficient graph is plotted with frequency as the horizontal axis and transmission coefficient as the vertical axis; and a sound absorption coefficient graph is plotted with frequency as the horizontal axis and sound absorption coefficient as the vertical axis.

[0064] A second aspect of the present invention provides a system for obtaining acoustic properties of a multi-layer composite structural rubber, the system comprising:

[0065] Collection unit: used to collect the dynamic modulus, density ρ and thickness d of each layer of rubber in the multi-layer composite structure rubber, set the frequency point f, the incident angle of the sound wave, and the transmission medium; the dynamic modulus includes: storage modulus E′ and loss factor tanδ;

[0066] Parameter calculation unit: connected to the acquisition unit, used to obtain the basic acoustic parameters of each layer of rubber: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ; obtain the incident angles of longitudinal and transverse waves of each layer of rubber, as well as the wave numbers of longitudinal and transverse waves in the x and z directions;

[0067] Matrix calculation unit: connected with the parameter calculation unit, used to obtain the transfer matrix of each layer of rubber, and obtain the total matrix using the transfer matrix of each layer of rubber;

[0068] Acoustic performance parameter acquisition unit: connected to the matrix calculation unit, used to obtain the sound pressure reflection coefficient, sound pressure transmission coefficient and sound absorption coefficient using the total matrix.

[0069] Compared with the prior art, the beneficial effects of the present invention are: the accuracy of obtaining the sound absorption coefficient is improved by utilizing the present invention, and the present invention is applicable to different sound wave incident conditions and different transmission media. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the transfer matrix model.

[0071] Figure 2 Schematic diagram of the method of the present invention.

[0072] Figure 3 Flow chart of the method of the present invention.

[0073] FIG. 4( a ) is a graph showing the dynamic modulus of the double-layer structure rubber (styrene-butadiene rubber without carbon black) measured in the embodiment.

[0074] FIG4( b ) is the dynamic modulus of the double-layer structure rubber (containing 30 parts of carbon black styrene-butadiene rubber) measured in the example.

[0075] FIG. 5( a ) is a comparison between the sound pressure reflection coefficient calculated by the acoustic performance model of the double-layer structure rubber and the measured value in the embodiment.

[0076] FIG. 5( b ) is a comparison between the sound pressure transmission coefficient calculated by the acoustic performance model of the double-layer structure rubber in the embodiment and the measured value.

[0077] FIG. 5( c ) is a comparison between the sound absorption coefficient calculated by the acoustic performance model of the double-layer structure rubber and the measured value in the embodiment. DETAILED DESCRIPTION

[0078] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0079] When a sound wave of a certain frequency is directed toward a material, the sound wave energy is converted into the following three parts:

[0080] (1) Sound waves are reflected, and part of their energy is converted into the energy of the reflected sound waves. The strength of a material's ability to reflect sound waves is expressed by the sound pressure reflection coefficient R.

[0081] (2) When sound waves are transmitted, part of their energy is converted into the energy of the transmitted sound waves. The strength of a material's ability to transmit sound waves is expressed by the sound pressure transmission coefficient T.

[0082] (3) Energy absorbed by the material. The strength of the material's ability to absorb sound waves is represented by the sound absorption coefficient al, which is calculated using the sound pressure reflection coefficient and the sound pressure transmission coefficient: al = 1-R 2 -T 2 .

[0083] In order to obtain the acoustic properties of a certain material, it is necessary to obtain the sound absorption coefficient of the material to sound waves at different frequencies. When actually measuring the sound absorption coefficient of a material, the sound absorption coefficient is also obtained indirectly by obtaining the sound pressure reflection coefficient and the sound pressure transmission coefficient.

[0084] Generally, sound pressure is used to measure the size of sound waves. In the present invention, the reflected sound pressure p is calculated. r and the incident sound pressure p i The ratio of the sound pressure reflection coefficient R is obtained, and then the transmitted sound pressure p is calculated. t and the incident sound pressure p i The ratio of the sound pressure transmission coefficient T is obtained, and finally the formula al = 1-R 2 -T 2 Get the sound absorption coefficient al.

[0085] Specifically, the present invention first measures the physical parameters of each layer of rubber in the multi-layer composite structure rubber (including dynamic modulus (i.e., the storage modulus and loss factor of the material change with the sound wave frequency)), then uses the physical parameters to obtain the basic acoustic parameters at the set frequency point, and uses the transfer matrix and the basic acoustic parameters to calculate the acoustic performance parameters of the multi-layer composite structure rubber at the set frequency point, and stores the acoustic performance parameters at the frequency point. The acoustic performance parameters include: sound pressure reflection coefficient, sound pressure transmission coefficient, and sound absorption coefficient.

[0086] In order to solve the problems existing in the existing transfer matrix method, in order to better guide the design of underwater sound absorbing materials. The present invention proposes a transfer matrix equation that uses particle velocity V and particle stress σ as the transfer parameters between interfaces, and decomposes the above two transfer parameters into two vectors of normal and tangential directions. Through the above transfer matrix equation, it is derived that the sound pressure reflection coefficient, sound pressure transmission coefficient and sound absorption coefficient of sound waves can be calculated, and the working conditions of oblique incidence of sound waves can be calculated, and the solution formula is unified, so that the acoustic performance of multi-layer composite structure rubber can be obtained.

[0087] The transfer matrix formula of the present invention is as follows, where V xn ,V zn are the vibration velocities of the particle in the x and z directions, σ zn ,σ xn are the stresses of the particle in the x and z directions, T n is the transfer matrix.

[0088]

[0089] The derivation process of the above formula is as follows Figure 2 As shown, the details are as follows:

[0090] (1) Assumptions for model establishment

[0091] Since the coupling between fluid flow and solid interface is relatively complex in actual situations, the present invention makes reasonable ideal assumptions on the connection and coupling between different media to reduce costs and obtain calculation accuracy that meets engineering requirements.

[0092] Figure 1 It is a schematic diagram of the transfer matrix model of the present invention, assuming that the system meets the following three initial conditions:

[0093] 1. At the interface of each layer of medium, the vibration velocity of the particles is continuous;

[0094] 2. The normal stress and tangential stress are continuous between each layer of medium and at each location within the layer;

[0095] 3. The n+1th layer and the 0th layer are both fluids (gas or liquid).

[0096] (2) Conversion between material mechanical parameters and acoustic parameters

[0097] First, the dynamic mechanical analyzer (DMA) was used to measure the multi-layer composite structure rubber to obtain the dynamic modulus of the multi-layer composite structure rubber (dynamic modulus refers to the storage modulus and loss factor of the material changing with the sound wave frequency), which are storage modulus E' and loss factor tanδ. The multi-layer composite structure rubber was measured using a rubber densitometer to obtain the density ρ of each layer of rubber material in the multi-layer composite structure rubber, and the thickness d of each layer of rubber material was measured at the same time. The Poisson's ratio v uses the typical value of rubber: 0.496.

[0098] The above measured parameters are converted to obtain the basic acoustic parameters of the material at the required calculation frequency, which are: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constant μ, the conversion formula is as follows:

[0099]

[0100]

[0101] μ=ρV s 2 ,

[0102] Where E' is the storage modulus, f is the frequency, and j is the imaginary unit.

[0103] The purpose of this step is to obtain the basic acoustic parameters of the material for use in subsequent calculation models.

[0104] (3) Construction of transfer matrix

[0105] The potential functions of longitudinal waves and transverse waves are given here, Φ and Ψ respectively.

[0106] Φ=[Aexp(jk vpz z)+Bexp(-jk vpz z)]exp[j(k vpx x-ωt)]

[0107] Ψ=[Cexp(jk vsz z)+Dexp(-jk vsz z)]exp[j(k vpx x-ωt)]

[0108] Among them, A and C are the reflected wave amplitudes of longitudinal wave and transverse wave respectively, and B and D are the incident wave amplitudes of longitudinal wave and transverse wave respectively. vpz is the component of the longitudinal wave number in the z direction, k vsz is the component of the shear wave number in the z direction, k vpx is the component of the longitudinal wave in the x direction, x represents the distance in the x direction, t represents the time, ω is the angular frequency, ω=2πf, z represents the distance in the z direction, j represents the imaginary part of the complex number, and the calculation formula is as follows:

[0109] k vpz =k vp cosθ i , k vsz =k vs cosγ i , k vpx =k vp sinθ i

[0110] Where i represents the i-th layer of n layers of rubber, and the longitudinal wave number k vp and the shear wave number k vs is obtained by conversion in step (2). Taking the i-th layer as an example, θ i , γ i are the incident angles (in radians) of the longitudinal and transverse waves in the i-th layer of the medium, and θ i , γ i Calculate using Snell's law:

[0111]

[0112]

[0113] by Figure 1 For example, Figure 1 The multi-layer composite structure rubber includes 1 to n layers of rubber medium, and the 0th layer and the n+1th layer are fluids located at the lower side and the upper side of the multi-layer composite structure rubber, namely, the transmission medium and the incident medium.

[0114] Since the sound wave enters the rubber from the water, there is no transverse wave in the fluid, so the transverse wave incident angle γ of the n+1th layer of the medium n+1 =0, the starting incident angle in the calculation model is θ n+1 , through the above formula, we can get θ n+1 Calculate θ n With γ n , and then by θ n With γ n Calculate θ n-1 With γ n-1 , and the incident angles of longitudinal waves and transverse waves in each layer of rubber medium are deduced downward.

[0115] To calculate the acoustic performance of a material at different angles of incidence, simply change θ n+1 (that is, only use the formula The present invention uses this method to calculate the working conditions under oblique incidence of sound waves.

[0116] The particle vibration velocity V at any position (x direction and z direction) of each layer interface x 、V z and particle stress σ x , σ z As follows:

[0117]

[0118]

[0119] V x is the particle velocity in the x direction, V z is the particle velocity in the z direction. x is the particle stress in the x direction, σ z is the particle stress in the z direction.

[0120] Among them, λ and μ are the Lame constants of each layer of the corresponding medium. Substituting the expressions of Φ and Ψ into the above four equations, taking the upper and lower interfaces of the i-th layer of the medium as an example, after complex function conversion and matrix arrangement, the following forms of particle velocity and stress at the upper and lower interfaces of the i-th layer of the medium can be obtained, where I upi ,I downi , A i , B i The subscript i represents that it is the corresponding parameter in the i-th layer of the medium. Similarly, the subscript (i-1) represents that it is the corresponding parameter in the (i-1)-th layer of the medium.

[0121]

[0122] Among them, A and C are the reflected wave amplitudes of longitudinal wave and transverse wave respectively, B and D are the incident wave amplitudes of longitudinal wave and transverse wave respectively, Iupi with I downi is a 4th-order matrix, which is the matrix of the inner layer of the i-th medium and the upper and lower interfaces. It is related to the dynamic modulus, thickness, Poisson's ratio and the incident angle of the sound wave of the rubber medium, and the form is as follows:

[0123]

[0124] in

[0125] Among them, z up For schematic diagram Figure 1 The coordinates of the upper interface of the layer of medium in the above four equations are p and shear wave velocity V s is the acoustic parameter of the layer of medium obtained by converting the input measurement value in the calculation model in step (2). vpz , k vsz With k vpx It is also calculated from the input measurement data.

[0126] I downi represents the matrix at the interface under the i-th layer of medium, which is related to I upi The form is the same, the difference is that z inside the matrix up The coordinate z of the interface under the i-th layer of medium is replaced by down ,The coordinates of the upper and lower interfaces of each layer can be calculated based on the thickness of each layer and the coordinate origin. down As shown below:

[0127]

[0128] in

[0129] Through elementary matrix transformation, we can get the relationship between particle velocity and stress at the upper and lower interfaces inside the i-th layer of the medium, where M i =I upi / I downi .

[0130]

[0131] The above formula is the form of the transfer matrix between each layer of rubber medium, and the transfer matrix of each layer of rubber is obtained using the following formula.

[0132] M i =I upi / I downi , i=1,2......n;

[0133] After obtaining the transfer matrix of each layer of rubber, multiply the matrices, such as Figure 1As shown, the relationship between the particle velocity and stress between the nth layer and the first layer of rubber can be obtained as shown in the following formula, where F = M n *M n-1 *...*M1, obviously, the number of M is equal to the number of rubber layers. F is a 4×4 matrix.

[0134]

[0135] (4) Substitute the boundary conditions

[0136] Since both sides of the multilayer composite rubber are fluid, the shear force in the x direction can be ignored inside the fluid, so σ x(n+1) =σ x0 =0, substituting it into the above formula, we get the following two formulas, where:

[0137] V zn =C 22 *V z0 +C 23 *σ z0

[0138] σ zn =C 32 *V z0 +C 33 *σ z0

[0139] Among them, C rc =F rc -F 4c *F r1 / F 41 , F=M n *M n-1 *…*M1, since F is a 4-order matrix, F rc Represents the element in the rth row and cth column of the matrix.

[0140] Arrange the above two equations into matrix form, and get the following equation:

[0141]

[0142] Due to the disappearance of shear force in the fluid, the transverse wave potential function is also 0. Let the incident wave amplitude be 1, then the sound pressure reflection coefficient R = A / B. Substitute the thickness term of the upper and lower interfaces of the multi-layer composite structure rubber into the longitudinal wave potential function Φ, and the following four equations are obtained:

[0143] V z(n+1) =jα n+1 (1-R), σ z(n+1) =-jρ n+1 ω(R+1)

[0144] V z0 =jα0B0,σz0 =-jρ0ωB0

[0145] (5) Solving simultaneous equations

[0146] Here are the characteristic impedances of the incident and transmission media of the sound wave:

[0147] Z0=ρ0V p0 / cosθ0

[0148] Combining all the above equations, we can get the expressions of the sound pressure reflection coefficient R and the sound pressure transmission coefficient T:

[0149]

[0150]

[0151] Then the sound absorption coefficient al is: αl = 1-R 2 -T 2 .

[0152] R and T in the above formula are the unified formula.

[0153] When switching the transmission medium, you only need to adjust the density and sound velocity of the transmission surface fluid to recalculate, without switching the formula. An example is as follows:

[0154] When the transmission medium is air, only ρ0 and V in the above formula need to be replaced by p0 The specific value is determined by the density of water and the longitudinal sound velocity (1000kg / m 3 , 1500m / s) are replaced by the density of air and the speed of longitudinal sound (1.29kg / m 3 , 343m / s), these two changes are reflected in Z0 in the solution formula of the sound pressure reflection coefficient R and the sound pressure transmission coefficient T, that is to say, after using the present invention, it is no longer necessary to use different calculation formulas for different transmission media, that is, it is no longer necessary to perform cumbersome conversion operations, which greatly reduces the complexity of the operation. After experimental verification, the average relative error between the sound absorption coefficient obtained by the present invention and the actual measurement value is 8.25%, which has a high accuracy.

[0155] The existing classical transfer matrix method has different solution formulas for different transmission media, as shown below:

[0156] For example, when the sound wave transmission medium is water, the formula of the classical transfer matrix method is as follows:

[0157]

[0158] When the transmission medium is air, the formula of the classical transfer matrix method is as follows:

[0159]

[0160] where a 12 ~a 22 is the corresponding element in the 2×2 matrix in the following formula

[0161]

[0162] It can be seen that the classical transfer matrix method requires different solution formulas for different working conditions, while the present invention adopts the same formula for all working conditions. After the unified formula, the calculation program is more convenient when converting the calculation conditions. For example, when the transmission medium changes from water to air, it is only necessary to replace the density and sound speed of water.

[0163] The above is the principle of the method of the present invention. The method of obtaining the acoustic performance parameters of the present invention is specifically as follows:

[0164] The multi-layer composite structure rubber includes n layers of rubber, which are the 1st layer, the 2nd layer, and the nth layer from bottom to top; the medium above the nth layer of rubber and below the 1st layer of rubber is a fluid. The fluid above is the n+1th layer, called the incident medium, and the fluid below is the 0th layer, called the transmission medium. For the convenience of description, the n-layer rubber is also called the n-layer medium, that is, the medium from the 1st layer to the nth layer is all rubber;

[0165] (1) Measurement and import of material parameters

[0166] The following parameters were collected:

[0167] Dynamic modulus (i.e. storage modulus E' and loss factor tanδ), density ρ, Poisson's ratio v and thickness d of each layer of rubber material. And set the frequency point range for calculation (if calculating one frequency point, just set one frequency point here, if calculating multiple frequency points, you can set the frequency point range as well as the initial frequency point and step size, or you can directly set multiple frequency points.), the incident angle of the sound wave, and whether the transmission medium is water or air.

[0168] (2) Obtain the basic acoustic parameters of each layer of rubber:

[0169] In the measurement parameters of step (1), the storage modulus and loss factor of each layer of rubber corresponding to the required calculation frequency are selected, and the basic acoustic parameters of the first layer and the second layer of rubber at this frequency point are calculated respectively, namely, the longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ.

[0170]

[0171]

[0172] μ=ρV s 2 ,

[0173] (3) Obtain the incident angles of the longitudinal and transverse waves in each layer of rubber, as well as the wave numbers of the longitudinal and transverse waves in the x and z directions:

[0174] The following formula is used to calculate the incident angles of longitudinal and transverse waves in each layer of the medium, as well as the wave numbers of longitudinal and transverse waves in the x and z directions.

[0175]

[0176]

[0177] k vpz =k vp cosθ i , k vsz =k vs cosγ i , k vpx =k vp sinθ i , where i represents the i-th layer of medium.

[0178] (4) Calculate the transfer matrix of each layer of rubber

[0179] For each layer of rubber, the matrix I of the upper interface of the layer of rubber is calculated using the following formula: upi :

[0180]

[0181] in z up is the z-axis coordinate of the interface on the layer of medium;

[0182] The matrix I of the lower interface of the rubber layer is calculated using the following formula: downi :

[0183]

[0184] in z down is the z-axis coordinate of the lower interface of the rubber layer.

[0185] The transfer matrix M of the rubber layer is calculated using the following formula: n :

[0186] M i =I upi / I downi , i=1,2......n;

[0187] The total matrix F is calculated using the following formula:

[0188] F=M n *M n-1 *…*M1,F are 4×4 matrices.

[0189] The function of the transfer matrix in the present invention is to obtain the relationship between the particle velocity and the particle stress between the interfaces of each layer. After obtaining this relationship, the boundary conditions are substituted to simplify the formula, and finally the sound pressure reflection coefficient and the sound pressure transmission coefficient are obtained through conversion.

[0190] The sound pressure reflection coefficient R is calculated using the following formula:

[0191]

[0192] The sound pressure transmission coefficient T is calculated using the following formula:

[0193]

[0194] The sound absorption coefficient αl is calculated using the following formula:

[0195] αl=1-R 2 -T 2

[0196] Among them, Z n+1 is the characteristic impedance of the incident medium, and Z0 is the characteristic impedance of the transmission medium, which can be calculated using the following formula:

[0197] Z0=ρ0V p0 / cosθ0

[0198] Among them, C rc =F rc -F 4c *F r1 / F 41 , F rc Represents the element in the rth row and cth column of the total matrix F.

[0199] The above introduces the complete process of obtaining the acoustic performance parameters at a certain frequency point. In practical applications, it is often necessary to obtain the acoustic performance parameters at multiple frequency points within a frequency range, such as 1kHz, 1.5kHz, 2kHz, 2.5kHz...9.5kHz, 10kHz. Each time, the acoustic performance parameters at a frequency point are calculated using the above process and the acoustic performance parameters are saved.

[0200] Figure 3 The flowchart shown is for actual use. Each cycle needs to calculate and save the calculation results at the current frequency. After the calculation is completed, the calculation of the next frequency point begins. In each cycle, the parameters that change in the formula are frequency f, storage modulus E1, and loss factor tanδ. Almost all parameters in the formula will change due to the change of these three parameters, such as the longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ, various parameters in the total transfer matrix F, C 22 , C 23 , C 32 , C 33 wait.

[0201] Figure 3 "Drawing and exporting data" in the text box means drawing the relationship between the sound pressure reflection coefficient R, sound pressure transmission coefficient T and sound absorption coefficient al of the multi-layer composite structure rubber and the frequency (i.e., drawing a graph with frequency (Freq) as the horizontal axis and the sound pressure reflection coefficient (or sound pressure transmission coefficient or sound absorption coefficient) as the vertical axis, and each point on the graph represents the corresponding sound pressure reflection coefficient (or sound pressure transmission coefficient or sound absorption coefficient) at a frequency). The format is as follows: Figure 5(a) to Figure 5(c) As shown in the figure, the exported data are the corresponding data points in these three figures.

[0202] The present invention also provides a system for obtaining the acoustic properties of a multi-layer composite structure rubber, the system comprising:

[0203] Collection unit: used to collect the dynamic modulus, density ρ and thickness d of each layer of rubber in the multi-layer composite structure rubber, set the frequency point f, the incident angle of the sound wave, and the transmission medium; the dynamic modulus includes: storage modulus E′ and loss factor tanδ;

[0204] Parameter calculation unit: connected to the acquisition unit, used to obtain the basic acoustic parameters of each layer of rubber: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ; obtain the incident angles of longitudinal and transverse waves of each layer of rubber, as well as the wave numbers of longitudinal and transverse waves in the x and z directions;

[0205] Matrix calculation unit: connected with the parameter calculation unit, used to obtain the transfer matrix of each layer of rubber, and obtain the total matrix using the transfer matrix of each layer of rubber;

[0206] Acoustic performance parameter acquisition unit: connected to the matrix calculation unit, used to obtain the sound pressure reflection coefficient, sound pressure transmission coefficient and sound absorption coefficient using the total matrix.

[0207] [Example]

[0208] An embodiment of the method of the present invention is as follows:

[0209] The multi-layer composite structure rubber in this embodiment adopts a double-layer structure rubber, that is, n=2, i=1 or 2, and the incident angle of the sound wave is vertical. The upper layer material of the double-layer structure rubber is styrene-butadiene rubber containing 30 parts of carbon black, and the lower layer material is styrene-butadiene rubber without carbon black, so as to distinguish the dynamic mechanical properties between the two layers.

[0210] (1) Measurement and import of material parameters

[0211] The following parameters were collected:

[0212] The dynamic modulus (i.e. storage modulus E' and loss factor tanδ), density ρ, Poisson's ratio ν and thickness d of each layer of rubber material are set. The frequency point range of the calculation, the incident angle of the sound wave, and the medium of the sound wave transmission surface are set to be water or air.

[0213] The thickness of the two layers of media is set to 50 mm, and the Poisson's ratio is set to the typical value of rubber 0.496. After measurement, the dynamic mechanical properties of the two layers of rubber media are shown in Figure 4 (a) and Figure 4 (b) respectively.

[0214] (2) Conversion calculation between material parameters:

[0215] Among the parameters measured in step (1), the storage modulus and loss factor of each layer of rubber corresponding to the required calculation frequency are used to calculate the basic acoustic parameters of the material at this frequency point, which are: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ.

[0216] The specific calculation formula is as follows:

[0217]

[0218]

[0219] μ=ρV s 2 ,

[0220] (3) Establish ideal conditions

[0221] Assume that the double-layer structure rubber meets the following three initial conditions:

[0222] 1. Between two layers of media, the vibration velocity of particles is continuous.

[0223] 2. The normal stress and tangential stress between the two layers and everywhere within the layer are continuous.

[0224] 3. The media before and after the material are all fluids (water in this embodiment).

[0225] (4) Construction of transfer matrix

[0226] Φ and Ψ are the potential functions of longitudinal and transverse waves respectively:

[0227] Φ=[Aexp(jk vpz z)+Bexp(-jk vpz z)]exp[j(k vpx x-ωt)]

[0228] Ψ=[Cexp(jk vsz z)+Dexp(-jk vsz z)]exp[j(k vpx x-ωt)]

[0229] Where A and B are the reflected wave amplitude and incident wave amplitude of the longitudinal wave, respectively, and C and D are the reflected wave amplitude and incident wave amplitude of the transverse wave, respectively. vpz z) is the expression of the reflected wave function, Bexp(-jk vpz z) is the incident wave function expression. exp[j(k vpx x-ωt)] is the time term and can be ignored.

[0230] k vpz is the component of the longitudinal wave number in the z direction, k vsz is the component of the shear wave number in the z direction, k vpx is the component of the longitudinal wave in the x direction, which is calculated by the following formula:

[0231] k vpz =k vp cosθ i , k vsz =k vs cosγ i , k vpx =k vp sinθ i

[0232] The longitudinal wave number k vp and the shear wave number k vsis the acoustic parameter converted from the measured data in step (1) of the embodiment. θ is the longitudinal wave incident angle, γ is the transverse wave incident angle (radian system), and the longitudinal wave and transverse wave incident angles in each layer of the medium are calculated using Snell's law:

[0233]

[0234]

[0235] Since the sound wave enters the rubber from the water, there is no transverse wave in the fluid, so γ n+1 =0, and θ n+1 Replace it with the sound wave incident angle set in step (1), and calculate the incident angles of the longitudinal wave and the transverse wave in each layer of the medium.

[0236] The particle vibration velocity V at any position (x and z directions) on each interface x 、V z and particle stress σ x , σ z As follows:

[0237]

[0238]

[0239] Among them, λ and μ are the Lame constants of each layer of the corresponding medium. Substituting the expressions of Φ and Ψ into the above four equations, and taking the upper and lower interfaces of the nth layer of medium as an example, after complex function conversion and matrix arrangement, the following forms of particle velocity and stress can be obtained:

[0240]

[0241] Among them, I up with I down is a 4th-order matrix, which is related to the dynamic modulus, thickness, Poisson's ratio and the incident angle of the sound wave of the rubber medium. In this embodiment, the matrices of the first layer of rubber are as follows, where I up1 ,I down1 、z up1 、z down1 The subscript 1 indicates that it is the corresponding parameter of the first layer of rubber.

[0242]

[0243] in z up1 for Figure 1 The coordinates of the upper interface of the first layer of rubber in the above four equations are p and shear wave velocity V sis the acoustic parameter of the layer of medium obtained by converting the input measurement value in the calculation model in step (2). vpz , k vsz With k vpx It is also calculated from the input measurement data.

[0244] I down1 Represents the matrix at the interface below the first layer of medium, which is related to I up1 The form is the same, the difference is that z inside the matrix up1 Change to the coordinate z at the interface under the nth layer of medium down1 , get I down1 .

[0245]

[0246] in Through the elementary transformation of the matrix, the relationship between the particle velocity and stress between the upper and lower interfaces inside the first layer of rubber is obtained, where M1 = I up1 / I down1 .

[0247]

[0248] The matrices of the second layer of rubber are as follows, where I up2 ,I down2 、z up2 、z down2 The subscript 2 indicates that it is the corresponding parameter of the second layer of rubber.

[0249]

[0250] in z up2 for Figure 1 The z-axis coordinate of the upper interface of the second rubber layer in the above four equations is p and shear wave velocity V s , k vpz , k vsz With k vpx It is the acoustic parameter calculated in step (3) using the dynamic modulus, density ρ, and Poisson's ratio ν of the second layer material.

[0251]

[0252] in z down2 For schematic diagram Figure 1 The z-axis coordinate of the lower interface of the second rubber layer.

[0253] Through elementary matrix transformation, the relationship between the particle velocity and stress between the upper and lower interfaces inside the first layer of rubber is obtained, where M22 =I up2 / I down2 .

[0254]

[0255] Based on this, the relationship between the vibration velocity and stress of the particle point between the upper and lower interfaces of the sound-absorbing material as a whole is obtained, as shown in the following formula, where F=M2*M1.

[0256]

[0257] (5) Substitute the boundary conditions

[0258] Since both sides of the double-layer rubber are filled with water, the shear force in the x direction can be ignored, so σ x3 =σ x0 =0, substituting it into the above formula, we get the following two formulas, where C rc =F rc -F 4c *F r1 / F 41 .

[0259] V z2 =C 22 *V z0 +C 23 *σ z0

[0260] σ z2 =C 32 *V z0 +C 33 *σ z0

[0261] Arrange the above two equations into matrix form, and get the following equation:

[0262]

[0263] Due to the disappearance of shear force in the fluid, the transverse wave potential function is also 0. Let the incident wave amplitude be 1, then the sound pressure reflection coefficient R = A / B. Substitute the thickness term of the upper and lower interfaces of the multi-layer composite structure rubber into the longitudinal wave potential function Φ, and the following four equations are obtained:

[0264] V z3 =jα3(1-R),σ z3 =-jρ3ω(R+1)

[0265] V z0 =jα0B0,σ z0 =-jρ0ωB0

[0266] (6) Solving simultaneous equations

[0267] Here are the characteristic impedances of the incident and transmission media of the sound wave:

[0268] Z0=ρ0c0 / cosθ0

[0269] Combining all the above equations, we can get the expressions of sound pressure reflection coefficient and sound pressure transmission coefficient:

[0270]

[0271]

[0272] Among them, p r is the reflected wave sound pressure, p i is the incident wave sound pressure, p t is the incident wave sound pressure.

[0273] The sound absorption coefficient is: αl = 1-R 2 -T 2

[0274] Taking the frequency of 5000 Hz as an example, the calculated values ​​of the key parameters in the embodiment are shown in Table 1.

[0275]

[0276] Table 1

[0277] also:

[0278]

[0279]

[0280] It can be seen from the table above that the sound pressure reflection coefficient R, sound pressure transmission coefficient T and sound absorption coefficient al of the composite material at 5000Hz are 0.2409, 0.3788 and 0.7985 respectively. By replacing the storage modulus and loss factor corresponding to the material at other frequency points in step (1), changing the corresponding frequency f, and then repeating the above calculation steps, the acoustic performance of the material at different frequencies can be calculated.

[0281] The comparison between the measured value of the acoustic performance of the double-layer composite structure rubber in this embodiment and the calculated value of the model is as follows: Figure 5(a) to Figure 5(c) As shown, in this field, if the relative error between the measured value and the theoretical calculated value is within 10%, the calculation model is considered to be accurate, and the average relative error of the sound absorption coefficient obtained by the method of the present invention is 8.25%, so the method of the present invention has a high accuracy.

[0282] Finally, it should be explained that the above technical solution is only one implementation method of the present invention. For those skilled in the art, it is easy to make various types of improvements or modifications based on the application methods and principles disclosed in the present invention, and it is not limited to the method described in the above specific implementation method of the present invention. Therefore, the method described above is only preferred and does not have a restrictive meaning.

Claims

1. A method for obtaining the acoustic properties of a multi-layer composite structure rubber, characterized in that: The method first measures the physical parameters of each layer of rubber in the multi-layer composite structure rubber, then obtains the basic acoustic parameters at a set frequency point using the physical parameters, and finally obtains the acoustic performance parameters of the multi-layer composite structure rubber at the set frequency point using the basic acoustic parameters and a transfer matrix; The acoustic performance parameters include: sound pressure reflection coefficient, sound pressure transmission coefficient, and sound absorption coefficient; The multi-layer composite structure rubber comprises n layers of rubber, which are the first layer, the second layer, and the nth layer from bottom to top; The incident medium above the nth layer of rubber and the transmission medium below the first layer of rubber are both fluids; The incident medium is the n+1th layer, and the transmission medium is the 0th layer; The method comprises: (1) Measuring the dynamic modulus, density ρ and thickness d of each layer of rubber in the multi-layer composite structure rubber, setting the frequency point f, the incident angle of the sound wave, and the transmission medium; the dynamic modulus includes: storage modulus E′ and loss factor tanδ; (2) Obtain the basic acoustic parameters of each layer of rubber: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ; (3) Obtaining the longitudinal wave and transverse wave incident angles of each layer of rubber, as well as the wave numbers of the longitudinal wave and transverse wave in the x-direction and z-direction; (4) obtaining the transfer matrix of each layer of rubber, and obtaining the total matrix using the transfer matrix of each layer of rubber; (5) Using the total matrix, obtain the sound pressure reflection coefficient, sound pressure transmission coefficient and sound absorption coefficient; The operation of step (5) includes: The sound pressure reflection coefficient R is calculated using the following formula: The sound pressure transmission coefficient T is calculated using the following formula: The sound absorption coefficient αl is calculated using the following formula: αl=1-R 2 -T 2 Among them, Z n+1 is the characteristic impedance of the incident medium, and Z0 is the characteristic impedance of the transmission medium, which can be calculated using the following formula: Among them, C rc =F rc -F 4c *F r1 / F 41 , F rc Represents the element in the rth row and cth column of the total matrix F; θ represents the incident angle of the longitudinal wave.

2. The method for obtaining the acoustic properties of a multi-layer composite structure rubber according to claim 1, characterized in that: The operation in step (2) includes: The basic acoustic parameters of each layer of rubber are calculated using the following formula: Where v is Poisson's ratio, using a typical value for rubber, and j is an imaginary unit.

3. The method for obtaining the acoustic properties of a multi-layer composite structural rubber according to claim 2, characterized in that: The operation of step (3) includes: The longitudinal wave incident angle θ of each layer of rubber is calculated using the following formula: i With the shear wave incident angle γ i , and the wave number k of the longitudinal wave in the x and z directions vpx , k vpz , the wave number k of the shear wave in the z direction vsz : k vpz =k vp cosθi,k vsz =k vs cosγ i ,k vpx =k vp sinθ i Here, i represents the i-th layer of medium.

4. The method for obtaining the acoustic properties of a multi-layer composite structure rubber according to claim 3, characterized in that: The operation of step (4) includes: For each layer of rubber, the matrix I of the upper interface of the layer of rubber is calculated using the following formula: upi : in z up is the z-axis coordinate of the interface on the layer of medium; The matrix I of the lower interface of the rubber layer is calculated using the following formula: downi : in z down is the z-axis coordinate of the lower interface of the rubber layer; The transfer matrix M of the rubber layer is calculated using the following formula: n : M i =I upi / I downi ,i=1,2......n; The total matrix F is calculated using the following formula: F=M n *M n-1 *...*M1, F are 4×4 matrices.

5. The method for obtaining the acoustic properties of a multi-layer composite structure rubber according to claim 4, characterized in that: Setting multiple frequency points, performing the operations from step (1) to step (5) at each frequency point in turn, obtaining the acoustic performance parameters at each frequency point, and storing the acoustic performance parameters at all frequency points; Then draw a reflection coefficient graph with frequency as the abscissa and reflection coefficient as the ordinate; The transmission coefficient graph is plotted with the frequency as the horizontal axis and the transmission coefficient as the vertical axis; the sound absorption coefficient graph is plotted with the frequency as the horizontal axis and the sound absorption coefficient as the vertical axis.

6. A system for obtaining acoustic properties of a multi-layer composite structure rubber, characterized in that: The system comprises: Collection unit: used to collect the dynamic modulus, density ρ and thickness d of each layer of rubber in the multi-layer composite structure rubber, set the frequency point f, the incident angle of the sound wave, and the transmission medium; the dynamic modulus includes: storage modulus E′ and loss factor tanδ; Parameter calculation unit: connected to the acquisition unit, used to obtain the basic acoustic parameters of each layer of rubber: longitudinal wave velocity V p , shear wave velocity V s , longitudinal wave number k vp , shear wave number k vs , Lamé constants μ, λ; obtain the incident angles of longitudinal and transverse waves of each layer of rubber, as well as the wave numbers of longitudinal and transverse waves in the x and z directions; Matrix calculation unit: connected with the parameter calculation unit, used to obtain the transfer matrix of each layer of rubber, and obtain the total matrix using the transfer matrix of each layer of rubber; Acoustic performance parameter acquisition unit: connected to the matrix calculation unit, used to obtain the sound pressure reflection coefficient, the sound pressure transmission coefficient and the sound absorption coefficient using the total matrix; The acoustic performance parameter acquisition unit performs the following operations: The sound pressure reflection coefficient R is calculated using the following formula: The sound pressure transmission coefficient T is calculated using the following formula: The sound absorption coefficient αl is calculated using the following formula: αl=1-R 2 -T 2 Among them, Z n+1 is the characteristic impedance of the incident medium, and Z0 is the characteristic impedance of the transmission medium, which can be calculated using the following formula: Z0=ρ0V p0 / cosθ0 Among them, C rc =F rc -F 4c *F r1 / F 41 , F rc represents the element in the rth row and cth column of the total matrix F; θ represents the incident angle of the longitudinal wave.

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