Semi-analytical method for calculating acoustic transmission loss of laminated wallboard

Abstract

The invention relates to the technical field of sound transmission loss calculation, in particular to a semi-analytical method for calculating sound transmission loss of a laminated wallboard. The method comprises the following steps: calculating potential energy and kinetic energy of a laminated wallboard system, and carrying out minimum action variation derivation to generate a displacement change control equation of the laminated wallboard system; unknown function extraction is carried out on the laminated wallboard system displacement change control equation and assumed as a first type Chebyshev multinomial expression; determining undetermined constants by using a Rayleigh-Riyz method, and solving a plane wave excitation response to obtain a displacement field response; carrying out radiation sound power calculation on the displacement field response by utilizing Rayleigh integral to obtain the radiation sound power of the laminated wall panel; and carrying out incident sound power and acoustic interlayer impedance accounting on the laminated wallboard system, and carrying out sound transmission loss calculation to obtain the sound transmission loss of the laminated wallboard system. The calculation method provided by the invention is convenient and efficient to operate, has relatively high precision, and can meet the requirements of actual engineering application.

Description

Technical Field

[0001] The invention relates to the field of sound transmission loss calculation, and in particular to a semi-analytical method for calculating the sound transmission loss of a laminated wallboard. Background Art

[0002] In the field of construction engineering, calculating the sound transmission loss of laminated wall panels is a crucial part of the design. Sound transmission loss is used to evaluate the isolation ability of building walls to sound waves, which is directly related to the noise control effect of the indoor environment. Laminated wall panels are usually made of multiple different materials stacked together. The acoustic properties of each layer of material, such as density, elastic modulus, and thickness, will affect the overall sound transmission performance. The current research direction includes optimizing the existing analytical model and combining the finite element method with semi-analytical technology to form a comprehensive solution. This method can combine the physical and acoustic properties of laminated wall panels and establish a simplified acoustic transmission model to more effectively calculate the sound transmission loss, while taking into account the interface effect of the material and the interaction of sound waves in different material layers. However, traditional calculation methods often use simplified models for calculation. These models can capture the propagation characteristics of sound waves in laminated structures to a certain extent, but they are still insufficient when dealing with complex structures, resulting in low accuracy in calculating sound transmission loss. Summary of the invention

[0003] Based on this, it is necessary for the present invention to provide a semi-analytical method for calculating the sound transmission loss of laminated wall panels to solve at least one of the above-mentioned technical problems.

[0004] To achieve the above object, a semi-analytical method for calculating the sound transmission loss of a laminated wall panel comprises the following steps:

[0005] By setting an acoustic plane wave excitation external force condition, and calculating the potential energy and kinetic energy of the laminated wall panel system based on the acoustic plane wave excitation external force condition, the acoustic excitation potential energy of the laminated wall panel system and the acoustic excitation kinetic energy of the laminated wall panel system are obtained;

[0006] Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall panel system, the displacement change control equation is derived by minimum action variation of the laminated wall panel system. It is assumed that the first-order Chebyshev polynomial expression containing unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by using the Rayleigh-Ritz method.

[0007] Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response and use Rayleigh integral to calculate the radiated sound power of the laminated wall panel to obtain the radiated sound power of the laminated wall panel;

[0008] Based on the acoustic plane wave excitation external force condition, the incident sound power and acoustic interlayer impedance of the laminated wall panel system are calculated, and the sound transmission loss is calculated to obtain the sound transmission loss of the laminated wall panel system.

[0009] Furthermore, the step of setting an acoustic plane wave excitation external force condition and calculating the potential energy and kinetic energy of the laminated wallboard system based on the acoustic plane wave excitation external force condition includes the following steps:

[0010] By setting an acoustic plane wave excitation external force condition, and based on the acoustic plane wave excitation external force condition, performing acoustic plane wave excitation field modeling on the laminated wall panel system, a laminated wall panel model under the acoustic plane wave excitation field is generated;

[0011] The elastic modulus of the laminated panel model under the acoustic plane wave excitation field is determined to obtain the elastic modulus of the laminated panel under the acoustic plane wave excitation field. Where F is the applied pressure under the acoustic plane wave excitation field, A is the plane wave excitation cross-sectional area of ​​the laminated wall panel, ΔL is the length stress deformation of the laminated wall panel, and L0 is the original length of the laminated wall panel. Based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field, the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field is calculated to obtain the boundary virtual spring potential energy U of the laminated wall panel. sp ;

[0012] The laminated wall panel stress σ and the laminated wall panel strain are obtained by decomposing the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field, and the wall panel strain energy of the laminated wall panel model under the acoustic plane wave excitation field is determined based on the laminated wall panel stress σ and the laminated wall panel strain to obtain the laminated wall panel strain energy Where V is the strain volume of the laminated wall panel, and the relationship between the laminated wall panel stress σ and the laminated wall panel strain is expressed by the laminated wall panel constitutive relationship σ=D, where D is the laminated wall panel stiffness matrix;

[0013] The plane wave excitation external force work of the laminated panel model under the acoustic plane wave excitation field is calculated to obtain the external excitation work W of the laminated panel e =∫ S p(t)udS, where S is the surface area of ​​the laminated panel, p(t) is the acoustic plane wave excitation pressure at acoustic excitation time t, and u is the plane wave excitation displacement;

[0014] According to the potential energy U of the virtual spring at the boundary of the laminated wall sp and the strain energy U of the laminated panel st The sum of the two minus the external excitation work W of the laminated panel e Perform a summary calculation of the potential energy of the wall panel system to obtain the acoustic excitation potential energy U of the laminated wall panel system;

[0015] The kinetic energy of the laminated panel system is calculated for the laminated panel model under the acoustic plane wave excitation field to obtain the acoustic excitation kinetic energy of the laminated panel system. Where ρ is the density, is the displacement change velocity due to plane wave excitation.

[0016] Further, the calculation of the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field includes the following steps:

[0017] Determine the virtual spring support boundary condition of the laminated wall panel model under the acoustic plane wave excitation field, and obtain the laminated wall panel spring support boundary condition determination result, wherein the laminated wall panel spring support boundary condition determination result is a fixed boundary condition or a hinged boundary condition;

[0018] Based on fixed boundary conditions or hinged boundary conditions, a virtual spring mechanics model is defined for the laminated wall panel model under an acoustic plane wave excitation field to obtain an acoustically excited fixed boundary virtual spring mechanics model or an acoustically excited hinged boundary virtual spring mechanics model;

[0019] Based on the elastic modulus E of the laminated wall under the acoustic plane wave excitation field, the boundary virtual spring stiffness of the acoustically excited fixed boundary virtual spring mechanical model or the acoustically excited hinged boundary virtual spring mechanical model is calculated to obtain the boundary virtual spring stiffness k of the laminated wall b ;

[0020] Based on the virtual spring stiffness k of the laminated panel boundary b The potential energy of the virtual springs at the boundary of the laminated panel model under the acoustic plane wave excitation field is calculated to obtain the potential energy of the virtual springs at the boundary of the laminated panel. where δ is the boundary displacement of the laminated panel.

[0021] Furthermore, the virtual spring stiffness k of the laminated panel boundary is b Specifically:

[0022] If the acoustically excited fixed boundary virtual spring mechanical model is determined, the virtual spring stiffness of the fixed boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary: Where h is the thickness of the laminated wall, v is the Poisson's ratio, and L is the boundary length of the laminated wall;

[0023] If the virtual spring mechanical model of the acoustically excited hinged boundary is determined, the virtual spring stiffness of the hinged boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary:

[0024] Furthermore, the displacement change control equation is derived by performing minimum action variation on the laminated wall panel system based on the acoustic excitation potential energy and the acoustic excitation kinetic energy of the laminated wall panel system, assuming that the first-order Chebyshev polynomial expression containing the unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by using the Rayleigh-Ritz method, including the following steps:

[0025] Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall system, the kinetic potential energy relationship of the laminated wall system is described using the Lagrangian function to obtain the Lagrangian kinetic potential energy description relationship of the laminated wall system.

[0026] The Lagrangian kinetic potential energy of the laminated panel is described by Perform a minimum action variational derivation to generate the governing equations for the displacement changes of the laminated panel system

[0027] Control equations for displacement changes of laminated panel systems Performing displacement field time response unknown function extraction processing to obtain the laminated wall panel displacement field time response unknown function u(x,t), where x is the displacement change;

[0028] The first kind Chebyshev polynomial T is used to calculate the unknown function u(x, t) of the time response of the displacement field of the laminated wall. n (x) Assume that we represent the first kind of Chebyshev polynomials containing the constants to be determined. Where N is the polynomial order, C n is a constant to be determined, φ n (t) is the time response basis function, where the time response basis function φ n (t) is further expanded to φ n (t) = A n cos(ωt)+B n sin(ωt), where ω is the frequency of the plane wave excitation, A n is the cosine variation coefficient of the time response, B n is the sinusoidal variation coefficient of the time response;

[0029] By converting the first kind Chebyshev polynomial expression containing the unknown constants Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants.

[0030] Furthermore, the Lagrangian kinetic potential energy of the laminated wall is described by The derivation of the minimum action variational method includes the following steps:

[0031] The Lagrangian kinetic potential energy of the laminated panel is described by Perform minimum action Lagrangian analysis to construct the basic form of the Lagrangian equation

[0032] The basic form of the Lagrange equation In The velocity field is varied to obtain

[0033] The basic form of the Lagrange equation In Perform a variational derivation of the displacement field to obtain

[0034] Will as well as Substitute into the basic form of the Lagrange equation and simplify the equation to generate the displacement change control equation of the laminated wall system

[0035] Furthermore, the first kind Chebyshev polynomial expression containing the unknown constants is Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants, including the following steps:

[0036] By transforming the displacement change control equation of the laminated panel system into Perform similar treatment on the second-order partial differential equation to obtain the similar partial differential equation for the displacement control of the laminated wall panel in is the operator related to the stiffness of the laminated panel, f(t) is the plane wave excitation;

[0037] By converting the first kind Chebyshev polynomial expression containing the unknown constants Substitute the similar partial equation of displacement control of laminated wall into and separate it into the spatial part and the temporal part to obtain the time-space separation expansion equation of the laminated wall displacement

[0038] The time response basis function φ n The further expansion of (t) is substituted into the time-space separation expansion equation of the laminated wall displacement and all the equations containing C are separated. n The items get:

[0039]

[0040] Transform the above equation into each polynomial T n(x) and balance the right side of the above equation f(t) with the polynomial T n (x) is expanded to: Among them U n is the time response basis function φ of f(t) n The coefficient under (t);

[0041] Multiply both sides of the above equation by T m (x) and integrate with respect to x to obtain:

[0042]

[0043] Using polynomial T n The orthogonality of (x) can simplify the above integral equation to:

[0044]

[0045] The above equation is solved using the Rayleigh-Ritz method to obtain the unknown constant

[0046] Furthermore, the step of substituting the undetermined constant into the first-order Chebyshev polynomial expression containing the undetermined constant to solve the plane wave excitation response and calculating the radiated sound power of the laminated wall panel by using Rayleigh integral includes the following steps:

[0047] Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response, and obtain the displacement field response of the laminated wall panel system under acoustic plane wave excitation, where the displacement field response of the laminated wall panel system is specifically:

[0048] The radiated sound power of the laminated panel system under the excitation of acoustic plane waves is calculated by using Rayleigh integral to obtain the radiated sound power of the laminated panel. Where ρ0 is the air density, c0 is the speed of sound, I n is the orthogonal integration constant of the Chebyshev polynomial.

[0049] Furthermore, the calculation of incident sound power and acoustic interlayer impedance of the laminated wall panel system based on the acoustic plane wave excitation external force condition and the calculation of sound transmission loss includes the following steps:

[0050] Based on the acoustic plane wave excitation external force condition, the incident sound power of the laminated wall panel system is calculated using the incident sound power calculation formula to obtain the incident sound power of the laminated wall panel;

[0051] The incident sound power calculation formula is as follows:

[0052]

[0053] Where P in is the incident sound power of the laminated wall panel, I is the incident sound density of the laminated wall panel, S is the surface area of ​​the laminated wall panel, P0 is the incident sound pressure peak of the laminated wall panel, ρ0 is the air density, and c0 is the sound speed;

[0054] Performing physical property analysis on each layer of siding material in the laminated siding system to obtain physical property parameters of each layer of siding material in the laminated siding system;

[0055] Based on the acoustic plane wave excitation external force conditions and the physical property parameters of each layer of the wall panel material in the laminated wall panel system, the acoustic interlayer impedance between each layer of the wall panel material in the laminated wall panel system is calculated to obtain the acoustic impedance value between each layer of the wall panel material in the laminated wall panel system;

[0056] The acoustic impedance values ​​between each layer of wall panel materials in the laminated wall panel system are calculated and summarized to obtain the total acoustic impedance between the laminated wall panels;

[0057] Based on the total acoustic interlayer impedance of the laminated wall panel, the incident sound power of the laminated wall panel and the radiated sound power of the laminated wall panel are calculated to obtain the sound transmission loss of the laminated wall panel system.

[0058] Furthermore, the acoustic interlayer impedance of the wall panel is calculated by using an acoustic interlayer impedance calculation formula, which is specifically:

[0059]

[0060] In the formula, κ ij is the acoustic impedance between the i-th and j-th wallboard materials in the laminated wallboard system, i and j are the wallboard layer index parameters of the laminated wallboard system, ρ0 is the air density, c0 is the sound speed, h i is the thickness of the i-th layer of siding material, h j is the thickness of the j-th layer of siding material, a i is the acoustic wave number of the i-th layer of wall material, b i is the acoustic wave elastic modulus of the i-th layer wall panel material, a j is the acoustic wave number of the jth layer of wall panel material, b j is the acoustic wave elastic modulus of the j-th layer wall panel material.

[0061] Beneficial effects of the present invention:

[0062] The semi-analytical method for calculating the acoustic transmission loss of laminated wall panels proposed in the present invention has the beneficial effect of, compared with the prior art, setting the acoustic plane wave excitation external force condition, and calculating the boundary virtual spring potential energy, strain energy and external excitation work of the laminated wall panel system based on the acoustic plane wave excitation external force condition, and summarizing the boundary virtual spring potential energy and strain energy and subtracting the external excitation work, so as to obtain the total potential energy under acoustic excitation. This process helps to understand the overall energy state of the laminated wall panel system under acoustic load, and can evaluate the comprehensive impact of acoustic excitation on the wall panel system. The acoustic excitation potential energy finally obtained provides important reference data for the subsequent calculation process. In addition, by calculating the kinetic energy of the wall panel system of the laminated wall panel model under the acoustic plane wave excitation field, it is helpful to comprehensively evaluate the dynamic characteristics of the laminated wall panel under the acoustic fluctuation conditions. The calculation of kinetic energy shows the energy propagation and conversion process of the acoustic plane wave in the wall panel, which is crucial for understanding the dynamic response of the material under different excitation conditions. This information can provide basic data guarantee for the subsequent calculation process. Secondly, by combining the description relationship between acoustic excitation potential energy and acoustic excitation kinetic energy, the laminated wall panel system is derived by the minimum action variational method, and the displacement change control equation of the laminated wall panel system can be generated by the integral variational derivation. In this way, the control equation derived by the variational method can provide the dynamic response law of the laminated wall panel system, and can accurately describe the movement and deformation of the laminated wall panel material under acoustic excitation, thereby providing a theoretical basis and calculation basis for the subsequent control equation calculation process. By extracting the unknown function of the displacement field time response of the displacement change control equation of the laminated wall panel system, this process aims to solve the time-dependent response in practical problems and transform the complex behavior of the dynamic system into an easy-to-handle form. By extracting the unknown function, the specific displacement distribution and time evolution of the laminated wall panel under acoustic excitation can be clarified, which not only helps to understand the specific response of the laminated wall panel system at different time points, but also provides direct data support for subsequent mathematical modeling and analytical solution. Mastering the time response of the displacement field is of great significance for the dynamic analysis of the structure, the design of the control strategy, and the prediction of the behavior of the system under different excitation conditions. By assuming the first-order Chebyshev polynomial representation of the unknown function of the time response of the displacement field of the laminated wall panel, an expression containing unknown constants can be generated. This hypothetical representation method can transform the complex time response problem into a linear combination of a set of adjustable polynomial functions and time basis functions, greatly simplifying the solution process. Specifically, the first-order Chebyshev polynomial can effectively capture the spatial variation characteristics of the displacement field. This method makes the mathematical expression of the problem clearer and also provides strong support for subsequent numerical solution and analysis.Moreover, by substituting the first-order Chebyshev polynomial expressions containing unknown constants obtained by previous assumptions into the displacement change control equation of the laminated wall panel system and using the Rayleigh-Ritz method to solve the unknown constants, this process can transform the complex dynamic equations into a set of algebraic equations that are easy to solve. The Rayleigh-Ritz method transforms the continuous partial differential equation problem into a discrete optimization problem by selecting appropriate trial functions and weight functions, thereby simplifying the solution process. This method can effectively determine the unknown constants and provide an accurate analytical solution for the displacement field of the laminated wall panel system, which not only improves the computational efficiency, but also ensures the accuracy of the understanding, making the understanding and prediction of the dynamic characteristics of the system more reliable, and providing strong theoretical support for its application in practical engineering, so that the complex structures within the laminated wall panel system can be better handled. Then, by substituting the previously quantified unknown constants into the first-order Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response, the displacement field response of the laminated wall panel system under acoustic plane wave excitation can be accurately obtained. The key to this step is to convert the complex dynamic behavior of the actual problem into a mathematical model for solution and analysis. Through the application of Chebyshev polynomials, the boundary conditions and complex excitation situations of the laminated wall panel system can be effectively handled. Through such a solution, the deformation of the wall panel under actual acoustic excitation can be grasped, providing important data for further acoustic analysis and design optimization, so as to meet specific acoustic performance requirements. The radiated sound power of the laminated wall panels is calculated by using the Rayleigh integral for the previously determined displacement field response of the laminated wall panel system under acoustic plane wave excitation. The key to this step is to convert the displacement field response of the laminated wall panel system into actual sound power output through the Rayleigh integral method. This calculation process can evaluate the actual radiated sound energy of the laminated wall panel system under specific acoustic excitation, that is, the sound power radiated by the wall panel during sound propagation. Through this calculation, the acoustic performance of the laminated wall panel system in actual use can be clarified, including its contribution to environmental sound waves and potential noise levels. The precise calculation process of the radiated sound power not only helps to evaluate whether the acoustic design of the laminated wall panel system meets the target requirements, but also guides the necessary adjustments in the design process to improve the overall acoustic performance of the laminated wall panel system. Finally, the incident sound power of the laminated wall panel system is calculated based on the external force conditions of acoustic plane wave excitation, where the incident sound power refers to the energy transmitted when the sound wave reaches the laminated wall panel system. This process is affected by factors such as power density, laminated wall panel surface area, air density and sound speed. By accurately calculating the incident sound power, basic data can be provided for subsequent acoustic analysis. This process ensures that the energy input to the system under acoustic excitation conditions is clearly quantified, and provides key input data for further calculation of transmission loss parameters.The acoustic interlayer impedance of each layer of wallboard material in the laminated wallboard system is also calculated based on the acoustic plane wave excitation external force condition. The main goal of this step is to calculate the acoustic impedance value between different layers, which is crucial to understanding the propagation characteristics of sound waves in the laminated wallboard system. Acoustic impedance reflects the degree of material resistance to sound wave propagation and is a key factor in the reflection and transmission of sound waves at the interface of different media. By accurately calculating the acoustic impedance value of each layer of material, the acoustic performance of the laminated wallboard system can be further analyzed and optimized, including the isolation effect of sound waves and the transmission efficiency of sound. This calculation provides basic data for subsequent acoustic performance evaluation and realizes the summary calculation of the acoustic impedance values ​​between each layer of material calculated previously. It can reflect the overall acoustic obstruction effect under the interaction of different layers of materials. Through the summary calculation, the comprehensive response of the entire laminated wallboard system to sound waves can be effectively evaluated, including how the acoustic characteristics of each layer of material jointly affect the propagation and isolation capabilities of sound waves, thereby providing basic data guarantee for the subsequent sound transmission loss calculation process. In addition, the sound transmission loss of the incident sound power and the radiated sound power of the laminated wall panels are calculated based on the total impedance between the acoustic layers of the laminated wall panels. This calculation quantifies the effectiveness of the sound wave penetration process through a formula. The sound transmission loss is a key indicator for measuring the sound wave isolation performance. It describes the ability of the laminated wall panel system to block sound waves. By accurately calculating the sound transmission loss, the sound insulation effect of the laminated wall panel system in practical applications can be evaluated, such as its performance in building sound insulation, automobile noise control, etc. This calculation not only helps to verify the effect of the system design, but also provides a basis for optimizing the design, so that the final laminated wall panel system can effectively control the transmission of sound waves and reduce noise in actual use, thereby improving the calculation accuracy of the sound transmission loss of the laminated wall panel. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments thereof made with reference to the following drawings:

[0064] Figure 1 A schematic flow chart of the steps of a semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to the present invention;

[0065] Figure 2 for Figure 1 Detailed step flow chart of S1 in FIG. DETAILED DESCRIPTION

[0066] The technical method of the present invention is described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by technicians in this field without creative work are within the scope of protection of the present invention.

[0067] To achieve this, please refer to Figure 1 to Figure 2 The present invention provides a semi-analytical method for calculating the sound transmission loss of a laminated wall panel, the method comprising the following steps:

[0068] By setting an acoustic plane wave excitation external force condition, and calculating the potential energy and kinetic energy of the laminated wall panel system based on the acoustic plane wave excitation external force condition, the acoustic excitation potential energy of the laminated wall panel system and the acoustic excitation kinetic energy of the laminated wall panel system are obtained;

[0069] Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall panel system, the displacement change control equation is derived by minimum action variation of the laminated wall panel system. It is assumed that the first-order Chebyshev polynomial expression containing unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by using the Rayleigh-Ritz method.

[0070] Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response and use Rayleigh integral to calculate the radiated sound power of the laminated wall panel to obtain the radiated sound power of the laminated wall panel;

[0071] Based on the acoustic plane wave excitation external force condition, the incident sound power and acoustic interlayer impedance of the laminated wall panel system are calculated, and the sound transmission loss is calculated to obtain the sound transmission loss of the laminated wall panel system.

[0072] In the embodiment of the present invention, please refer to Figure 1 FIG. 1 is a schematic diagram of the steps of a semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to the present invention. In this example, the semi-analytical method for calculating the sound transmission loss of a laminated wall panel includes the following steps:

[0073] S1: By setting the acoustic plane wave excitation external force condition, and calculating the potential energy and kinetic energy of the laminated wall panel system based on the acoustic plane wave excitation external force condition, the acoustic excitation potential energy of the laminated wall panel system and the acoustic excitation kinetic energy of the laminated wall panel system are obtained;

[0074] In an embodiment of the present invention, by using the external force conditions of acoustic plane wave excitation of the device in the computer simulation software, which includes defining the frequency, wavelength and speed of the acoustic plane wave and the corresponding air density, and inputting these parameters (that is, the external force conditions of acoustic plane wave excitation) into the acoustic simulation module in the laminated wall panel system, a laminated wall panel model under the acoustic plane wave excitation field is simulated and generated, and by measuring the pressure F applied to the laminated wall panel under the acoustic plane wave excitation field, the cross-sectional area A of the laminated wall panel where the pressure is applied, and at the same time using a displacement sensor or calculation software to record the length deformation ΔL of the wall panel under the acoustic plane wave excitation and the original length L0 of the wall panel before the excitation is applied, and then by substituting these data into the formula The corresponding elastic modulus is calculated in , and the boundary virtual spring potential energy of the laminated wall model under the acoustic plane wave excitation field is quantitatively calculated by combining the elastic modulus E of the laminated wall panel obtained by the previous quantitative calculation. The specific formula is: where k b is the virtual spring stiffness of the laminated wall panel boundary, δ is the displacement of the laminated wall panel boundary, and the virtual spring potential energy U of the laminated wall panel boundary is calculated. sp Secondly, by combining the elastic modulus E of the laminated wall panel obtained by quantitative calculation previously with the constitutive relation of the laminated wall panel (that is, the stress-strain relation σ=D, where D is the laminated wall panel stiffness matrix), the corresponding elastic modulus is decomposed and calculated to obtain the laminated wall panel stress σ and the laminated wall panel strain. The laminated wall panel strain energy is obtained by using the integral calculation method and combining the product of the laminated wall panel stress σ and the laminated wall panel strain to perform an integral operation in the laminated wall panel strain volume V. Then, the acoustic plane wave excitation pressure p(t) and the displacement u of the laminated wall panel model surface under the acoustic plane wave excitation field at different time points are measured or calculated, and the pressure p(t) and the displacement u are integrated within the surface area S of the laminated wall panel by using the integral calculation tool, so as to calculate the external excitation work W of the laminated wall panel. e =∫ S p(t)udS. And, by using mathematical calculation tools, the spring potential energy U sp and strain energy U st Add and subtract the external excitation work W e , and the acoustic excitation potential energy of the laminated wall system under the acoustic plane wave excitation field is summarized and calculated as U = U sp +U st -W e Finally, the displacement u under the excitation field determined previously is calculated by using the numerical integration tool to calculate the displacement change rate. And obtain the density ρ of the material on the laminated wall model, and at the same time obtain the displacement change speed by combining The material density ρ is integrated in the volume V to obtain the acoustic excitation kinetic energy of the laminated panel system:

[0075] S2: Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall panel system, the displacement change control equation is derived by minimum action variation of the laminated wall panel system. It is assumed that the first-order Chebyshev polynomial expression containing the unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by the Rayleigh-Ritz method;

[0076] In the embodiment of the present invention, the acoustic excitation potential energy U of the laminated wall panel system obtained by combining the previously quantified calculation is U=U st +U sp -W e and the acoustic excitation kinetic energy of the laminated panel system Combined with the mechanical response of the Lagrangian function, it can be seen that the Lagrangian function is the difference between the total potential energy and the kinetic energy (also known as UK) to describe the relationship between the kinetic potential energy of the laminated wall system. The previously determined kinetic potential energy description relationship is derived by using the principle of least action to solve the Lagrangian function with respect to the displacement field u, and the variational equation is set by the variational principle. To derive the corresponding displacement change control equation, and thus derive the displacement change control equation of the laminated wall panel system Secondly, the displacement change control equation of the laminated wall system derived previously is combined with the time response of the laminated wall system under the acoustic plane wave excitation field. The displacement field time response related unknown function extraction process is performed to extract the displacement field u into a specific time response form, and its time response form u(x, t) is assumed to be an unknown function of the displacement change x and time t, thereby obtaining the laminated wall panel displacement field time response unknown function u(x, t). Then, the first kind Chebyshev polynomial T is used to extract the laminated wall panel displacement field time response unknown function u(x, t) extracted previously. n (x) is assumed to represent the unknown function u(x,t) of the time response of the laminated wall displacement field as a linear combination of a series of Chebyshev polynomials, thereby assuming that the first kind of Chebyshev polynomial expression containing the unknown constants is generated. Where N is the polynomial order, C n is a constant to be determined, φ n (t) is the time response basis function. Further, the time response basis function φ can be n (t) is expanded to φ n (t) = A n cos(ωt)+B n sin(ωt), where ω is the frequency of the plane wave excitation, A n and B nare the cosine and sine variation coefficients of the time response, respectively. This embodiment requires the accurate calculation of the value of each variation coefficient. Special mathematical tools (such as Matlab or calculus tools) can be used to complete the expansion and coefficient calculation of the Chebyshev polynomial. In addition, the first-class Chebyshev polynomial expression containing the unknown constants generated by the previous assumption is substituted into the displacement variation control equation of the laminated wall panel system derived previously to obtain a displacement variation control equation containing the unknown constants C n The equations are solved by using the corresponding numerical calculation or analytical method of the Rayleigh-Ritz method, and finally the unknown constant C is obtained. n The specific value of n Specifically Among them U n is the acoustic external excitation in the time response basis function φ n The coefficient under (t).

[0077] S3: Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response and use Rayleigh integral to calculate the radiated sound power of the laminated wall panel to obtain the radiated sound power of the laminated wall panel;

[0078] In the embodiment of the present invention, the previously solved unknown constants are Substitute the first-order Chebyshev polynomial expression obtained previously with the unknown constants into The time response of the displacement field under plane wave excitation is solved in the simulation, so as to obtain the displacement field response of the laminated panel system under acoustic plane wave excitation. Then, the preset Rayleigh integral form is used to construct the calculation formula for the radiated sound power of the laminated wall system Substitute the previously solved displacement field response of the laminated panel system under acoustic plane wave excitation into the above radiated sound power calculation formula to Perform quantization calculations to calculate the square of the time derivative and expand it to simplify it to:

[0079]

[0080] Substitute it into the Rayleigh integral formula, and according to the Chebyshev polynomial T n (x) is usually orthogonal on S, which allows some of the integral forms to be simplified to Among them I n is the orthogonal integral constant of the Chebyshev polynomial. Since the integral is orthogonal, the integral term is non-zero only when n=m. The radiated sound power of the laminated panel is finally calculated.

[0081] S4: Based on the acoustic plane wave excitation external force condition, the incident sound power and acoustic interlayer impedance of the laminated wall panel system are calculated, and the sound transmission loss is calculated to obtain the sound transmission loss of the laminated wall panel system.

[0082] In an embodiment of the present invention, the density of the incident sound wave of the laminated wall panel is quantitatively calculated by obtaining the peak value of the incident sound pressure, air density and sound velocity of the laminated wall panel from the acoustic plane wave excitation external force conditions, and a suitable incident sound power calculation formula is formed by combining the calculated density of the incident sound wave of the laminated wall panel and the surface area parameters under the incident acoustic excitation in the laminated wall panel system to calculate the incident sound power of the laminated wall panel system, so as to quantitatively calculate the incident sound power value of the laminated wall panel, wherein the density of the incident sound wave can be calculated using the root mean square sound pressure value, air density and sound velocity, that is, And because the relationship between the root mean square sound pressure value and the peak sound pressure P0 is Therefore, the density of the incident sound wave on the laminated wall is The incident sound power of the laminated panel can be obtained by multiplying it with the surface area parameter S At the same time, the physical property parameters of each layer of the wall panel material in the laminated wall panel system are measured and analyzed by using corresponding measuring instruments (such as ultrasonic thickness gauges or vibration testing equipment), so as to statistically analyze and record the basic physical property parameters of each layer of the wall panel material according to the experimental measurement data or standard data table of each layer of the wall panel material, including characteristic parameters such as acoustic wave number, elastic modulus and thickness, and by using the air density and sound velocity previously obtained from the acoustic plane wave excitation external force conditions, and combining the physical property parameters of each layer of the wall panel material in the laminated wall panel system The acoustic impedance between each layer of the laminated wallboard system is quantitatively calculated by using the acoustic impedance values ​​between each layer of the wallboard material in the laminated wallboard system (including characteristic parameters such as acoustic wave number, elastic modulus and thickness), so as to calculate the change in acoustic interlayer impedance based on the acoustic interface theory. Secondly, the acoustic impedance values ​​between each layer of the wallboard material in the laminated wallboard system obtained by all previous quantitative calculations are accumulated layer by layer according to the hierarchical order of the laminated wallboard to quantitatively calculate the acoustic interlayer impedance of the laminated wallboard as a whole, thereby obtaining the total acoustic interlayer impedance of the laminated wallboard. Then, the sound transmission loss is quantitatively calculated by using the total acoustic interlayer impedance of the laminated wallboard obtained by the previous summary calculation and combining the incident sound power of the laminated wallboard and the radiated sound power of the laminated wallboard, and then substituting it into the calculation formula for the sound transmission loss. The sound transmission loss of the laminated wall panel system is accurately calculated, and finally the sound transmission loss of the laminated wall panel system is obtained.

[0083] Further, as an embodiment of the present invention, refer to Figure 2 As shown, Figure 1The detailed step flow diagram of S1 in this embodiment is as follows. In this embodiment, the acoustic plane wave excitation external force condition is set, and the potential energy and kinetic energy of the laminated wall panel system are calculated based on the acoustic plane wave excitation external force condition, including the following steps:

[0084] S11: by setting an acoustic plane wave excitation external force condition, and based on the acoustic plane wave excitation external force condition, performing acoustic plane wave excitation field modeling on the laminated wall panel system, so as to generate a laminated wall panel model under the acoustic plane wave excitation field;

[0085] In an embodiment of the present invention, by using the external force conditions of acoustic plane wave excitation of the device in the computer simulation software, which includes defining the frequency, wavelength and speed of the acoustic plane wave and the corresponding air density, and inputting these parameters (that is, the external force conditions of acoustic plane wave excitation) into the acoustic simulation module in the laminated wall panel system, then, constructing the laminated wall panel system to simulate under the set acoustic plane wave excitation condition field, and finally simulating and generating a laminated wall panel model under the acoustic plane wave excitation field, the model will show the influence of acoustic plane wave excitation on the laminated wall panel, including stress distribution and deformation.

[0086] S12: Determine the elastic modulus of the laminated panel model under the acoustic plane wave excitation field to obtain the elastic modulus of the laminated panel under the acoustic plane wave excitation field Where F is the applied pressure under the acoustic plane wave excitation field, A is the plane wave excitation cross-sectional area of ​​the laminated wall panel, ΔL is the length stress deformation of the laminated wall panel, and L0 is the original length of the laminated wall panel. Based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field, the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field is calculated to obtain the boundary virtual spring potential energy U of the laminated wall panel. sp ;

[0087] In the embodiment of the present invention, the pressure F applied to the laminated wall panel under the acoustic plane wave excitation field is measured, and the cross-sectional area A of the laminated wall panel where the pressure is applied is measured. At the same time, a displacement sensor or calculation software is used to record the length deformation ΔL of the wall panel under the acoustic plane wave excitation and the original length L0 of the wall panel before the excitation is applied. Then, by substituting these data into the formula The corresponding elastic modulus is calculated in , and finally the elastic modulus E of the laminated wall under the acoustic plane wave excitation field is obtained. At the same time, the boundary virtual spring potential energy of the corresponding laminated wall model under the acoustic plane wave excitation field is quantitatively calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field obtained by the previous quantitative calculation. The specific formula is: where k bis the virtual spring stiffness of the laminated wall panel boundary, δ is the displacement of the laminated wall panel boundary, and the virtual spring potential energy U of the laminated wall panel boundary is finally calculated. sp .

[0088] S13: The laminated wall panel stress σ and the laminated wall panel strain are obtained by decomposing the laminated wall panel elastic modulus E under the acoustic plane wave excitation field, and the wall panel strain energy of the laminated wall panel model under the acoustic plane wave excitation field is determined based on the laminated wall panel stress σ and the laminated wall panel strain to obtain the laminated wall panel strain energy Where V is the strain volume of the laminated wall panel, and the relationship between the laminated wall panel stress σ and the laminated wall panel strain is expressed by the laminated wall panel constitutive relationship σ=D, where D is the laminated wall panel stiffness matrix;

[0089] In an embodiment of the present invention, by combining the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field obtained by previous quantitative calculation and the constitutive relationship of the laminated wall panel (that is, the stress-strain relationship σ=D, where D is the laminated wall panel stiffness matrix), the corresponding elastic modulus is decomposed and calculated to obtain the laminated wall panel stress σ and the laminated wall panel strain. At the same time, by using an integral calculation method and combining the product between the laminated wall panel stress σ and the laminated wall panel strain, an integral operation is performed in the laminated wall panel strain volume V, and finally the laminated wall panel strain energy is obtained.

[0090] S14: Calculate the plane wave excitation external force work of the laminated wall model under the acoustic plane wave excitation field to obtain the laminated wall external excitation work W e =∫ S p(t)udS, where S is the surface area of ​​the laminated panel, p(t) is the acoustic plane wave excitation pressure at acoustic excitation time t, and u is the plane wave excitation displacement;

[0091] In the embodiment of the present invention, the acoustic plane wave excitation pressure p(t) and the displacement u of the laminated wall panel model surface under the acoustic plane wave excitation field at different time points are measured or calculated, and the pressure p(t) and the displacement u are integrated within the surface area S of the laminated wall panel by using an integral calculation tool, so as to calculate the external excitation work W of the laminated wall panel. e =∫ S p(t)udS.

[0092] S15: Based on the virtual spring potential energy U of the laminated wall boundary sp and the strain energy U of the laminated panel st The sum of the two minus the external excitation work W of the laminated panel e Perform a summary calculation of the potential energy of the wall panel system to obtain the acoustic excitation potential energy U of the laminated wall panel system;

[0093] In the embodiment of the present invention, the virtual spring potential energy U of the laminated wall panel boundary obtained by quantitative calculation is calculated by using a mathematical calculation tool. sp and the strain energy U of the laminated panel st Add and subtract the external excitation work W of the laminated panel e , and the total potential energy of the laminated panel system under the acoustic plane wave excitation field is calculated and obtained as U = U sp +U st -W e This process ensures that all relevant energy terms are accurately considered and calculated to reflect the total energy state of the laminated panel system under acoustic excitation, and finally the acoustic excitation potential energy U of the laminated panel system is obtained.

[0094] S16: Calculate the kinetic energy of the laminated panel system under the acoustic plane wave excitation field to obtain the acoustic excitation kinetic energy of the laminated panel system Where ρ is the density, is the displacement change velocity due to plane wave excitation.

[0095] In the embodiment of the present invention, the displacement u previously determined under the excitation field is calculated by using a numerical integration tool to calculate the displacement change speed: And obtain the density ρ of the material on the laminated wall model, and at the same time obtain the displacement change speed by combining The material density ρ is integrated in the volume V to obtain the acoustic excitation kinetic energy of the laminated panel system:

[0096] Further, the calculation of the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field includes the following steps:

[0097] Determine the virtual spring support boundary condition of the laminated wall panel model under the acoustic plane wave excitation field, and obtain the laminated wall panel spring support boundary condition determination result, wherein the laminated wall panel spring support boundary condition determination result is a fixed boundary condition or a hinged boundary condition;

[0098] In an embodiment of the present invention, a finite element analysis tool is used to analyze and determine the spring support boundary conditions of a previously established laminated wall panel model under an acoustic plane wave excitation field, so as to apply acoustic excitation to the model to analyze its response, and identify whether it is a fixed boundary or a hinged boundary based on the boundary performance of the wall panel in the acoustic wave field, that is, determine whether the corresponding boundary is a connecting boundary between two wall panel materials, so as to accurately identify the actual boundary conditions of the laminated wall panel model, and finally obtain the determination result of the spring support boundary conditions of the laminated wall panel, wherein the determination result of the spring support boundary conditions of the laminated wall panel is a fixed boundary condition or a hinged boundary condition.

[0099] Preferably, a virtual spring mechanical model is defined for the laminated wall panel model under the acoustic plane wave excitation field based on the fixed boundary condition or the hinged boundary condition to obtain an acoustically excited fixed boundary virtual spring mechanical model or an acoustically excited hinged boundary virtual spring mechanical model;

[0100] In an embodiment of the present invention, a virtual spring mechanical model is defined by combining a previously determined fixed boundary condition or a hinged boundary condition, so as to define the specific model of the corresponding laminated wall panel model under the acoustic plane wave excitation field according to whether the previously determined boundary condition is a fixed boundary or a hinged boundary. For a fixed boundary, its model is defined as a corresponding fixed boundary virtual spring mechanical model; and for a hinged boundary, its model is defined as a hinged boundary virtual spring mechanical model. This step utilizes structural mechanics analysis software, and the model is set according to the boundary conditions and the elastic modulus and geometric parameters of the laminated wall panel, and appropriate boundary conditions are set to match the actual support conditions, thereby ensuring that the boundary conditions of the model correctly reflect the actual physical environment, and finally obtaining an acoustically excited fixed boundary virtual spring mechanical model or an acoustically excited hinged boundary virtual spring mechanical model.

[0101] Preferably, the boundary virtual spring stiffness of the acoustically excited fixed boundary virtual spring mechanical model or the acoustically excited hinged boundary virtual spring mechanical model is calculated based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field to obtain the boundary virtual spring stiffness k of the laminated wall panel. b ;

[0102] In the embodiment of the present invention, the boundary virtual spring stiffness k of the previously defined virtual spring mechanical model is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field. b The quantitative calculation is performed by obtaining the relevant geometric parameters of the laminated wall, including the thickness h, Poisson's ratio v and boundary length L of the laminated wall. For the fixed boundary, the formula is used. The virtual spring stiffness is calculated for fixed boundary conditions, while for hinged boundaries the formula is used The calculation is performed and finally the accurate virtual spring stiffness k of the laminated panel boundary is quantitatively calculated according to the corresponding boundary conditions. b .

[0103] Preferably, based on the virtual spring stiffness k of the laminated panel boundary b The potential energy of the virtual springs at the boundary of the laminated panel model under the acoustic plane wave excitation field is calculated to obtain the potential energy of the virtual springs at the boundary of the laminated panel. where δ is the boundary displacement of the laminated panel.

[0104] In the embodiment of the present invention, the virtual spring stiffness k of the laminated wall panel boundary obtained by combining the previously quantified calculation b The spring potential energy of the laminated panel model corresponding to the acoustic plane wave excitation field is quantified to measure or calculate the actual displacement δ of the laminated panel boundary, and the calculation formula of the spring potential energy is applied The stiffness k b The virtual spring potential energy state of the laminated panel under acoustic excitation is accurately reflected by substituting the displacement δ into the calculation, and finally the virtual spring potential energy of the laminated panel boundary is obtained.

[0105] Furthermore, the virtual spring stiffness k of the laminated panel boundary is b Specifically:

[0106] If the acoustically excited fixed boundary virtual spring mechanical model is determined, the virtual spring stiffness of the fixed boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary: Where h is the thickness of the laminated wall, v is the Poisson's ratio, and L is the boundary length of the laminated wall;

[0107] In an embodiment of the present invention, if the boundary condition of the corresponding acoustic excitation is determined to be a fixed boundary, that is, when the generated virtual spring mechanical model is determined to be an acoustically excited fixed boundary virtual spring mechanical model, then the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field obtained by combining the previously quantified calculation and obtaining the thickness h, Poisson's ratio v and boundary length L of the corresponding laminated wall panel, these parameters are usually obtained through material testing or design documents, and these parameters are substituted into the virtual spring stiffness calculation formula under the fixed boundary condition: The calculation is performed in which E (elastic modulus) is used to quantify the stiffness of the laminated panel material, h (thickness) determines the effect of the panel thickness on the stiffness, and v (Poisson's ratio) and L (boundary length) are used to correct for changes in stiffness caused by the geometry and mechanical behavior of the material.

[0108] If the virtual spring mechanical model of the acoustically excited hinged boundary is determined, the virtual spring stiffness of the hinged boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary:

[0109] In an embodiment of the present invention, if the boundary condition of the corresponding acoustic excitation is determined to be a hinged boundary, that is, when the generated virtual spring mechanical model is determined to be an acoustically excited hinged boundary virtual spring mechanical model, then the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field obtained by combining the previously quantified calculation and the thickness h and boundary length L of the corresponding laminated wall panel are obtained. These parameters are usually obtained through material testing or design documents, and these parameters are substituted into the virtual spring stiffness calculation formula under the hinged boundary condition: The calculation is performed in , where the elastic modulus E reflects the elastic properties of the material, the thickness h affects the elastic response, and the boundary length L affects the stiffness value, which is used to accurately describe the material behavior under the hinged boundary.

[0110] Furthermore, the displacement change control equation is derived by performing minimum action variation on the laminated wall panel system based on the acoustic excitation potential energy and the acoustic excitation kinetic energy of the laminated wall panel system, assuming that the first-order Chebyshev polynomial expression containing the unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by using the Rayleigh-Ritz method, including the following steps:

[0111] Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall system, the kinetic potential energy relationship of the laminated wall system is described using the Lagrangian function to obtain the Lagrangian kinetic potential energy description relationship of the laminated wall system.

[0112] In the embodiment of the present invention, the acoustic excitation potential energy U of the laminated wall panel system obtained by combining the previously quantified calculation is U=U st +U sp -W e and the acoustic excitation kinetic energy of the laminated panel system Combined with the mechanical response of the Lagrangian function, it can be seen that the Lagrangian function is the difference between the total potential energy and the kinetic energy (ie UK) to describe the relationship between the kinetic potential energy of the laminated wall system. Finally, the Lagrangian kinetic potential energy description relationship of the laminated wall is obtained as follows:

[0113]

[0114] The Lagrangian kinetic potential energy of the laminated panel is described by Perform a minimum action variational derivation to generate the governing equations for the displacement changes of the laminated panel system

[0115] In the embodiment of the present invention, the Lagrangian kinetic potential energy of the laminated wall panel previously determined is described by the least action principle. The variational derivation is performed to solve the variation of the Lagrangian function with respect to the displacement field u, and the variational equation is set according to the variational principle. To derive the corresponding displacement change control equation, and finally derive the displacement change control equation of the laminated wall panel system

[0116] Control equations for displacement changes of laminated panel systems Performing displacement field time response unknown function extraction processing to obtain the laminated wall panel displacement field time response unknown function u(x,t), where x is the displacement change;

[0117] In the embodiment of the present invention, the displacement change control equation of the laminated wall panel system derived previously is obtained by combining the time response of the laminated wall panel system under the acoustic plane wave excitation field. The unknown functions related to the time response of the displacement field are extracted to extract the displacement field u into a specific time response form, and its time response form u(x, t) is assumed to be an unknown function of the displacement change x and time t, and finally the unknown function u(x, t) of the time response of the laminated wall panel displacement field is obtained.

[0118] The first kind Chebyshev polynomial T is used to calculate the unknown function u(x, t) of the time response of the displacement field of the laminated wall. n (x) Assume that we represent the first kind of Chebyshev polynomials containing the constants to be determined. Where N is the polynomial order, C n is a constant to be determined, φ n (t) is the time response basis function, where the time response basis function φ n (t) is further expanded to φ n (t) = A n cos(ωt)+B n sin(ωt), where ω is the frequency of the plane wave excitation, A n is the cosine variation coefficient of the time response, B n is the sinusoidal variation coefficient of the time response;

[0119] In the embodiment of the present invention, the first kind Chebyshev polynomial T is used to calculate the unknown function u(x, t) of the time response of the displacement field of the laminated wall panel extracted previously. n (x) is assumed to represent the unknown function u(x,t) of the time response of the laminated wall displacement field as a linear combination of a series of Chebyshev polynomials, and finally the first kind of Chebyshev polynomial expression containing unknown constants is generated. Where N is the polynomial order, C n is a constant to be determined, φ n (t) is the time response basis function. Further, the time response basis function φ can be n (t) is expanded to φ n (t) = A ncos(ωt)+B n sin(ωt), where ω is the frequency of the plane wave excitation, A n and B n They are the cosine and sine variation coefficients of the time response respectively. This embodiment requires accurate calculation of the value of each variation coefficient. Special mathematical tools (such as Matlab or calculus tools) can be used to complete the expansion of the Chebyshev polynomial and coefficient calculation.

[0120] By converting the first kind Chebyshev polynomial expression containing the unknown constants Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants.

[0121] In the embodiment of the present invention, the first-order Chebyshev polynomial expression containing unknown constants generated by the previous assumption is Substitute into the previously derived displacement variation control equation of the laminated panel system to obtain a constant C n The equations are solved by using the corresponding numerical calculation or analytical method of the Rayleigh-Ritz method, and finally the unknown constant C is obtained. n The specific value of .

[0122] Furthermore, the Lagrangian kinetic potential energy of the laminated wall is described by The derivation of the minimum action variational method includes the following steps:

[0123] The Lagrangian kinetic potential energy of the laminated panel is described by Perform minimum action Lagrangian analysis to construct the basic form of the Lagrangian equation

[0124] In the embodiment of the present invention, the corresponding action G can be defined as the Lagrangian kinetic potential energy description relation of the corresponding laminated wall panel by using the principle of least action: Integration over time t: Where t1 is the initial time of action, t2 is the end time of action. For the physical process of acoustic excitation of laminated panels, it can be assumed that the Lagrangian kinetic potential energy of laminated panels can be described by: where q is the generalized displacement, is the generalized displacement velocity, and according to the principle of least action, the action G is made to obtain the extreme value condition, then G is varied with respect to q to obtain And using Taylor expansion we get in By integration by parts (also Move out of the integral), and use the boundary conditions (the perturbation is zero on the boundary), we can get: Since dq is arbitrary, the variation dG must be zero, that is, This is also the standard form of the Lagrange equation, and finally the basic form of the Lagrange equation is constructed.

[0125] Preferably, the basic form of the Lagrange equation is In The velocity field is varied to obtain

[0126] In the embodiment of the present invention, the basic form of the Lagrange equation obtained by the previous analysis is In The velocity field is derived by variational method to describe the Lagrangian kinetic potential energy of the laminated panel. The velocity field The relevant variable parameters are differentiated by the velocity field, and the other variables irrelevant to the velocity field are all zero. Finally, we can get

[0127] Preferably, the basic form of the Lagrange equation is In Perform a variational derivation of the displacement field to obtain

[0128] In the embodiment of the present invention, the basic form of the Lagrange equation obtained by the previous analysis is In The variational derivation of the displacement field is carried out to describe the Lagrangian kinetic potential energy of the laminated wall. The variable parameters related to the displacement field (i.e., U st and W e ) is used to differentiate the displacement field, where The expression of strain can be expressed by the gradient of the displacement field u. Under the assumption of small deformation, the strain can be here is the gradient of the displacement field u. In order to obtain the matrix form of stiffness, the strain is also expressed in matrix form and substituted into the calculation formula of strain energy: where · represents the inner product in matrix form, so it can be transformed into therefore The variational form of in addition, Finally, we get

[0129] Preferably, as well as Substitute into the basic form of the Lagrange equation and simplify the equation to generate the displacement change control equation of the laminated wall system

[0130] In the embodiment of the present invention, the previously obtained variational derivation is as well as Substituting into the basic form of Lagrange equation The equations are simplified and finally the displacement change control equation of the laminated wall system is simplified and generated.

[0131] Furthermore, the first kind Chebyshev polynomial expression containing the unknown constants is Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants, including the following steps:

[0132] By transforming the displacement change control equation of the laminated panel system into Perform similar treatment on the second-order partial differential equation to obtain the similar partial differential equation for the displacement control of the laminated wall panel in is the operator related to the stiffness of the laminated panel, f(t) is the plane wave excitation;

[0133] In the embodiment of the present invention, for the convenience of calculation, the specific form of the displacement change control equation of the laminated wall panel system determined previously is It is similar to a second-order partial differential equation, and finally the displacement control of the laminated wall panel is similar to the partial differential equation in is the operator related to the stiffness of the laminated panel, and f(t) is the plane wave excitation.

[0134] Preferably, the first kind Chebyshev polynomial expression containing the unknown constants is expressed by Substitute the similar partial equation of displacement control of laminated wall into and separate it into the spatial part and the temporal part to obtain the time-space separation expansion equation of the laminated panel displacement:

[0135]

[0136] In the embodiment of the present invention, the first kind Chebyshev polynomial expression containing the unknown constants obtained previously is obtained. Substitute into the similar partial equation of displacement control of the laminated wall that has been similarly determined u, and separate the space part and time part in it, and finally expand and calculate to obtain the time-space separation expansion equation of the laminated wall displacement

[0137] Preferably, the time response basis function φ n The further expansion of (t) is substituted into the time-space separation expansion equation of the laminated wall displacement and all the equations containing C are separated. n The items get:

[0138]

[0139] In the embodiment of the present invention, the time response basis function φ in the time-space separation expansion equation of the laminated wall panel displacement after time-space separation expansion is used. n (t) = A n cos(ωt)+B n Substitute sin(ωt) into the corresponding place to solve the time integral, and convert the corresponding A n cos(ωt)+B n sin(ωt) is rearranged and substituted back to φ n (t), and simultaneously separately integrate all the n The data items are finally sorted out

[0140] Preferably, the above equation is converted into each polynomial T n (x) and balance the right side of the above equation f(t) with the polynomial T n (x) is expanded to: Among them U n is the time response basis function φ of f(t) n The coefficient under (t);

[0141] In the embodiment of the present invention, the equation obtained after the above separation and integration is converted into each polynomial T n By balancing the coefficients of the terms of (x), the right side of the equation f(t) can be expressed in polynomial expansion form as Among them U n is the time response basis function φ of f(t) n (t), and substituting into this representation, we get:

[0142]

[0143] Preferably, multiply both sides of the above equation by T m (x) and integrate with respect to x to obtain:

[0144]

[0145] In the embodiment of the present invention, both sides of the equation obtained by the above balancing determination are multiplied by T m (x) and integrate x to obtain:

[0146]

[0147] Preferably, using the polynomial T n The orthogonality of (x) can simplify the above integral equation to:

[0148]

[0149] In the embodiment of the present invention, by using the polynomial T n Orthogonality of (x) Among them I n is the orthogonal integral constant of the Chebyshev polynomial. Since the integral is orthogonal, the integral term is non-zero only when n = m to obtain And replace I on both sides of the equation n By making an appointment, we can finally simplify it to

[0150] Preferably, the above equation is solved using the Rayleigh-Ritz method to obtain the unknown constant:

[0151]

[0152] In the embodiment of the present invention, the simplified equation is approximately solved by using the Rayleigh-Ritz method to obtain And because the left side of the equation obtained above is - It is not zero, so we can solve for the unknown constant C n The specific values ​​are:

[0153]

[0154] Furthermore, the step of substituting the undetermined constant into the first-order Chebyshev polynomial expression containing the undetermined constant to solve the plane wave excitation response and calculating the radiated sound power of the laminated wall panel by using Rayleigh integral includes the following steps:

[0155] Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response, and obtain the displacement field response of the laminated wall panel system under acoustic plane wave excitation, where the displacement field response of the laminated wall panel system is specifically:

[0156] In the embodiment of the present invention, the previously solved unknown constants are Substitute the first-order Chebyshev polynomial expression obtained previously with the unknown constants into The time response of the displacement field under plane wave excitation is solved in the simulation, and finally the displacement field response of the laminated panel system under acoustic plane wave excitation is obtained.

[0157] The radiated sound power of the laminated panel system under the excitation of acoustic plane waves is calculated by using Rayleigh integral to obtain the radiated sound power of the laminated panel. Where ρ0 is the air density, c0 is the speed of sound, I n is the orthogonal integration constant of the Chebyshev polynomial.

[0158] In the embodiment of the present invention, the preset Rayleigh integral form is used to construct a calculation formula for the radiated sound power of the laminated wall panel system. Substitute the previously solved displacement field response of the laminated panel system under acoustic plane wave excitation into the above radiated sound power calculation formula to Perform quantitative calculations to calculate the square of the time derivative and expand it to simplify it to Substitute it into the Rayleigh integral formula According to the Chebyshev polynomial T n (x) is usually orthogonal in S, which simplifies the integral to Among them I n is the orthogonal integral constant of the Chebyshev polynomial. Since the integral is orthogonal, the integral term is non-zero only when n=m. The radiated sound power of the laminated panel is finally calculated.

[0159] Furthermore, the calculation of incident sound power and acoustic interlayer impedance of the laminated wall panel system based on the acoustic plane wave excitation external force condition and the calculation of sound transmission loss includes the following steps:

[0160] Based on the acoustic plane wave excitation external force condition, the incident sound power of the laminated wall panel system is calculated using the incident sound power calculation formula to obtain the incident sound power of the laminated wall panel;

[0161] In an embodiment of the present invention, the density of the incident sound wave of the laminated wall panel is quantitatively calculated by obtaining the peak value of the incident sound pressure, air density and sound velocity of the laminated wall panel from the acoustic plane wave excitation external force conditions, and a suitable incident sound power calculation formula is formed by combining the calculated density of the incident sound wave of the laminated wall panel and the surface area parameters under the incident acoustic excitation in the laminated wall panel system to calculate the incident sound power of the laminated wall panel system, so as to quantitatively calculate the incident sound power value of the laminated wall panel, wherein the density of the incident sound wave can be calculated using the root mean square sound pressure value, air density and sound velocity, that is, And because the relationship between the root mean square sound pressure value and the peak sound pressure P0 is Therefore, the density of the incident sound wave on the laminated wall is Finally, the product of the incident sound power of the laminated panel and the surface area parameter S is obtained.

[0162] The incident sound power calculation formula is as follows:

[0163]

[0164] Where P in is the incident sound power of the laminated wall panel, I is the incident sound density of the laminated wall panel, S is the surface area of ​​the laminated wall panel, P0 is the incident sound pressure peak of the laminated wall panel, ρ0 is the air density, and c0 is the sound speed;

[0165] The present invention obtains an incident sound power calculation formula by using a specific mathematical model and verifying it, which is used to calculate the incident sound power of the laminated wall panel system. The formula fully considers the incident sound power P of the laminated wall panel. in , the incident sound density I of the laminated wall, the surface area S of the laminated wall, the peak value of the incident sound pressure P0 of the laminated wall, the air density ρ0, the sound speed c0, according to the incident sound power P of the laminated wall in The correlation between the above parameters constitutes a functional relationship This formula can realize the incident sound power calculation process of the laminated wall panel system, and can also help determine the initial energy of the acoustic plane wave entering the laminated wall panel system, which is the basic data for acoustic analysis and ensures that other calculations (such as sound transmission loss) have an accurate starting point. At the same time, the incident sound power can be accurately calculated through this formula, which is crucial for understanding the intensity of acoustic plane waves and how sound energy propagates in the laminated wall panel system, which helps to better design and adjust acoustic materials and structures to meet specific sound insulation or sound absorption requirements. In addition, the incident sound power is a key parameter for predicting acoustic performance (such as transmission loss). Accurate incident sound power data makes the calculation of acoustic interlayer impedance and sound transmission loss more reliable, which can improve the accuracy of the prediction of the acoustic performance of the overall system, thereby improving the accuracy and applicability of the incident sound power calculation formula.

[0166] Performing physical property analysis on each layer of siding material in the laminated siding system to obtain physical property parameters of each layer of siding material in the laminated siding system;

[0167] In an embodiment of the present invention, the physical property parameters of each layer of wall panel material in the laminated wall panel system are measured and analyzed by using corresponding measuring instruments (such as ultrasonic thickness gauges or vibration testing equipment), so that according to the experimental measurement data or standard data tables of each layer of wall panel material, the basic physical property parameters of each layer of wall panel material, including characteristic parameters such as acoustic wave number, elastic modulus and thickness, are statistically analyzed and recorded, and finally the physical property parameters of each layer of wall panel material in the laminated wall panel system are obtained.

[0168] Based on the acoustic plane wave excitation external force conditions and the physical property parameters of each layer of the wall panel material in the laminated wall panel system, the acoustic interlayer impedance between each layer of the wall panel material in the laminated wall panel system is calculated to obtain the acoustic impedance value between each layer of the wall panel material in the laminated wall panel system;

[0169] In an embodiment of the present invention, by using the air density and sound speed previously obtained from the external force conditions of acoustic plane wave excitation, and combining the physical property parameters of each layer of wall panel material in the laminated wall panel system (including characteristic parameters such as acoustic wave number, elastic modulus and thickness), a suitable acoustic interlayer impedance calculation formula is constructed to quantitatively calculate the acoustic impedance between each corresponding layer of wall panel material in the laminated wall panel system, so as to calculate the change value of the acoustic interlayer impedance according to the acoustic interface theory, and finally obtain the acoustic impedance value between each layer of wall panel material in the laminated wall panel system.

[0170] The acoustic impedance values ​​between each layer of wall panel materials in the laminated wall panel system are calculated and summarized to obtain the total acoustic impedance between the laminated wall panels;

[0171] In an embodiment of the present invention, the acoustic impedance values ​​between each layer of wall panel materials in the laminated wall panel system obtained by all previous quantitative calculations are accumulated layer by layer according to the hierarchical order of the laminated wall panels to quantitatively calculate the acoustic interlayer impedance of the laminated wall panels as a whole, and finally the total acoustic interlayer impedance of the laminated wall panels is obtained.

[0172] Based on the total acoustic interlayer impedance of the laminated wall panel, the incident sound power of the laminated wall panel and the radiated sound power of the laminated wall panel are calculated to obtain the sound transmission loss of the laminated wall panel system.

[0173] In the embodiment of the present invention, the acoustic interlayer total impedance of the laminated wall panel obtained by the previous summary calculation is combined with the incident sound power of the laminated wall panel and the radiated sound power of the laminated wall panel to quantify the sound transmission loss, and substitute it into the calculation formula of the sound transmission loss: The sound transmission loss of the laminated wall panel system is accurately calculated, and finally the sound transmission loss of the laminated wall panel system is obtained.

[0174] Furthermore, the acoustic interlayer impedance of the wall panel is calculated by using an acoustic interlayer impedance calculation formula, which is specifically:

[0175]

[0176] In the formula, κ ij is the acoustic impedance between the i-th and j-th wallboard materials in the laminated wallboard system, i and j are the wallboard layer index parameters of the laminated wallboard system, ρ0 is the air density, c0 is the sound speed, h i is the thickness of the i-th layer of siding material, h j is the thickness of the j-th layer of siding material, a i is the acoustic wave number of the i-th layer of wall material, b i is the acoustic wave elastic modulus of the i-th layer wall panel material, a j is the acoustic wave number of the jth layer of wall panel material, b j is the acoustic wave elastic modulus of the j-th layer wall panel material.

[0177] The present invention obtains an acoustic interlayer impedance calculation formula by using a specific mathematical model and after verification, which is used to calculate the acoustic interlayer impedance of each layer of wallboard materials in the laminated wallboard system. The formula fully considers the acoustic impedance value κ between the i-th layer and the j-th layer of wallboard materials in the laminated wallboard system. ij , the panel layer index parameters i and j of the laminated panel system, air density ρ0, sound speed c0, thickness h of the i-th panel material i , the thickness of the j-th layer of wall material h j , the acoustic wave number a of the i-th layer of wall material i , the acoustic wave elastic modulus b of the i-th layer wall material i , the acoustic wave number a of the jth layer of wall material j , the acoustic wave elastic modulus b of the jth layer wall material j , according to the acoustic impedance value κ between the i-th and j-th layer wall materials in the laminated wall system ij The correlation between the above parameters constitutes a functional relationship This formula can realize the calculation process of the acoustic interlayer impedance of the wall panels between each layer of wall panel materials in the laminated wall panel system. The acoustic interlayer impedance calculation formula can accurately evaluate the acoustic impedance between different layers in the laminated wall panel system by considering the physical property parameters of each layer of wall panel material (that is, parameters such as material thickness, acoustic wave number and elastic modulus). This helps to understand the acoustic behavior of the laminated wall panel system, including the propagation characteristics and impedance matching of sound waves between different layers. This accurate evaluation is crucial for designing an effective acoustic isolation system. Through detailed calculation of the acoustic interlayer impedance, the design of the laminated wall panels can be optimized, so that the material selection and hierarchical structure of the wall panels can be adjusted according to the calculation results, thereby improving the acoustic isolation effect or achieving specific acoustic performance requirements, thereby providing an effective tool to analyze and predict the propagation and reflection characteristics of sound waves between different layers, providing a scientific basis for the subsequent sound transmission loss calculation process.

[0178] The above description is only a specific embodiment of the present invention, so that those skilled in the art can understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but should conform to the widest scope consistent with the principles and novel features invented herein.

Claims

1. A semi-analytical method for calculating the sound transmission loss of a laminated wall panel, characterized in that: The following steps are involved: By setting an acoustic plane wave excitation external force condition, and calculating the potential energy and kinetic energy of the laminated wall panel system based on the acoustic plane wave excitation external force condition, the acoustic excitation potential energy of the laminated wall panel system and the acoustic excitation kinetic energy of the laminated wall panel system are obtained; Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall panel system, the displacement change control equation is derived by minimum action variation of the laminated wall panel system. It is assumed that the first-order Chebyshev polynomial expression containing unknown constants is substituted into the displacement change control equation, and the unknown constants are determined by using the Rayleigh-Ritz method. Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response and use Rayleigh integral to calculate the radiated sound power of the laminated wall panel to obtain the radiated sound power of the laminated wall panel; Based on the acoustic plane wave excitation external force condition, the incident sound power and acoustic interlayer impedance of the laminated wall panel system are calculated, and the sound transmission loss is calculated to obtain the sound transmission loss of the laminated wall panel system.

2. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 1, characterized in that: The method of setting an acoustic plane wave excitation external force condition and calculating the potential energy and kinetic energy of the laminated wall panel system based on the acoustic plane wave excitation external force condition comprises the following steps: By setting an acoustic plane wave excitation external force condition, and based on the acoustic plane wave excitation external force condition, performing acoustic plane wave excitation field modeling on the laminated wall panel system, a laminated wall panel model under the acoustic plane wave excitation field is generated; The elastic modulus of the laminated panel model under the acoustic plane wave excitation field is determined to obtain the elastic modulus of the laminated panel under the acoustic plane wave excitation field. Where F is the applied pressure under the acoustic plane wave excitation field, A is the plane wave excitation cross-sectional area of ​​the laminated wall panel, ΔL is the length stress deformation of the laminated wall panel, and L0 is the original length of the laminated wall panel. Based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field, the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field is calculated to obtain the boundary virtual spring potential energy U of the laminated wall panel. sp ; The laminated wall panel stress σ and the laminated wall panel strain ∈ are obtained by decomposing the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field, and the wall panel strain energy of the laminated wall panel model under the acoustic plane wave excitation field is determined based on the laminated wall panel stress σ and the laminated wall panel strain ∈ to obtain the laminated wall panel strain energy Where V is the strain volume of the laminated wall panel, and the relationship between the laminated wall panel stress σ and the laminated wall panel strain ∈ is expressed by the laminated wall panel constitutive relation σ=D∈, where D is the laminated wall panel stiffness matrix; The plane wave excitation external force work of the laminated wall model under the acoustic plane wave excitation field is calculated, and the external excitation work W of the laminated wall is obtained. e =∫ S p(t)udS, where S is the surface area of ​​the laminated panel, p(t) is the acoustic plane wave excitation pressure at acoustic excitation time t, and u is the plane wave excitation displacement; According to the potential energy U of the virtual spring at the boundary of the laminated wall sp and the strain energy U of the laminated panel st The sum of the external excitation work W of the laminated panel is subtracted e Perform a summary calculation of the potential energy of the wall panel system to obtain the acoustic excitation potential energy U of the laminated wall panel system; The kinetic energy of the laminated panel system is calculated for the laminated panel model under the acoustic plane wave excitation field to obtain the acoustic excitation kinetic energy of the laminated panel system. Where ρ is the density, is the displacement change velocity due to plane wave excitation.

3. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 2, characterized in that: The method of calculating the boundary virtual spring potential energy of the laminated wall panel model under the acoustic plane wave excitation field based on the elastic modulus E of the laminated wall panel under the acoustic plane wave excitation field comprises the following steps: Determine the virtual spring support boundary condition of the laminated wall panel model under the acoustic plane wave excitation field, and obtain the laminated wall panel spring support boundary condition determination result, wherein the laminated wall panel spring support boundary condition determination result is a fixed boundary condition or a hinged boundary condition; Based on the fixed boundary condition or the hinged boundary condition, a virtual spring mechanical model is defined for the laminated wall panel model under the acoustic plane wave excitation field to obtain an acoustically excited fixed boundary virtual spring mechanical model or an acoustically excited hinged boundary virtual spring mechanical model; Based on the elastic modulus E of the laminated wall under the acoustic plane wave excitation field, the boundary virtual spring stiffness of the acoustically excited fixed boundary virtual spring mechanical model or the acoustically excited hinged boundary virtual spring mechanical model is calculated to obtain the boundary virtual spring stiffness k of the laminated wall b ; Based on the virtual spring stiffness k of the laminated panel boundary b The potential energy of the virtual springs at the boundary of the laminated panel model under the acoustic plane wave excitation field is calculated to obtain the potential energy of the virtual springs at the boundary of the laminated panel. where δ is the boundary displacement of the laminated panel.

4. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 3, characterized in that: The virtual spring stiffness k of the laminated panel boundary b Specifically: If the acoustically excited fixed boundary virtual spring mechanical model is determined, the virtual spring stiffness of the fixed boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary: Where h is the thickness of the laminated wall, v is the Poisson's ratio, and L is the boundary length of the laminated wall; If the virtual spring mechanical model of the acoustically excited hinged boundary is determined, the virtual spring stiffness of the hinged boundary is calculated by combining the elastic modulus E of the laminated wall under the acoustic plane wave excitation field to obtain the virtual spring stiffness of the laminated wall boundary:

5. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 1, characterized in that: The method of performing minimum action variation on the laminated wall panel system based on the acoustic excitation potential energy and the acoustic excitation kinetic energy of the laminated wall panel system to derive the displacement change control equation, assuming that the first-order Chebyshev polynomial expression containing the unknown constants is substituted into the displacement change control equation, and using the Rayleigh-Ritz method to determine the unknown constants includes the following steps: Based on the acoustic excitation potential energy and acoustic excitation kinetic energy of the laminated wall system, the kinetic potential energy relationship of the laminated wall system is described using the Lagrangian function to obtain the Lagrangian kinetic potential energy description relationship of the laminated wall system. The Lagrangian kinetic potential energy of the laminated panel is described by Perform a minimum action variational derivation to generate the governing equations for the displacement changes of the laminated panel system Control equations for displacement changes of laminated panel systems Performing displacement field time response unknown function extraction processing to obtain the laminated wall panel displacement field time response unknown function u(x,t), where x is the displacement change; The first kind Chebyshev polynomial T is used to calculate the unknown function u(x, t) of the time response of the displacement field of the laminated wall. n (x) Assume that we represent the first kind of Chebyshev polynomials containing the constants to be determined. Where N is the polynomial order, C n is a constant to be determined, φ n (t) is the time response basis function, where the time response basis function φ n (t) is further expanded to φ n 9t)=A n cos(ωt)+B n sin(ωt), where ω is the frequency of the plane wave excitation, A n is the cosine variation coefficient of the time response, B n is the sinusoidal variation coefficient of the time response; By converting the first kind Chebyshev polynomial expression containing the unknown constants Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants.

6. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 5, characterized in that: The Lagrangian kinetic potential energy of the laminated wall is described by the following relation: The derivation of the minimum action variational method includes the following steps: The Lagrangian kinetic potential energy of the laminated panel is described by Perform minimum action Lagrangian analysis to construct the basic form of the Lagrangian equation The basic form of the Lagrange equation In The velocity field is varied to obtain The basic form of the Lagrange equation In Perform a variational derivation of the displacement field to obtain Will as well as Substitute into the basic form of the Lagrange equation and simplify the equation to generate the displacement change control equation of the laminated wall system 7. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 5, characterized in that: The first kind Chebyshev polynomial expression containing the unknown constants is described by Substitute into the displacement change control equation of the laminated panel system The Rayleigh-Ritz method is used to solve the unknown constants, including the following steps: By transforming the displacement change control equation of the laminated panel system into Perform similar treatment on the second-order partial differential equation to obtain the similar partial differential equation for the displacement control of the laminated wall panel in is the operator related to the stiffness of the laminated panel, f(t) is the plane wave excitation; By converting the first kind Chebyshev polynomial expression containing the unknown constants Substitute the similar partial equation of displacement control of laminated wall into and separate it into the spatial part and the temporal part to obtain the time-space separation expansion equation of the laminated wall displacement The time response basis function φ n The further expansion of (t) is substituted into the time-space separation expansion equation of the laminated wall displacement and all the equations containing C are separated. n The items get: Transform the above equation into each polynomial T n (x) and balance the right side of the above equation f(t) with the polynomial T n (x) is expanded to: Among them U n is the time response basis function φ of f(t) n The coefficient under (t); Multiply both sides of the above equation by T m (x) and integrate with respect to x to obtain: Using polynomial T n The orthogonality of (x) can simplify the above integral equation to: The above equation is solved using the Rayleigh-Ritz method to obtain the unknown constant 8. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 1, characterized in that: Substituting the undetermined constant into the first-order Chebyshev polynomial expression containing the undetermined constant to solve the plane wave excitation response and using Rayleigh integral to calculate the radiated sound power of the laminated wall panel includes the following steps: Substitute the unknown constants into the first kind Chebyshev polynomial expression containing the unknown constants to solve the plane wave excitation response, and obtain the displacement field response of the laminated wall panel system under acoustic plane wave excitation, where the displacement field response of the laminated wall panel system is specifically: The radiated sound power of the laminated panel system under the excitation of acoustic plane waves is calculated by using Rayleigh integral to obtain the radiated sound power of the laminated panel. Where ρ0 is the air density, c0 is the speed of sound, I n is the orthogonal integration constant of the Chebyshev polynomial.

9. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 1, characterized in that: The method of calculating the incident sound power and acoustic interlayer impedance of the laminated wall panel system based on the acoustic plane wave excitation external force condition and calculating the sound transmission loss includes the following steps: Based on the acoustic plane wave excitation external force condition, the incident sound power of the laminated wall panel system is calculated using the incident sound power calculation formula to obtain the incident sound power of the laminated wall panel; The incident sound power calculation formula is as follows: Where P in is the incident sound power of the laminated wall panel, I is the incident sound density of the laminated wall panel, S is the surface area of ​​the laminated wall panel, P0 is the incident sound pressure peak of the laminated wall panel, ρ0 is the air density, and c0 is the sound speed; Performing physical property analysis on each layer of siding material in the laminated siding system to obtain physical property parameters of each layer of siding material in the laminated siding system; Based on the acoustic plane wave excitation external force conditions and the physical property parameters of each layer of the wall panel material in the laminated wall panel system, the acoustic interlayer impedance between each layer of the wall panel material in the laminated wall panel system is calculated to obtain the acoustic impedance value between each layer of the wall panel material in the laminated wall panel system; The acoustic impedance values ​​between each layer of wall panel materials in the laminated wall panel system are calculated and summarized to obtain the total acoustic impedance between the laminated wall panels; Based on the total acoustic interlayer impedance of the laminated wall panel, the incident sound power of the laminated wall panel and the radiated sound power of the laminated wall panel are calculated to obtain the sound transmission loss of the laminated wall panel system.

10. The semi-analytical method for calculating the sound transmission loss of a laminated wall panel according to claim 9, characterized in that: The acoustic interlayer impedance of the wall panel is calculated by the acoustic interlayer impedance calculation formula, and the acoustic interlayer impedance calculation formula is specifically: In the formula, κ ij is the acoustic impedance between the i-th and j-th wallboard materials in the laminated wallboard system, i and j are the wallboard layer index parameters of the laminated wallboard system, ρ0 is the air density, c0 is the sound speed, h i is the thickness of the i-th layer of siding material, h j is the thickness of the j-th layer of siding material, a i is the acoustic wave number of the i-th layer of wall material, b i is the acoustic wave elastic modulus of the i-th layer wall panel material, a j is the acoustic wave number of the jth layer of wall panel material, b j is the acoustic wave elastic modulus of the j-th layer wall panel material.

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