Wave finite element and boundary element mixed composite board structure sound insulation performance prediction method

Abstract

The invention provides a wave finite element and boundary element mixed composite board structure sound insulation performance prediction method, and the method belongs to the acoustics field, and comprises the steps: carrying out the post-processing of a wave finite element model based on the wave finite element model of a composite board structure and a corresponding equivalent nodal force, and obtaining the wave finite element equation of the whole composite board structure; based on a sound-structure coupling equation, through a boundary element method, a discrete boundary element equation related to the surface vibration speed of the composite board and the radiation sound wave pressure is constructed; coupling the wave finite element equation and the discrete boundary element equation of the whole composite board structure, and determining the sound pressure of radiation sound waves of the composite board structure and the surface vibration speed of the composite board; and based on the sound pressure of the radiation sound wave of the composite board structure and the surface vibration speed of the composite board, obtaining a sound insulation performance prediction result by calculating the sound power of the incident sound wave and the radiation sound wave, and completing prediction of the sound insulation performance of the composite board structure. The problems that the sound transmission loss of large plates and medium-high frequency plates is difficult to predict and the calculation cost is high are solved.

Description

Technical Field

[0001] This manual relates to the field of acoustics, and in particular to a method for predicting the sound insulation performance of composite plate structures using a hybrid wave finite element method and boundary element method. Background Technology

[0002] The increasing demand for lightweight construction in high-speed transportation vehicles such as trains, ships, and airplanes has led to a surge in the use of lightweight composite panels, including honeycomb sandwich panels, laminated composite panels, and extruded aluminum composite panels. However, the sound insulation performance of these lightweight composite panels is not ideal at certain frequencies. Therefore, studying the vibrational acoustic characteristics of composite panels to reduce radiated noise is becoming increasingly important. Current methods mainly involve meshing the overall structure of large composite panels and mid-to-high frequency materials or using transfer matrices to calculate sound insulation, but these methods are computationally very costly. Summary of the Invention

[0003] To address the aforementioned shortcomings in existing technologies, this specification provides a method for predicting the sound insulation performance of composite panel structures using a hybrid wave finite element and boundary element method, which solves the problems of difficulty in predicting sound transmission loss in large panels and mid-to-high frequency panels, as well as high computational costs.

[0004] To achieve the aforementioned objectives, the technical solution adopted in this invention is: a method for predicting the sound insulation performance of composite plate structures using a hybrid wave finite element method and boundary element method, comprising: S1: Based on the composite plate structure design data and acoustic excitation data, the acoustic-structure coupling equation is determined through fluid-structure interaction boundary conditions; S2: Obtain the wave finite element model of a periodic element of the composite plate structure using the wave finite element method; S3: Obtain the equivalent nodal forces of the wave finite element model through acoustic excitation simulation method; S4: Based on the wave finite element model of a periodic element of the composite plate structure and the equivalent nodal force of the wave finite element model, the wave finite element model is post-processed using Bloch wave theory to obtain the wave finite element equation of the entire composite plate structure. S5: Based on the aforementioned acoustic-structure coupling equation, a discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure is constructed using the boundary element method. S6: Couple the wave finite element equation of the entire composite plate structure with the discrete boundary element equation relating the vibration velocity of the composite plate surface to the sound pressure of the radiated sound wave to determine the sound pressure of the radiated sound wave of the composite plate structure and the vibration velocity of the composite plate surface. S7: Based on the sound pressure of the radiated sound waves of the composite board structure and the vibration velocity of the composite board surface, the sound insulation performance prediction results are obtained by calculating the sound power of the incident sound waves and the radiated sound waves, thus completing the prediction of the sound insulation performance of the composite board structure.

[0005] Furthermore, the expression for the acoustic-structure coupling equation is as follows: ; ; in, This represents the parameters related to the acoustic field boundary at the bottom of the composite panel. This indicates the sound pressure level at the bottom of the composite panel. This represents the parameters related to the acoustic field boundary at the top of the composite panel. This indicates the sound pressure level at the top of the composite panel. This represents the spatial derivative of a variable with respect to the boundary normal. This indicates the bottom and top surfaces of the composite panel. and For the observation point, These represent the bottom and top surfaces of the composite panel structure, respectively. This represents the normal velocity of the corresponding surface. and This represents the normal acceleration of the corresponding composite panel surface. They represent the surfaces of two infinitely large hemispheres. Indicates the density of the fluid at the bottom. Indicates the density of the fluid at the top. Indicates incident on The superposition of sound pressure from sound waves and their reflected sound waves on a plane. This represents the dimension along the thickness direction of the composite material in a three-dimensional coordinate system. Indicates the thickness of the composite board. Let Green's functions of the lower and upper half-spaces satisfy the Helmholtz equations. This indicates that the area is being integrated.

[0006] In some embodiments of this specification, the processor obtains the relationship between sound velocity and spatial position using a fluid-structure interaction boundary condition method. This approach allows for accurate acquisition of changes in sound pressure within the fluid, taking into account the magnitude of the reaction forces exerted by the fluids on the composite plate structure from both sides, resulting in more accurate predictions.

[0007] Further, S2 includes: A periodic element of the truncated composite plate structure is modeled using the wave finite element method, and the degree-of-freedom vectors of the nodes in the left region of the model section are obtained. Internal region node degree of freedom vector and the right region node degree of freedom vector ; Based on degree of freedom vectors and By constructing dynamic equations related to the boundary degrees of freedom of the wave finite element model, a wave finite element model of a one-period element of the composite plate structure is obtained: ; Where K and M represent the stiffness matrix and mass matrix of the cross section, respectively. q represents the angular frequency, and q represents the set of degrees of freedom of the nodes. and The set of internal forces, f represents the vector set of internal forces. and The set of external forces, where e represents the vector set of external forces. and A set of.

[0008] In some embodiments, the processor seeks out special scenarios and eliminates internal degrees of freedom through dynamic condensation to obtain the vibration equation of the composite plate structure, which can reduce the number of unknown variables in the equation and improve the calculation speed.

[0009] Furthermore, the construction of the dynamic equations related to the boundary degrees of freedom of the wave finite element model includes: By setting the sum of the nodal forces in the internal region to zero, and eliminating the internal degrees of freedom of the wave finite element model through dynamic condensation, the dynamic equations related to the boundary degrees of freedom of the wave finite element model are obtained: ; in, This represents the dynamic stiffness matrix of the composite plate structure.

[0010] Further, S3 includes: Based on plane sound waves, the equivalent nodal forces of the wave finite element model are determined using an acoustic excitation simulation method: ; in, , These represent the fluid sound velocities at the bottom and top, respectively. , These represent the bottom sound pressure level and the top sound pressure level, respectively.

[0011] In some embodiments, the processor determines the relationship between nodal forces in the wave finite element model and surface pressures in the composite plate structure by calculating the virtual work done by the fluid load on the elements. By establishing the relationship between nodal forces and surface pressures, more accurate nodal force equations can be obtained, leading to more accurate subsequent calculation results.

[0012] Further, S4 includes: The equivalent nodal forces of the wave finite element model are input into the wave finite element model of a periodic element of the composite plate structure. By applying periodicity and force balance boundary conditions, the wave finite element equations of the entire composite plate structure are determined: ; in, and These represent the matrices generated by applying periodic and force equilibrium boundary conditions, respectively. Represents the dynamic stiffness matrix. Represents the nodal force vector. Both represent coefficient matrices.

[0013] In some embodiments, the processor obtains the propagation equation of elastic waves in the composite plate structure by applying periodicity and force balance conditions. In this way, a more accurate vibration equation for the composite plate structure can be obtained based on a wave-based approach.

[0014] Further, S5 includes: Performing a Fourier transform on the acoustic-structure coupling equation yields the discrete boundary element equations relating the surface vibration velocity of the composite plate to the radiated sound pressure at the acoustic field boundary: ; in, These represent the vibration velocities of the lower and upper surfaces of the composite board, respectively. , All of these represent parameters generated during the discretization process of the boundary element integral equation. These represent the bottom sound pressure level and the top sound pressure level, respectively.

[0015] In some embodiments, the processor models the radiated sound pressure in the wavenumber domain using the two-dimensional Helmholtz equations, obtaining the discrete boundary element equations relating the surface vibration velocity of the composite plate to the radiated sound pressure. In this process, by employing an improved Green's function, the integration of the Helmholtz equations over the composite plate is avoided, transforming the integration domain to the structural surface and significantly optimizing computational efficiency.

[0016] Further, S7 includes: The sound pressure and the surface vibration velocity of the composite board are input into the radiated sound power formula and the incident sound power formula to determine the radiated sound power and the incident sound power. Based on the radiated sound power and the incident sound power, the sound insulation performance prediction result is obtained: ; in, This indicates the predicted sound insulation performance. This represents the transmission loss coefficient of acoustic wave excitation. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0017] In some embodiments, the processor obtains the transmission loss in the reverberant sound field by optimizing the transmission loss coefficient. This method allows for a more accurate assessment of the transmission loss of composite materials in real-world sound fields, expanding the application scope and making the results more consistent with actual conditions.

[0018] Furthermore, the expression for the radiated acoustic power is: ; in, Indicates radiated acoustic power. Let S denote the real part of the complex number, and let S denote the coefficients obtained by integrating the product of the solid and fluid shape functions. Indicates the sound pressure level at the top. Indicates the vibration velocity on the upper surface of the composite board; The expression for the incident sound power is: ; in, Indicates the incident sound power. Indicates the width of the composite panel structure. Indicates the fluid density at the bottom of the composite board. This indicates the sound velocity of the fluid at the bottom. Indicates the amplitude of the incident sound wave sound pressure. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0019] Furthermore, the transmission loss coefficient of the acoustic wave excitation includes the transmission loss coefficient of single-track acoustic wave excitation and the transmission loss coefficient under reverberant field acoustic wave excitation: ; ; in, This represents the transmission loss coefficient of a single-column acoustic wave excitation. This represents the transmission loss coefficient under reverberant field acoustic wave excitation. Indicates the lower limit of the angle of incidence. Indicates radiated acoustic power. Indicates the incident sound power. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0020] In some embodiments of this specification, the processor obtains the sound insulation of the composite panel structure by processing the composite panel structure design data and the excitation sound field data of the composite panel structure using the wave finite element method and the boundary element method. In this way, only a single periodic element region of the composite panel structure needs to be modeled using finite element methods, and the data of the entire structure can be obtained through wave finite element post-processing, greatly reducing the computational load. This allows for the calculation of the sound insulation of large composite panel structures and composite panel structures in the mid-to-high frequency range, expanding the application range. Attached Figure Description

[0021] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is an exemplary flowchart of a method for predicting the sound insulation performance of a composite panel structure using a hybrid finite element and boundary element method, as shown in some embodiments of this specification. Detailed Implementation

[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0023] Example Figure 1 This is an exemplary flowchart of a method for predicting the sound insulation performance of a composite panel structure using a hybrid finite element and boundary element method, as shown in some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process may be executed by a processor.

[0024] S1: Based on the composite plate structure design data and acoustic excitation data, the acoustic-structure coupling equation is determined through fluid-structure interaction boundary conditions.

[0025] Composite panel structural design data refers to the structural data of periodic lightweight composite panels. For example, composite panel structural design data can include structural data such as the thickness h, width b, and viscous damping coefficient η of composite panels used in high-speed train car body structures, floor composite panel structures, aircraft skins, building walls, and ship hull structures.

[0026] In some embodiments, the processor can measure the thickness and width of the target composite plate using a steel ruler and vernier calipers, obtain the damping data of the target composite plate through a hammer impact test, and obtain composite plate structural design data.

[0027] Acoustic excitation data refers to data on the fluid properties surrounding the target composite panel. For example, acoustic excitation data may include the air density on the upper and lower surfaces of the composite panel. and the speed of sound in air Inherent properties, etc.

[0028] In some embodiments, the processor may determine the inherent properties of a fluid by looking up data based on the fluid type.

[0029] The acoustic-structure coupling equation is an equation that reflects the relationship between the sound pressure generated by an external sound source and the frequency of sound excitation in space.

[0030] In some embodiments, the processor can construct a Helmholtz integral equation system by applying spatial domain fluid-structure interaction boundary conditions based on the composite plate structure design data and the acoustic excitation data; and apply wavenumber domain fluid-structure interaction boundary conditions to the Helmholtz integral equation system to obtain the acoustic-structure coupling equation.

[0031] In some embodiments, the expression for the acoustic-structure coupling equation can be: ; ; in, This represents the parameters related to the acoustic field boundary at the bottom of the composite panel. This indicates the sound pressure level at the bottom of the composite panel. This represents the parameters related to the acoustic field boundary at the top of the composite panel. This indicates the sound pressure level at the top of the composite panel. This represents the spatial derivative of a variable with respect to the boundary normal. This indicates the bottom and top surfaces of the composite panel. and For the observation point, These represent the bottom and top surfaces of the composite panel structure, respectively. This represents the normal velocity of the corresponding surface. and This represents the normal acceleration of the corresponding composite panel surface. They represent the surfaces of two infinitely large hemispheres. Indicates the density of the fluid at the bottom. Indicates the density of the fluid at the top. Indicates incident on The superposition of sound pressure from sound waves and their reflected sound waves on a plane. This represents the dimension along the thickness direction of the composite material in a three-dimensional coordinate system. Indicates the thickness of the composite board. Let Green's functions of the lower and upper half-spaces satisfy the Helmholtz equations. This indicates that the area is being integrated.

[0032] The Helmholtz integral equations are the boundary integral equations of the upper and lower half-space of the incident sound wave, which can reflect the relationship between the sound pressure on the surface of the composite board and the vibration velocity of air molecules.

[0033] In some embodiments, the processor can use a spatial domain fluid-structure interaction boundary condition calculation method to excite the sound wave emitted by a harmonic source Q below the bottom of the composite plate structure, and obtain the Helmholtz integral equations through the fluid-structure interaction boundary conditions: ; ; in, This indicates the sound velocity of the fluid at the bottom. Indicates the sound pressure level at the bottom. Indicates the sound velocity of the fluid at the top. Indicates the top sound pressure level. and For the observation point, This represents the spatial derivative of the variable with respect to the boundary normal. This indicates the bottom and top surfaces of the composite panel. These represent the bottom and top surfaces of the composite panel structure, respectively. This represents the lateral velocity of the corresponding surface. To represent angular frequency, and This indicates the displacement of the corresponding surface composite plate. These represent the surfaces of two infinitely large hemispheres. Indicates the density of the fluid at the bottom. Indicates the density of the fluid at the top. Indicates incident on The pressure of the sound waves on and reflected from its half-plane, This represents the dimension along the thickness direction of the composite material in a three-dimensional coordinate system. Indicates the thickness of the composite board. Let Green's function represent the half-space Green's function of the lower and upper half-spaces that satisfy the Helmholtz equation. This indicates that the area is being integrated.

[0034] In some embodiments, the processor can utilize the Helmholtz integral equations to apply fluid-structure interaction boundary conditions in the wavenumber domain, thereby obtaining the acoustic-structure interaction equations: ; in, Represents the Hamiltonian operator. Denotes the Green's function of a half-space that satisfies the Helmholtz equation. , Indicates wave number, Represents angular frequency. This indicates the speed of sound in air. Let represent the Dirac delta function at point P, satisfying the boundary conditions: .

[0035] In some embodiments of this specification, the processor obtains the relationship between sound velocity and spatial position using a fluid-structure interaction boundary condition method. This approach allows for accurate acquisition of changes in sound pressure within the fluid, taking into account the magnitude of the reaction forces exerted by the fluids on the composite plate structure from both sides, resulting in more accurate predictions.

[0036] S2: Obtain the wave finite element model of a periodic element of the composite plate structure using the wave finite element method.

[0037] The wave finite element model of a periodic element in a composite plate structure is an equation that reflects the relationship between the degrees of freedom of each node in the composite plate structure and the nodal forces acting on that node.

[0038] In some embodiments, the processor can use relevant commercial modeling software to perform overall modeling of the composite plate structure, obtain information such as the mass and stiffness matrix of the composite plate structure, and obtain a wave finite element model of a periodic element of the composite plate structure.

[0039] In some embodiments, the processor may implement S3 based on the following steps: modeling a periodic element of the truncated composite plate structure using the wave finite element method, and obtaining the degree-of-freedom vectors of the nodes in the left region of the model section. Internal region node degree of freedom vector and the right region node degree of freedom vector Based on degree of freedom vectors and By constructing dynamic equations related to the boundary degrees of freedom of the wave finite element model, a wave finite element model of a periodic element of the composite plate structure is obtained.

[0040] The nodal degree of freedom vector is a parameter that reflects the vibration displacement at the node.

[0041] In some embodiments, the processor can model a small portion of the composite plate structure and collect the degree of freedom of each node in the model.

[0042] In some embodiments, the processor can perform finite element discretization on the composite plate structure to obtain the stiffness matrix and mass matrix of the composite plate structure, and combine them with the nodal degrees of freedom to determine the vibration equation of the structure. ; Where K and M represent the stiffness matrix and mass matrix of the composite plate structure, respectively. Let q represent the angular frequency, and q represent the degrees of freedom on the left, inside, and right sides of the model. and The set of internal force vectors on the left, inside, and right sides of the model, f represents the set of internal force vectors. and The set of forces, where e represents the vector set of external forces on the left, inside, and right sides of the model. and A set of.

[0043] In some embodiments, the processor may use a complex stiffness matrix. This allows the vibration equation of the composite plate structure to take into account the damping of the composite plate structure; where, It is the viscous damping coefficient.

[0044] In some embodiments, the division of degrees of freedom can be expressed as: ; in, This represents the dynamic stiffness matrix of the composite plate structure. The subscripts "S", "I", and "R" represent the left, inner, and right regions of the model, respectively. The submatrix at the top left corner of the matrix. Submatrices representing the center position of a matrix, etc.

[0045] In some embodiments, the process by which the processor constructs dynamic equations related to the boundary degrees of freedom of the wave finite element model may include: setting the sum of the nodal internal forces in the internal region to 0, eliminating the internal degrees of freedom of the wave finite element model through dynamic condensation, and obtaining dynamic equations related to the boundary degrees of freedom of the wave finite element model.

[0046] In some embodiments, the expression for the dynamic equations related to the boundary degrees of freedom of the wave finite element model can be: ; in, This represents the dynamic stiffness matrix of the composite plate structure.

[0047] In some embodiments, the processor can be determined directly through matrix calculation methods: , , , , , , , .

[0048] In some embodiments, the expression for the wave finite element model of a single periodic element of a composite plate structure can be: ; Where K and M represent the stiffness matrix and mass matrix of the cross section, respectively. q represents the angular frequency, and q represents the set of degrees of freedom of the nodes. and The set of internal forces, f represents the vector set of internal forces. and The set of external forces, where e represents the vector set of external forces. and A set of.

[0049] In some embodiments, the processor seeks out special scenarios and eliminates internal degrees of freedom through dynamic condensation to obtain the vibration equation of the composite plate structure, which can reduce the number of unknown variables in the equation and improve the calculation speed.

[0050] S3: Obtain the equivalent nodal forces of the wave finite element model through acoustic excitation simulation.

[0051] The equivalent nodal force in the wave finite element model is the external force that is equivalently transformed from the external sound pressure in the region to which the node belongs to the external force on the node.

[0052] In some embodiments, the processor can concentrate the external forces on the nodes and calculate the vector sum to obtain the magnitude of the nodal force received by the nodal load, which can be used as the equivalent nodal force of the wave finite element model.

[0053] In some embodiments, the processor can determine the equivalent nodal forces of the wave finite element model based on planar acoustic waves using an acoustic excitation simulation method.

[0054] Plane sound waves It is a theoretical sound wave with multiple wavenumber components constructed based on preset parameters, wherein, Indicates having wavenumber components The vibration amplitude of a plane sound wave, The three dimensions of a sound wave.

[0055] In some embodiments, the processor can acquire plane acoustic waves by randomly generating parameters.

[0056] In some embodiments, the processor can obtain the external nodal forces acting on the nodes of the wave finite element model through finite element discretization. The virtual work done by fluid load on structural vibration is obtained by measuring the normal displacement and nodal force of the nodes. The magnitude of nodal forces is determined through calculation. For example, external nodal forces. non-zero elements It can be determined based on the formula: ; in, This represents the integration region associated with the j-th node. It represents the shape function related to the nodal normal displacement.

[0057] In some embodiments, the virtual work done by the fluid load on the structural unit It can be expressed as: ; in, This indicates virtual work per unit; the superscript "*" indicates complex conjugate. Indicates the first The area of ​​each element, This represents the vector of external forces acting on node e. Represents the Jacobian matrix related to coordinate transformation.

[0058] In some embodiments, the first The normal vibration displacement and sound pressure in each element can be expressed by the following formula: ; ; ; The superscript "T" indicates transpose. The column vector representing the shape function. This represents the sound pressure level at node e. This represents the sound pressure level after conversion at node e. The vector representing the degrees of freedom of node e, and the coupling vector. This represents the normal vibration displacement.

[0059] In some embodiments, the formulas for the normal vibration displacement and sound pressure of the element can be substituted into the virtual work equation to obtain the nodal force equation: ; ; The superscript "H" indicates the Hermitian transpose. This refers to the external nodal forces generated by fluid loads acting on the surface of the composite plate structure.

[0060] In some embodiments, nodal force By means of Determined using Gaussian numerical integration: ; in, These represent parameters related to the sound field boundaries at the bottom and top of the plate, respectively, and can be solved using standard finite element methods. , These represent the bottom sound pressure level and the top sound pressure level, respectively.

[0061] In some embodiments, the processor can enable the internal node count to be set to 0, thereby , Determine the nodal forces generated by the fluid loads acting on the top and bottom surfaces. and : ; ; in, These represent the nodal pressures on the left and right hypernodes on the upper surface of the model, respectively. These represent the nodal pressures on the left and right hypernodes on the lower surface of the model, respectively. Let L represent the finite element assembly matrix, U represent the upper surface, and LL, LR, RL, and RR represent the submatrices of the upper left, lower left, upper right, and lower right parts of the matrix, respectively.

[0062] In some embodiments, the expression for the equivalent nodal force of the wave finite element model can be: ; in, , These represent the fluid sound velocities at the bottom and top, respectively. , These represent the bottom sound pressure level and the top sound pressure level, respectively.

[0063] In some embodiments, the processor determines the relationship between nodal forces in the wave finite element model and surface pressures in the composite plate structure by calculating the virtual work done by the fluid load on the elements. By establishing the relationship between nodal forces and surface pressures, more accurate nodal force equations can be obtained, leading to more accurate subsequent calculation results.

[0064] S4: Based on the wave finite element model of a periodic element of the composite plate structure and the equivalent nodal force of the wave finite element model, the wave finite element model is post-processed using Bloch wave theory to obtain the wave finite element equation of the entire composite plate structure.

[0065] The wave finite element equation for the entire composite panel structure reflects the minute vibrations of the composite panel itself. For example, the free vibration equation of the composite panel structure can reflect the minute vibrations and displacements of the composite panel.

[0066] In some embodiments, the processor can combine the nodal force equations with the free vibration equations of the composite plate structure to obtain the wave finite element equations of the entire composite plate structure.

[0067] In some embodiments, the processor can input the equivalent nodal forces of the wave finite element model into the wave finite element model of a periodic element of the composite plate structure, apply periodic and force balance boundary conditions, and determine the wave finite element equation of the entire composite plate structure.

[0068] In some embodiments, the processor can input the nodal force into the vibration equation of the corresponding node to obtain the wave finite element equation of the entire composite plate structure.

[0069] In some embodiments, the processor can substitute the summative point force vector equation into the equation of structural vibration, ignoring internal degrees of freedom, to obtain the expanded equation of structural vibration: ; The summative force vector equation is as follows: .

[0070] In some embodiments, the processor can obtain the expression for the wave finite element equation of the entire composite plate structure by substituting periodicity and equilibrium conditions into the expanded structural vibration equation: ; in, , , , This represents the extended matrix representing the periodic equilibrium condition. and These represent the matrices generated by applying periodic and force equilibrium boundary conditions, respectively. Represents the dynamic stiffness matrix. Represents the nodal force vector. Both represent coefficient matrices.

[0071] In some embodiments, the coefficient matrix and It can be expressed as: ; ; in, This represents the propagation constant of elastic waves.

[0072] In some embodiments, the processor obtains the propagation equation of elastic waves in the composite plate structure by applying periodicity and force balance conditions. In this way, a more accurate vibration equation for the composite plate structure can be obtained based on a wave-based approach.

[0073] S5: Based on the aforementioned acoustic-structure coupling equation, a discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure is constructed using the boundary element method.

[0074] The discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure is an equation that describes the relationship between sound pressure and the surface vibration velocity of the composite plate.

[0075] In some embodiments, the processor can use the Helmholtz integral equation to perform a Fourier transform on the radiated sound pressure in the wavenumber domain to obtain the discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure.

[0076] In some embodiments, the processor can perform a Fourier transform on the acoustic-structure coupling equation to obtain a discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure at the sound field boundary.

[0077] In some embodiments, the processor can define the sound field boundary. Discretize into several elements, and place observation points sequentially on each node of the boundary element. Thus, the boundary integral is solved element by element over the entire boundary to obtain the discrete boundary element equation relating the vibration velocity of the composite plate surface to the sound pressure of the radiated sound wave.

[0078] In some embodiments, the expression for the discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure can be: ; in, These represent the vibration velocities of the lower and upper surfaces of the composite board, respectively. , All of these represent parameters generated during the discretization process of the boundary element integral equation. These represent the bottom sound pressure level and the top sound pressure level, respectively.

[0079] In some embodiments, the processor can obtain G and H using the integration method described above. , ;in, , This represents a block diagonal matrix, where each main diagonal block represents the lateral displacement of the structural surface. The relationship between velocity and displacement is expressed by... Differentiation yields, This represents the degrees of freedom of the nodes on the lower and upper surfaces.

[0080] In some embodiments, the processor can perform a Fourier transform on the acoustic-structure coupling equation to obtain the transformed equation: ; ; ; in, Represents a two-dimensional Green's function. Indicates wave number, Represents the wavenumber component in the x-direction. The boundary of the radiated sound field is determined by the coupling interface between the composite plate structure and the fluid.

[0081] In one embodiment, the Green function The boundary conditions for the incident sound field and the radiated sound field need to be satisfied such that: ; in, This represents the first-order Hankel function of the second kind. and These represent the original sound sources. Mirror sound source and observation points The distance between them This indicates the use of the boundary element method, assuming a sound source located above the composite plate, and P represents any observation point in space.

[0082] In some embodiments, the processor models the radiated sound pressure in the wavenumber domain using the two-dimensional Helmholtz equations, obtaining the discrete boundary element equations relating the surface vibration velocity of the composite plate to the radiated sound pressure. In this process, by employing an improved Green's function, the integration of the Helmholtz equations over the composite plate is avoided, transforming the integration domain to the structural surface and significantly optimizing computational efficiency.

[0083] S6: Couple the wave finite element equation of the entire composite plate structure with the discrete boundary element equation relating the vibration velocity of the composite plate surface to the sound pressure of the radiated sound wave to determine the sound pressure of the radiated sound wave of the composite plate structure and the vibration velocity of the composite plate surface.

[0084] Sound pressure is the pressure exerted by sound waves in a sound field on the surface of a composite board structure.

[0085] The surface vibration velocity of composite panels is data reflecting the influence of the vibration of the composite panels themselves.

[0086] In some embodiments, the processor can couple the wave finite element equation of the entire composite plate structure with the discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure, to obtain the coupled equation: ; in, The total spectrum dynamic stiffness matrix is ​​explicitly represented as the sum of three terms. The first term represents the vacuum structure dynamic stiffness matrix (DSM), which is obtained by transforming the D matrix. The second and third parts can represent the effects of fluid loads.

[0087] In some embodiments, the processor introduces known quantities G and H. Solve the problem to determine the solution. To obtain data on sound pressure level and surface vibration velocity of composite panels.

[0088] S7: Based on the sound pressure of the radiated sound waves of the composite board structure and the vibration velocity of the composite board surface, the sound insulation performance prediction results are obtained by calculating the sound power of the incident sound waves and the radiated sound waves, thus completing the prediction of the sound insulation performance of the composite board structure.

[0089] Transmission loss is the percentage of energy lost when sound waves pass through a composite material.

[0090] In some embodiments, the processor may implement S7 based on the following steps: inputting the sound pressure and the surface vibration velocity of the composite board into the radiated sound power formula and the incident sound power formula to determine the radiated sound power and the incident sound power; and obtaining the sound insulation performance prediction result based on the radiated sound power and the incident sound power.

[0091] The transmission loss coefficient of acoustic wave excitation includes the transmission loss coefficient of single-row acoustic wave excitation and the transmission loss coefficient of reverberant field acoustic wave excitation.

[0092] In some embodiments, the processor can input the sound pressure and the surface vibration velocity of the composite material into the radiated sound power formula and the incident sound power formula to determine the radiated sound power and the incident sound power; and determine the transmission loss coefficient of the sound wave excitation based on the ratio of the radiated sound power and the incident sound power.

[0093] Radiated acoustic power is the transmission power of sound waves radiated by the vibration of a composite plate structure.

[0094] The sound insulation performance prediction results are the predicted sound insulation values ​​of the composite panel structure under the excitation of single-row sound waves and reverberant field sound waves.

[0095] In some embodiments, the expression for the sound insulation performance prediction result can be: ; in, This indicates the predicted sound insulation performance. This represents the transmission loss coefficient of acoustic wave excitation. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0096] In some embodiments, the processor can discretize the time-averaged power formula to obtain an expression for the radiated acoustic power: ; in, Indicates radiated acoustic power. Let S denote the real part of the complex number, and let S denote the coefficients obtained by integrating the product of the solid and fluid shape functions. Indicates the sound pressure level at the top. This indicates the vibration velocity on the upper surface of the composite board.

[0097] In some embodiments, the processor can construct the time-averaged power radiated per unit length of waveguide structure using the following formula: ; in, It represents the boundary of the radiated sound field.

[0098] Incident sound power is the power transmitted when a sound wave propagates to the surface of a composite plate structure.

[0099] In some embodiments, the processor can input sound pressure and surface vibration velocity data of the composite board into the incident sound power calculation formula to obtain the incident sound power.

[0100] In some embodiments, the expression for incident sound power can be: ; in, Indicates the incident sound power. Indicates the width of the composite panel structure. Indicates the fluid density at the bottom of the composite board. This indicates the sound velocity of the fluid at the bottom. Indicates the amplitude of the incident sound wave sound pressure. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0101] In some embodiments, the processor can determine the transmission loss using the radiated sound power and the incident sound power, according to the transmission loss calculation formula. For example, the formula for calculating sound transmission loss can be expressed as: .

[0102] In some embodiments, the expression for the transmission loss coefficient of a single-track acoustic wave excitation can be: ; in, This represents the transmission loss coefficient of a single-column acoustic wave excitation.

[0103] In some embodiments, the expression for the transmission loss coefficient under reverberant field acoustic wave excitation can be: ; in, This represents the transmission loss coefficient under reverberant field acoustic wave excitation. Indicates the lower limit of the angle of incidence. Indicates radiated acoustic power. Indicates the incident sound power. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

[0104] In some embodiments, the processor may, based on the actual situation, [determine / implement / distribute] Set to 12° Indicates the angle of incidence The lower limit.

[0105] In some embodiments, the processor obtains the transmission loss in the reverberant sound field by optimizing the transmission loss coefficient. This method allows for a more accurate assessment of the transmission loss of composite materials in real-world sound fields, expanding the application scope and making the results more consistent with actual conditions.

[0106] In some embodiments of this specification, the processor obtains the sound insulation of the composite panel structure by processing the composite panel structure design data and the excitation sound field data of the composite panel structure using the wave finite element method and the boundary element method. In this way, only a single periodic element region of the composite panel structure needs to be modeled using finite element methods, and the data of the entire structure can be obtained through wave finite element post-processing, greatly reducing the computational load. This allows for the calculation of the sound insulation of large composite panel structures and composite panel structures in the mid-to-high frequency range, expanding the application range.

Claims

1. A method for predicting the sound insulation performance of composite plate structures using a hybrid finite element method and boundary element method, characterized in that, include: S1: Based on the composite plate structure design data and acoustic excitation data, the acoustic-structure coupling equation is determined through fluid-structure interaction boundary conditions; S2: Obtain the wave finite element model of a periodic element of the composite plate structure using the wave finite element method; S3: Obtain the equivalent nodal forces of the wave finite element model through acoustic excitation simulation method; S4: Based on the wave finite element model of a periodic element of the composite plate structure and the equivalent nodal force of the wave finite element model, the wave finite element model is post-processed using Bloch wave theory to obtain the wave finite element equation of the entire composite plate structure. S5: Based on the aforementioned acoustic-structure coupling equation, a discrete boundary element equation relating the surface vibration velocity of the composite plate to the radiated sound pressure is constructed using the boundary element method. S6: Couple the wave finite element equation of the entire composite plate structure with the discrete boundary element equation relating the vibration velocity of the composite plate surface to the sound pressure of the radiated sound wave to determine the sound pressure of the radiated sound wave of the composite plate structure and the vibration velocity of the composite plate surface. S7: Based on the sound pressure of the radiated sound waves of the composite board structure and the vibration velocity of the composite board surface, the sound insulation performance prediction results are obtained by calculating the sound power of the incident sound waves and the radiated sound waves, thus completing the prediction of the sound insulation performance of the composite board structure.

2. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, The expression for the acoustic-structure coupling equation is as follows: ； ； in, This represents the parameters related to the acoustic field boundary at the bottom of the composite panel. This indicates the sound pressure level at the bottom of the composite panel. This represents the parameters related to the acoustic field boundary at the top of the composite panel. This indicates the sound pressure level at the top of the composite panel. This represents the spatial derivative of a variable with respect to the boundary normal. This indicates the bottom and top surfaces of the composite panel. and For the observation point, These represent the bottom and top surfaces of the composite panel structure, respectively. This represents the normal velocity of the corresponding surface. and This represents the normal acceleration of the corresponding composite panel surface. They represent the surfaces of two infinitely large hemispheres. Indicates the density of the fluid at the bottom. Indicates the density of the fluid at the top. Indicates incident on The superposition of sound pressure from sound waves and their reflected sound waves on a plane. This represents the dimension along the thickness direction of the composite material in a three-dimensional coordinate system. Indicates the thickness of the composite board. Let Green's functions of the lower and upper half-spaces satisfy the Helmholtz equations. This indicates that the area is being integrated.

3. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, S2 includes: A periodic element of the truncated composite plate structure is modeled using the wave finite element method, and the degree-of-freedom vectors of the nodes in the left region of the model section are obtained. Internal region node degree of freedom vector and the right region node degree of freedom vector ; Based on degree of freedom vectors and By constructing dynamic equations related to the boundary degrees of freedom of the wave finite element model, a wave finite element model of a one-period element of the composite plate structure is obtained: ； Where K and M represent the stiffness matrix and mass matrix of the cross section, respectively. q represents the angular frequency, and q represents the set of degrees of freedom of the nodes. and The set of internal forces, f represents the vector set of internal forces. and The set of external forces, where e represents the vector set of external forces. and A set of.

4. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 3, characterized in that, The dynamic equations related to the boundary degrees of freedom of the wave finite element model include: By setting the sum of the nodal forces in the internal region to zero, and eliminating the internal degrees of freedom of the wave finite element model through dynamic condensation, dynamic equations related to the boundary degrees of freedom of the wave finite element model are constructed: ； in, This represents the dynamic stiffness matrix of the composite plate structure.

5. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, S3 includes: Based on plane sound waves, the equivalent nodal forces of the wave finite element model are determined using an acoustic excitation simulation method: ； in, , These represent the fluid sound velocities at the bottom and top, respectively. , These represent the bottom sound pressure level and the top sound pressure level, respectively.

6. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, S4 includes: The equivalent nodal forces of the wave finite element model are input into the wave finite element model of a periodic element of the composite plate structure. By applying periodicity and force balance boundary conditions, the wave finite element equations of the entire composite plate structure are determined: ； in, and These represent the matrices generated by applying periodic and force equilibrium boundary conditions, respectively. Represents the dynamic stiffness matrix. Represents the nodal force vector. Both represent coefficient matrices.

7. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, S5 includes: Performing a Fourier transform on the acoustic-structure coupling equation yields the discrete boundary element equations relating the surface vibration velocity of the composite plate to the radiated sound pressure at the acoustic field boundary: ； in, These represent the vibration velocities of the lower and upper surfaces of the composite board, respectively. , All of these represent parameters generated during the discretization process of the boundary element integral equation. These represent the bottom sound pressure level and the top sound pressure level, respectively.

8. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 1, characterized in that, S7 includes: The sound pressure and the surface vibration velocity of the composite board are input into the radiated sound power formula and the incident sound power formula to determine the radiated sound power and the incident sound power. Based on the radiated sound power and the incident sound power, the sound insulation performance prediction result is obtained: ； in, This indicates the predicted sound insulation performance. This represents the transmission loss coefficient of acoustic wave excitation. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

9. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 8, characterized in that, The expression for the radiated acoustic power is: ； in, Indicates radiated acoustic power. Let S denote the real part of the complex number, and let S denote the coefficients obtained by integrating the product of the solid and fluid shape functions. Indicates the sound pressure level at the top. Indicates the vibration velocity on the upper surface of the composite board; The expression for the incident sound power is: ； in, Indicates the incident sound power. Indicates the width of the composite panel structure. Indicates the fluid density at the bottom of the composite board. This indicates the sound velocity of the fluid at the bottom. Indicates the amplitude of the incident sound wave sound pressure. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

10. The method for predicting the sound insulation performance of a composite plate structure using a hybrid wave finite element and boundary element method according to claim 8, characterized in that, The transmission loss coefficient of the acoustic wave excitation includes the transmission loss coefficient of single-track acoustic wave excitation and the transmission loss coefficient under reverberant field acoustic wave excitation: ； ； in, This represents the transmission loss coefficient of a single-column acoustic wave excitation. This represents the transmission loss coefficient under reverberant field acoustic wave excitation. Indicates the lower limit of the incident angle. Indicates radiated acoustic power. Indicates the incident sound power. This represents the angle between the incident plane wave and the positive x-axis. This represents the angle between the trace projected onto the yz plane and the positive y-axis.

Images