Sound-vibration coupling plane structure topological optimization method based on energy finite element

Abstract

An acoustic vibration coupling plane structure topological optimization method based on an energy finite element is characterized in that discretization processing and unit assembly of the energy finite element are carried out on an acoustic system by utilizing a unit independent grid method, an energy finite element model is constructed, and then the optimization of the acoustic performance of an acoustic vibration system is realized by combining the energy finite element model with the topological optimization method; according to the method, a unified analysis framework is provided for an acoustic vibration system, the dynamic change of a discontinuous interface of an energy density field in iterative optimization can be adapted, and a high-degree-of-freedom design space is provided; the calculation cost is reduced, the calculation efficiency is improved, and the accuracy of an analysis result is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimization design of acoustic-vibration coupling structures, and in particular relates to a topology optimization method for acoustic-vibration coupling planar structures based on energy finite elements. Technical Background

[0002] As the speed of equipment increases, the vibration and noise generated during operation gradually become the bottleneck restricting the design of high-performance equipment, and the vibration and noise reduction of the structure are becoming more and more important. When solving the optimization problem of high-frequency acoustic vibration system, the grid size of the classical finite element method should be less than one-sixth of the wavelength of the mechanical wave to ensure the accuracy of the calculation results (Atalla N, Bernhard RJ. Review of numerical solutions for low-frequency structural-acoustic problems. Applied Acoustics, 1994, 43). This leads to a sharp increase in the number of grids and an increase in the calculation cost. In addition, the modal density phenomenon in the high-frequency range makes the local response function very sensitive to structural uncertainty, and a small modeling deviation may lead to a large calculation error. It has high requirements on hardware level and modeling accuracy, which brings difficulties to ordinary designers. Another commonly used statistical energy analysis method has the problem of not being able to calculate the energy response of each node inside the subsystem, with low optimization freedom and limited ability to optimize material distribution (Zhu Danhui, Jie Miaoxia, Kong Xiangjie. Research on finite element method for high-frequency dynamic response energy in complex mechanical structures. China Engineering Science, 2013, 15(1): 106-112).

[0003] At the same time, the acoustic-vibration system has the characteristics of a discontinuous physical field. In the analysis of discontinuous physical fields, the common finite element method (Liu Zhihui. Research on the dynamic characteristics of closed coupled structures based on the energy finite element method [D]. Shandong: Shandong University, 2017) usually inserts nodes at discontinuities to simulate the discontinuity of the physical field; when the structural distribution in the analysis domain changes, the finite element mesh needs to be rebuilt; when performing structural optimization, the mesh needs to be continuously rebuilt, which has low computational efficiency and becomes a bottleneck in the iterative optimization calculation of acoustic-vibration coupled structures.

[0004] In summary, there is an urgent need for a structural optimization method with low computational cost and high degree of optimization freedom to achieve the optimal iterative design of acoustic-vibration coupled structures. Summary of the Invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a topology optimization method for acoustic-vibration coupled planar structures based on energy finite elements, which provides a unified analysis framework for acoustic-vibration systems, can adapt to the dynamic changes of discontinuous interfaces of energy density fields during iterative optimization, and provide a design space with high degrees of freedom. It not only reduces computational costs and improves computational efficiency, but also ensures the accuracy of analysis results.

[0006] In order to achieve the above objectives, the technical solution adopted by the present invention is:

[0007] A topology optimization method for acoustic-vibration coupled planar structures based on energy finite elements (FEs) is proposed. The "unit independent grid" method is used to discretize the acoustic system using FEs and assemble units. An energy finite element model is then constructed, which is then combined with a topology optimization method to optimize the acoustic performance of the acoustic-vibration system.

[0008] A topology optimization method for a planar structure with acoustic-vibration coupling based on energy finite element method comprises the following steps:

[0009] 1) Finite Element Analysis: Density, elastic modulus, and Poisson's ratio are defined based on material properties. The design domain is the solid structure in the acoustic-vibration system. The load to be borne by the design domain is set according to the design requirements. The wave group transmission interface changes at the intersection of different thicknesses in the design domain, and the energy transfer relationship at the acoustic-vibration coupling interface also changes with structural changes.

[0010] 2) Discretization: The design domain is discretized into a grid consisting of several four-node rectangular cells. The computational domain other than the design domain is discretized into a grid consisting of several eight-node solid cells. The cells are independent of each other and use their own nodes, without sharing nodes or boundaries. Each cell is numbered counterclockwise starting from the lower left corner node, resulting in a grid with no common nodes, named "cell-independent grid". The cells do not use common nodes, but instead arrange the nodes belonging to each cell at the same spatial position, named "collocated nodes", and the boundary formed by collocated nodes is called "collocated boundary".

[0011] 3) Constructing the energy balance control equation: The energy balance control equation is established based on the energy flow balance conditions on the unit and the continuity of the energy flow transferred between the coupled systems:

[0012]

[0013] In the above formula, the subscripts s and a represent the structure and acoustic cavity, respectively; K is the unit energy matrix, which represents the transfer and dissipation of energy within the unit; e is the energy density at the unit node; Q is the boundary energy matrix, which represents the transfer of energy between units; F is the energy of the vibration input; and [C] represents the energy coupling matrix at the coupling interface. The expressions of each matrix and vector are as follows:

[0014]

[0015] Where [N] is the shape function matrix, η and η e are the damping coefficients of the structure and the acoustic cavity, ω is the excitation angular frequency of the dynamic force load, c g is the group velocity, c is the speed of sound in the acoustic medium, π in (x,y) is the energy input at the node (x,y), τ sa , τ as is the energy transfer coefficient of the coupling interface, Ω e is the cell in the “cell-independent grid”, Γ e is the unit Ω e The boundary of the unit Ω e The energy balance control equation is established based on the energy flow balance condition, where 〈〉 represents the average variable in time and space;

[0016] 4) "Unit-independent grid" assembly method: The vibroacoustic system consists of a structure, a coupling interface, and an acoustic cavity. The energy matrix of the entire vibroacoustic system is assembled from the energy matrices of the structure, the coupling interface, and the acoustic cavity. The unit energy matrix, the boundary energy matrix, and the energy coupling matrix of the coupling interface in the "unit-independent grid" form are assembled to obtain the total matrix form of the vibroacoustic system.

[0017] The assembly of independent grids for planar structural units is described in the patent application titled "An Energy Finite Element Analysis Method Adapting to Dynamic Changes in Wave Group Transfer Interfaces" (Publication No. CN111832205A). The independent grids for the three-dimensional acoustic cavity units use the same coupling method, without the need for boundary energy matrix coupling.

[0018] After the coupling between the planar structure and the acoustic cavity subsystem is completed, the subsystem energy matrix and the acoustic-vibration coupling interface coupling matrix are assembled to obtain the total energy matrix of the entire system;

[0019] 5) Construct the boundary conditions of the energy finite element model: Initialize the maximum number of iterations k max , the maximum allowable error ε of initialization optimization termination, the upper limit of initialization material consumption M upp , define the loaded node number, size and constraint node number under the unit independent grid according to the actual working conditions;

[0020]

[0021] F is the load magnitude of the node, J is the Jacobian matrix;

[0022] 6) Constructing a level set description model: Initializing the rib layout, using the movable deformable component method, using the superposition and overlap of several components to describe the ribs on the structure, initializing the component design variables based on the rib layout of the initial structure, including length, width, center point coordinates, and tilt angle, completing the initial component layout, and using the level set description function to complete the geometric description of the component in the planar structure space;

[0023]

[0024] Where: φ(x,y) is the level set of the component at point (x,y); L, T, θ, x0, y0 are the length, width, tilt angle and center point coordinates of a component respectively;

[0025] 7) Constructing energy finite element calculation model:

[0026] 7.1) Constructing the constraint function: Project the level set description model of the reinforcement onto the unit independent grid using the density method to obtain the thickness of the reinforcement at each unit. Calculate the material consumption of the reinforcement according to formula (3) as the optimization constraint function.

[0027]

[0028] Where M is the amount of reinforcement material, h is the unit thickness, i.e., the surface thickness + the reinforcement thickness, S is the unit area, o is the unit number, and n is the total number of units;

[0029] 7.2) Constructing the objective function: The acoustic energy in the acoustic cavity is used to evaluate the acoustic performance of the structure. The objective function is to minimize the acoustic energy. The specific expression is as follows:

[0030]

[0031] Where E(D,x) represents the sound energy in the acoustic space D;

[0032] 7.3) Constructing the optimization model: Using the moving asymptote method as the optimization method, based on the relationship between the design variables and the objective function and constraint function, the sensitivity of the objective function and constraint function to the design variables are defined, and the objective function, constraint function and their sensitivity are brought into the moving asymptote optimizer to achieve optimization convergence and iterative update of the design variables. When the number of iterations reaches the maximum number of iterations k, the optimization is completed. max When , or when the change of the objective function is lower than the maximum allowable error ε, the optimization is terminated and the optimization design results are output;

[0033]

[0034] Where: x is both the geometric parameter of the component and the optimization design variable, including the center point coordinates, length, width and tilt angle, j is the component number, n is the component number, andcom is the number of components, M(x) and M upp are the actual material usage and the upper limit of material usage, respectively, min and x max are the lower and upper limits of the design variables respectively;

[0035] 8) Analysis and verification of the optimized reinforcement configuration of the acoustic-vibration coupled plane structure before and after optimization: Finite element analysis was performed on the optimized design configuration obtained by energy-based finite element topology optimization and the initial configuration, and the acoustic performance was compared to verify the effectiveness of the optimization method;

[0036] 9) Adaptive processing: Apply the energy finite element topology optimization method of the medium- and high-frequency acoustic-vibration coupled structure, complete the assembly of the overall matrix through the unit independent grid assembly rules, solve the energy distribution of the acoustic-vibration system, and complete the topology optimization design.

[0037] The energy finite element-based acoustic-vibration coupled planar structure topology optimization method is not limited to the coupled system consisting of a stiffened plate and an acoustic cavity, but is also applicable to the coupled system consisting of a structure with a damping layer and an acoustic cavity, and the coupled system between structures.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] Since the present invention starts from the energy perspective and obtains the acoustic energy response level in the acoustic cavity by analyzing the energy density distribution of the acoustic vibration system, it can avoid the modal superposition problem of the structure when solving the medium and high frequency acoustic vibration system using the classical finite element method, reduce the number of grids, and obtain more accurate analysis results; the present invention combines the energy finite element method with the topology optimization method with high design freedom to obtain a new reinforced configuration of the acoustic vibration coupling structure, thereby improving the acoustic performance under medium and high frequency vibrations; in order to adapt to the discontinuous distribution characteristics of energy in the acoustic vibration system and the iterative evolution during the topology optimization process, the present invention develops "unit independent grids" for planes, three-dimensional and coupling interfaces, as well as matrix assembly forms under unit independent grids, which avoids grid reconstruction, greatly reduces the amount of calculation, and accelerates optimization efficiency; the present invention provides a set of efficient and feasible solutions for the optimal design of acoustic vibration coupling structures under medium and high frequency working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flowchart of an embodiment of the present invention.

[0041] Figure 2 Schematic diagram of boundary conditions of an embodiment of the present invention.

[0042] Figure 3 Schematic diagram of unit independent grid division according to an embodiment of the present invention.

[0043] Figure 4This is a comparison diagram of the effects of the independent EFEM unit grid of an embodiment of the present invention and the traditional EFEM grid.

[0044] Figure 5 Schematic diagram of the assembly process of the acoustic vibration system according to an embodiment of the present invention.

[0045] Figure 6 This is a coupling relationship diagram of the acoustic cavity stereo units according to an embodiment of the present invention.

[0046] Figure 7 This is an example diagram of the XY plane coupling of the acoustic cavity according to an embodiment of the present invention.

[0047] Figure 8 Schematic diagram of the geometric description of the planar structural components of an embodiment of the present invention.

[0048] Figure 9 Schematic diagram of optimization iteration according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0050] Reference Figure 1 , a topology optimization method for acoustic-vibration coupled planar structures based on energy finite element, comprising the following steps:

[0051] 1) Finite Element Analysis: Density, elastic modulus, and Poisson's ratio are defined based on material properties. The design domain is the solid structure in the acoustic-vibration system. The load to be borne by the design domain is set according to the design requirements. The wave group transmission interface changes at the intersection of different thicknesses in the design domain, and the energy transfer relationship at the acoustic-vibration coupling interface also changes with structural changes.

[0052] The object of this embodiment is an acoustic vibration system, including a planar structure and its coupled acoustic cavity; the structure is a rectangular reinforced flat plate structure, consisting of a rectangular flat plate base and reinforcing ribs, both of which are made of homogeneous steel; the size parameters of the rectangular flat plate base are 1000×1000×5mm 3 , the thickness of the reinforcement rib is 5mm; the four corners of the rectangular flat substrate are fixed, and the upper surface is evenly subjected to high-frequency dynamic loads, such as Figure 2 As shown; the acoustic cavity coupled with the structure is filled with air, and the acoustic cavity size parameters are 1000×1000×1000mm 3 , the other boundaries of the non-coupled boundary are open boundaries; the elastic modulus of steel is 210GPa, and the density is 7800kg / m 3 , Poisson's ratio is 0.3, damping coefficient is 0.08; air density is 1.225kg / m 3 , the sound velocity is 340m / s, the loss factor is 0.0006; the target optimization frequency is 1000Hz;

[0053] 2) Discretization: The design domain is discretized into a grid composed of several units, and the unit type is a four-node rectangular unit; the other computational domains except the design domain are discretized into a grid composed of several three-dimensional units, and the unit type is an eight-node three-dimensional unit; in order to adapt to the discontinuous distribution characteristics of energy in the curved structure and the iterative evolution during the topology optimization process, the grid is processed independently, and the units are independent of each other, each using its own nodes, and not sharing nodes and boundaries; each unit is numbered counterclockwise starting from the lower left corner node to obtain a grid with no common nodes, named "unit-independent grid". As the basis of the energy finite element model, the unit-independent grid can represent any configuration without the need for grid reconstruction; instead of using common nodes between units, the nodes belonging to each unit are arranged at the same spatial position, named "collocated nodes", and the boundaries formed by collocated nodes are called "collocated boundaries";

[0054] In this embodiment, the rectangular stiffened plate design domain is discretized into a grid composed of 40×40 four-node rectangular elements; the acoustic cavity is discretized into a grid composed of 40×40×40 eight-node cubic elements, such as Figure 3 As shown in the figure, the effect of the independent grid of this embodiment and the traditional energy finite element grid is compared. Figure 4 As shown;

[0055] 3) Constructing the energy balance control equation: The energy balance control equation is established based on the energy flow balance conditions on the unit and the continuity of the energy flow transferred between the coupled systems:

[0056]

[0057] In the above formula, the subscripts s and a represent the structure and acoustic cavity, respectively; K is the unit energy matrix, which represents the transfer and dissipation of energy within the unit; e is the energy density at the unit node; Q is the boundary energy matrix, which represents the transfer of energy between units; F is the energy of the vibration input; and [C] represents the energy coupling matrix at the coupling interface. The expressions of each matrix and vector are as follows:

[0058]

[0059] Where [N] is the shape function matrix, η and η e are the damping coefficients of the structure and the acoustic cavity, ω is the excitation angular frequency of the dynamic force load, which is 1000Hz, and c g is the wave group velocity in steel, which is calculated from the wave group velocity formula of metal, c is the sound speed in the acoustic medium, which is 340m / s, π in (x,y) is the energy input at the node (x,y), τ sa , τ asis the energy transfer coefficient of the coupling interface. The specific calculation can be found in existing academic research (Bernhard RJ, Huff JE. Structural-acoustic design at high frequency using the energy finite element method. Journal of Vibration and Acoustics, Transactions of the ASME 1999; 121.), which will not be repeated here. Ω e is the cell in the “cell-independent grid”, Γ e is the unit Ω e The boundary of the unit Ω e The energy balance control equation is established based on the energy flow balance condition, where 〈〉 represents the average variable in time and space;

[0060] 4) “Independent Unit Grid” Assembly Method: The assembly process of the acoustic vibration system in this embodiment is as follows: Figure 5 As shown in the figure, the acoustic vibration system consists of a structure, a coupling interface, and an acoustic cavity. The energy matrix of the entire acoustic vibration system is assembled from the energy matrices of the structure, the coupling interface, and the acoustic cavity. The unit energy matrix, the boundary energy matrix, and the energy coupling matrix of the coupling interface in the form of "unit independent grid" are assembled to obtain the total matrix form of the acoustic vibration system.

[0061] The assembly of the independent grid of the planar structure unit can be found in the patent application entitled "An Energy Finite Element Analysis Method Adapting to the Dynamic Changes of the Wave Group Transfer Interface" (Publication No. CN111832205A), which will not be described in detail here. The independent grid of the three-dimensional unit of the acoustic cavity adopts the same coupling method, but because it is the same homogeneity, it does not need to couple the boundary energy matrix. There are seven types of coupling relationships of its unit energy matrix, such as Figure 6 As shown, it includes three coupling relationships of XY, two coupling relationships of XZ, one coupling relationship of YZ, and three-dimensional diagonal coupling; taking the energy matrix coupling of nodes 2 and 21, 3 and 24 of unit 1 and unit 3 in the XY plane as an example, as shown Figure 7 As shown, all elements in the row are exchanged to complete the coupling. After the coupling of all units is completed, the common nodes need to be multiplied by (1 / 2) m (m is the number of shared nodes);

[0062] After the coupling between the planar structure and the acoustic cavity subsystem is completed, the subsystem energy matrix and the acoustic-vibration coupling interface coupling matrix are assembled to obtain the total energy matrix of the entire system;

[0063] 5) Construct the boundary conditions of the energy finite element model: Initialize the maximum number of iterations k max is 1000, and the maximum allowable error ε for initialization optimization termination is 1e-6 , initialize the material consumption limit M upp The four corners of the rectangular reinforced plate are fixed and uniformly loaded. All structural nodes under the unit independent grid are loaded. The structural constraint nodes are numbered as [1, 2, 161, 4, 3, 164, 5, 6, 165, 156, 155, 316, 157, 158, 317, 160, 159, 320, 6082, 6241, 6242, 6083, 6244, 5243, 6086, 6245, 6246, 6235, 6396, 6395, 6238, 6397, 6398, 6239, 6400, 6399].

[0064]

[0065] F is the load magnitude of the node, which is 1000W, and J is the Jacobian matrix;

[0066] 6) Constructing a level set description model: Initializing the rib layout, using the movable deformable component method, using the superposition and overlap of several components to describe the ribs on the structure, initializing the component design variables based on the rib layout of the initial structure, the design variables include length, width, center point coordinates and tilt angle, and completing the initial component layout; in the initial rectangular reinforced flat plate structure of this embodiment, the orthogonally distributed rib components are evenly distributed on the entire rectangular flat plate substrate surface, the component length, width and tilt angle are 400mm, 40mm and 45° respectively, the center coordinates are the centers of each component after uniform arrangement, and the total number of components is 32; after completing the initial component layout, the level set description function is used to complete the geometric description of the components in the plane structure space, such as Figure 8 As shown;

[0067]

[0068] Where: φ(x,y) is the level set of the component at point (x,y); L, T, θ, x0, y0 are the length, width, tilt angle and center point coordinates of a component respectively;

[0069] 7) Constructing energy finite element calculation model:

[0070] 7.1) Constructing the constraint function: The level set description model of the reinforcement is projected onto the unit independent grid using the density method to obtain the thickness of the reinforcement on each unit. The unit reinforcement thickness is divided into 5mm, 3.75mm, 2.5mm, 1.25mm, and 0mm according to the ratio of the projection density. The material consumption of the reinforcement is calculated according to formula (3) as the optimization constraint function;

[0071]

[0072] Where M is the amount of reinforcement material, h is the unit thickness (surface thickness + reinforcement thickness), S is the unit area, o is the unit number, and n is the total number of units, 1600.

[0073] 7.2) Constructing the objective function: The acoustic energy in the acoustic cavity is used to evaluate the acoustic performance of the structure. The objective function is to minimize the acoustic energy. The specific expression is as follows:

[0074]

[0075] Where E(D,x) represents the acoustic energy in the acoustic cavity space D;

[0076] 7.3) Constructing the optimization model: Using the moving asymptote method as the optimization method, based on the relationship between the design variables and the objective function and constraint function, the sensitivity of the objective function and constraint function to the design variables are defined, and the objective function, constraint function and their sensitivity are brought into the moving asymptote optimizer to achieve optimization convergence and iterative update of the design variables. When the number of iterations reaches the maximum number of iterations k, the optimization is completed. max When , or when the change of the objective function is lower than the maximum allowable error ε, the optimization is terminated and the optimization design results are output, such as Figure 9 As shown in the figure, the material usage of the structure is reduced from 74% to 30% during the iteration process, and the objective function, i.e., the sound energy at the target position, is reduced from 5.05×10 -7 Reduced to 4.45×10 -7 , decreased by 11.88%;

[0077]

[0078] Where: x is both the geometric parameter of the component and the optimization design variable, including the center point coordinates, length, width and tilt angle, j is the component number, n is the component number, and com is the number of components, M(x) and M upp are the actual material usage and the upper limit of material usage, respectively, min and x max are the lower and upper limits of the design variables respectively;

[0079] 8) Analysis and Verification of the Optimized Reinforced Configuration of the Acoustic-Vibration Coupled Plane Structure: Finite element analysis was performed on the optimized design configuration obtained using energy-based finite element topology optimization and the initial configuration. Comparing the acoustic performance, the sound pressure levels at the measuring point for the original and optimized structures were 104.04dB and 101.05dB, respectively, a reduction of 2.99dB. Based on the definition of sound pressure level, the sound energy was calculated to be reduced by 49.8%. Compared to the original structure, the optimized structure improved the overall stiffness of the structure by adjusting the rib layout and reduced the noise response within the acoustic cavity by suppressing the structural vibration amplitude.

[0080] 9) Adaptive processing: Apply the energy finite element topology optimization method of the medium- and high-frequency acoustic-vibration coupled structure, complete the assembly of the overall matrix through the unit independent grid assembly rules, solve the energy distribution of the acoustic-vibration system, and complete the topology optimization design.

[0081] In order to adapt to different design requirements, the use of this method is not limited to the coupling system consisting of a stiffened plate and an acoustic cavity, but is also applicable to the coupling system consisting of a structure with a damping layer and an acoustic cavity, and the coupling system between structures.

Claims

1. A topology optimization method for acoustic-vibration coupled planar structures based on energy finite element method, characterized by: The "unit independent mesh" method is used to discretize the acoustic system using energy finite elements and assemble units. An energy finite element model is constructed, which is then combined with topology optimization methods to optimize the acoustic performance of the vibroacoustic system.

2. The method for topology optimization of a planar structure using acoustic-vibration coupling based on energy finite element analysis according to claim 1, characterized in that: The following steps are involved: 1) Finite Element Analysis: Density, elastic modulus, and Poisson's ratio are defined based on material properties. The design domain is the solid structure in the acoustic-vibration system. The load to be borne by the design domain is set according to the design requirements. The wave group transmission interface changes at the intersection of different thicknesses in the design domain, and the energy transfer relationship at the acoustic-vibration coupling interface also changes with structural changes. 2) Discretization: The design domain is discretized into a grid consisting of several four-node rectangular cells. The computational domain other than the design domain is discretized into a grid consisting of several eight-node solid cells. Each cell is independent of the others and uses its own nodes, without sharing nodes or boundaries. Each cell is numbered counterclockwise starting from the lower left corner node, resulting in a grid with no shared nodes, called a "cell-independent grid." Instead of using shared nodes, cells arrange their own nodes at the same spatial position, called "collocated nodes," and the boundary formed by collocated nodes is called a "collocated boundary." 3) Constructing the energy balance control equation: The energy balance control equation is established based on the energy flow balance conditions on the unit and the continuity of the energy flow transferred between the coupled systems: In the above formula, the subscripts s and a represent the structure and acoustic cavity, respectively; K is the unit energy matrix, which represents the transfer and dissipation of energy within the unit; e is the energy density at the unit node; Q is the boundary energy matrix, which represents the transfer of energy between units; F is the energy of the vibration input; and [C] represents the energy coupling matrix at the coupling interface. The expressions of each matrix and vector are as follows: Where [N] is the shape function matrix, η and η e are the damping coefficients of the structure and the acoustic cavity, ω is the excitation angular frequency of the dynamic force load, c g is the group velocity, c is the speed of sound in the acoustic medium, π in (x,y) is the energy input at the node (x,y), τ sa , τ as is the energy transfer coefficient of the coupling interface, Ω e is the cell in the "cell-independent grid", Γ e is the unit Ω e The boundary of the unit Ω e The energy balance control equation is established based on the energy flow balance condition, where 〈〉 represents the average variable in time and space; 4) "Unit-independent grid" assembly method: The vibroacoustic system consists of a structure, coupling interfaces, and an acoustic cavity. The energy matrix of the entire vibroacoustic system is assembled from the energy matrices of the structure, coupling interfaces, and acoustic cavity. The unit energy matrix, boundary energy matrix, and energy coupling matrix of the coupling interfaces in the "unit-independent grid" format are assembled to obtain the total matrix of the vibroacoustic system. The assembly of independent grids for planar structural units is described in the patent application titled "An Energy Finite Element Analysis Method Adapting to Dynamic Changes in Wave Group Transfer Interfaces" (Publication No. CN111832205A). The independent grids for the three-dimensional acoustic cavity units use the same coupling method, eliminating the need for boundary energy matrix coupling. After the coupling between the planar structure and the acoustic cavity subsystem is completed, the subsystem energy matrix and the acoustic-vibration coupling interface coupling matrix are assembled to obtain the total energy matrix of the entire system; 5) Construct the boundary conditions of the energy finite element model: Initialize the maximum number of iterations k max , the maximum allowable error ε of initialization optimization termination, the upper limit of initialization material consumption M upp , define the loaded node number, size and constraint node number under the unit independent grid according to the actual working conditions; F is the load magnitude of the node, J is the Jacobian matrix; 6) Constructing a level set description model: Initializing the rib layout, using the movable deformable component method, using the superposition and overlap of several components to describe the ribs on the structure, initializing the component design variables based on the rib layout of the initial structure, including length, width, center point coordinates, and tilt angle, completing the initial component layout, and using the level set description function to complete the geometric description of the component in the planar structure space; Where: φ(x,y) is the level set of the component at point (x,y); L, T, θ, x0, y0 are the length, width, tilt angle and center point coordinates of a component respectively; 7) Constructing energy finite element calculation model: 7.1) Constructing the constraint function: Project the level set description model of the reinforcement onto the unit independent grid using the density method to obtain the thickness of the reinforcement at each unit. Calculate the material consumption of the reinforcement according to formula (3) as the optimization constraint function. Where M is the amount of reinforcement material, h is the unit thickness, i.e., the surface thickness + the reinforcement thickness, S is the unit area, o is the unit number, and n is the total number of units; 7.2) Constructing the objective function: The acoustic energy in the acoustic cavity is used to evaluate the acoustic performance of the structure. The objective function is to minimize the acoustic energy. The specific expression is as follows: Where E(D,x) represents the sound energy in the acoustic space D; 7.3) Constructing the optimization model: Using the moving asymptote method as the optimization method, based on the relationship between the design variables and the objective function and constraint function, the sensitivity of the objective function and constraint function to the design variables are defined, and the objective function, constraint function and their sensitivity are brought into the moving asymptote optimizer to achieve optimization convergence and iterative update of the design variables. When the number of iterations reaches the maximum number of iterations k, the optimization is completed. max When , or when the change of the objective function is lower than the maximum allowable error ε, the optimization is terminated and the optimization design results are output; Where: x is both the geometric parameter of the component and the optimization design variable, including the center point coordinates, length, width and tilt angle, j is the component number, n is the component number, and com is the number of components, M(x) and M upp are the actual material usage and the upper limit of material usage, respectively, min and x max are the lower and upper limits of the design variables respectively; 8) Analysis and verification of the optimized reinforcement configuration of the acoustic-vibration coupled plane structure before and after optimization: Finite element analysis was performed on the optimized design configuration obtained by energy-based finite element topology optimization and the initial configuration, and the acoustic performance was compared to verify the effectiveness of the optimization method; 9) Adaptive processing: Apply the energy finite element topology optimization method of the medium- and high-frequency acoustic-vibration coupled structure, complete the assembly of the overall matrix through the unit independent grid assembly rules, solve the energy distribution of the acoustic-vibration system, and complete the topology optimization design.

3. The method for topology optimization of a planar structure using acoustic-vibration coupling based on energy finite element analysis according to claim 2, characterized in that: The energy finite element-based acoustic-vibration coupled planar structure topology optimization method is not limited to the coupled system consisting of a stiffened plate and an acoustic cavity, but is also applicable to the coupled system consisting of a structure with a damping layer and an acoustic cavity, and the coupled system between structures.

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