A method for optimizing the layout of a porous material layer for sound cavity surface noise reduction

Abstract

The application discloses a porous material layer layout optimization method for sound cavity surface noise reduction, comprising the following steps: 1, a material interpolation model of the noise reduction porous material layer is constructed by a variable density method; 2, a topological optimization model is established by taking the sound cavity characteristic frequency as a target function; 3, a solving method of the sound cavity structure characteristic frequency is established by a contour integral method; 4, the characteristic frequency sensitivity is calculated by a direct differential method; and 5, the topological optimization mathematical model is iteratively solved by using a moving asymptote algorithm, so that the optimal laying layout of the sound cavity surface noise reduction porous material layer is obtained. The application can optimize the layout of the noise reduction porous material layer on the surface of a sound cavity with an arbitrary shape, so that the noise reduction performance is improved, and the amount of the porous sound absorption material is reduced.

Description

Technical Field

[0001] This invention relates to the field of noise control, and more specifically to an optimized design method for the layout of porous material layers for noise reduction on the surface of acoustic cavities. Technical Background

[0002] In engineering, noise control of acoustic cavity structures has always been a research focus. For example, in automobiles, the vehicle acoustic cavity and tire acoustic cavity are hot topics in automotive NVH performance research. Similar to other structural systems, acoustic cavity structures have modal frequencies and mode shapes. When the external excitation frequency is close to the characteristic frequency of the acoustic cavity system, resonance occurs, exacerbating the noise problem. Laying porous sound-absorbing materials or sound-absorbing structures at the cavity boundaries is a commonly used method in engineering to suppress acoustic cavity noise. The traditional method is to completely lay sound-absorbing materials at the boundaries of the entire acoustic cavity system. However, this method not only increases noise reduction costs but also adds significant weight to the structure. More importantly, this method often fails to achieve optimal vibration and noise reduction effects. Summary of the Invention

[0003] To address the shortcomings of the existing technology, this invention provides a method for optimizing the layout of porous material layers for noise reduction on the surface of acoustic cavities. This method aims to optimize the distribution of sound-absorbing materials on the surface of complex acoustic cavity systems, maintain sound absorption performance, and reduce the amount of sound-absorbing material used, thereby saving material costs while ensuring vibration reduction and noise reduction effects.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] The present invention provides a method for optimizing the layout of porous material layers for noise reduction on acoustic cavity surfaces, characterized by the following steps:

[0006] Step 1: Establish a three-dimensional acoustic cavity geometric model and divide the boundary region S of the three-dimensional acoustic cavity geometric model into H two-dimensional units, with each two-dimensional unit containing Y nodes; [The text then abruptly shifts to a different topic:] ...the interior of the three-dimensional acoustic cavity geometric model... It is divided into Q three-dimensional units, and each three-dimensional unit contains U nodes;

[0007] Step 2: Calculate the q-th three-dimensional unit in the three-dimensional acoustic cavity geometric model using equations (1) and (2). Acoustic element stiffness matrix and unit mass matrix Thus, the acoustic stiffness matrices of the Q three-dimensional units constitute the overall acoustic stiffness matrix of dimension o×o. The overall acoustic mass matrix, consisting of the mass matrices of Q three-dimensional units, has a dimension of o×o. Where o represents the total number of nodes in the acoustic cavity finite element model;

[0008] (1)

[0009] (2)

[0010] In equations (1) and (2), It is the Hamiltonian operator. Represents the q-th three-dimensional unit The volume of the infinitesimal element, Represents the transpose of a matrix; For the q-th three-dimensional unit The vector formed by the finite element shape functions of each node in the vector;

[0011] Step 3: Calculate the first equation in the three-dimensional acoustic cavity geometric model using equation (3). Two-dimensional unit Damping matrix :

[0012] C ′ h = ∫∫ S h [ Z h ] − 1 ( N h ) T N h d S h (3)

[0013] In equation (3), Let h represent the area of ​​the h-th two-dimensional unit; It is the Y-order diagonal matrix of the h-th two-dimensional unit, and Each diagonal element in the diagram represents the acoustic impedance at each node in the h-th two-dimensional element. [ ] − 1 Describes the inverse of a matrix. This represents the vector formed by the finite element shape functions of each node in the h-th two-dimensional element;

[0014] Step 4: Use equation (4) to obtain the first... The updated element damping matrix of the two-dimensional element Thus, the updated element damping matrices of H two-dimensional elements constitute the global element damping matrix of dimension o×o. :

[0015] (4)

[0016] In equation (4), Indicates the first The artificial density of each two-dimensional unit, and ρ h ∈ [ ρ min , 1 ] , Here, n represents the lower limit of artificial density, and n is the penalty factor.

[0017] Step 5: Construct the acoustic finite element equations of the three-dimensional acoustic cavity geometric model using equation (5):

[0018] (5)

[0019] In equation (5), Let be the coefficient matrix of the acoustic finite element equation, and , where k is the wave number, and , Let be the speed of sound wave propagation within the three-dimensional acoustic cavity geometry model. It is the frequency of the sound wave. This represents the vector formed by the sound pressure at each node in the three-dimensional acoustic cavity finite element model;

[0020] Step 6: Substitute the variables in equation (5) to obtain the constraints of the topology optimization model using equation (6):

[0021] (6)

[0022] In equation (6), These are the eigenvalues ​​of the three-dimensional acoustic cavity geometric model; These are the feature vectors of the three-dimensional acoustic cavity geometric model;

[0023] Step 7: The noise-reducing porous material attached to the boundary region area S of the three-dimensional acoustic cavity geometric model is equivalent to the impedance boundary condition, and the constraint conditions of the impedance boundary of the topology optimization model are obtained by using equation (7):

[0024] (7)

[0025] In equation (7), The acoustic impedance of the noise-reducing porous material over the boundary region area S is given by x; x represents the boundary region area. any point on; Indicates the direction of the outward normal at point x. This represents the sound pressure at point x, where i is the imaginary unit. The density of the material medium inside the three-dimensional acoustic cavity geometric model;

[0026] Step 8: Construct two constraints for the topology optimization model of the three-dimensional acoustic cavity geometric model using equation (8);

[0027] (8)

[0028] In equation (8), The number of two-dimensional units is set. , Area of ​​the boundary region The area of ​​the h-th two-dimensional unit. This indicates the area constraint ratio of a two-dimensional element;

[0029] Step 9: Construct the objective function F of the topology optimization model using equation (9):

[0030] (9)

[0031] In equation (9), The first-order characteristic frequency of the three-dimensional acoustic cavity geometric model. yes The imaginary part;

[0032] Step 10: Define the current iteration number as w, and initialize w=0. Initialize the artificial density of the h-th two-dimensional unit in the w-th iteration. The area of ​​the noise-reducing porous material laid in the wth iteration is ;

[0033] Step 11: According to The global element damping matrix under the w-th iteration is obtained using equation (4). Thus, the constraints of the topology optimization model under the w-th iteration can be obtained using equations (5) and (6);

[0034] Step 12: Solve the constraint conditions under the w-th iteration using the perimeter integral method to obtain the laying area of ​​the noise-reducing porous material in the w-th iteration. characteristic frequency of time and their corresponding mode shapes ,as well as right Sensitivity information ;

[0035] Step 13: Solve the topology optimization model for the (w+1)th time using the moving asymptote iterative optimization algorithm to obtain the artificial density of the h-th two-dimensional cell under the (w+1)-th iteration. and the area of ​​laying noise-reducing porous materials ;

[0036] Step 14: Determine whether equation (11) is true. If it is true, then it means... This is the optimal laying area of ​​the surface noise reduction porous material of the three-dimensional acoustic cavity geometric model; otherwise, assign w+1 to w and return to execute step 11 sequentially.

[0037] (11)

[0038] In equation (11), This is the allowable value.

[0039] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the porous material layer layout optimization method, and the processor is configured to execute the program stored in the memory.

[0040] The present invention discloses a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program is executed by a processor to perform the steps of the porous material layer layout optimization method.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] 1. For acoustic cavity structures with boundary-laid noise-reducing porous materials, the characteristic frequency is a complex number. The imaginary part of the characteristic frequency represents the damping loss, which can more realistically reflect the damping loss characteristics of the acoustic cavity structure. This allows for adaptation to various complex acoustic cavity structure design requirements, making the material distribution design more flexible and better meeting the noise reduction needs of different application scenarios. This invention uses the imaginary part of the characteristic frequency as a quantitative indicator of the sound absorption effect of the noise-reducing porous material. This method avoids the simplification assumptions or errors that may exist in traditional evaluation methods, making the evaluation of the sound absorption effect more scientific and accurate. Using the imaginary part of the characteristic frequency as the objective function for topology optimization makes the optimization results more reliable and better fits the actual needs of sound absorption performance.

[0043] 2. This invention transforms the computationally complex and difficult-to-solve nonlinear eigenvalue problem into a linear eigenvalue problem using the enveloping integral method, greatly simplifying the calculation process, improving solution efficiency, and enhancing the accuracy and reliability of the solution results. By iteratively solving the above optimization problem using the moving asymptote method, combining the enveloping integral method and the moving asymptote method, it provides a new approach to the optimization design of acoustic structures, enriching the theoretical and methodological system of acoustic design.

[0044] 3. This invention can be applied to any complex acoustic cavity structure. While ensuring sound absorption performance, it can reduce the amount of noise-reducing porous material used, which is beneficial to saving materials and reducing product weight. It provides a new method for optimizing the layout of noise-reducing porous material attached to the acoustic cavity surface. This optimized layout method is an innovative breakthrough of traditional acoustic design, which can significantly improve acoustic performance and meet higher standards of noise reduction requirements. Attached Figure Description

[0045] Figure 1 This is a schematic flowchart of the method of the present invention;

[0046] Figure 2 This is a geometric model diagram of the cylindrical example of the present invention;

[0047] Figure 3 The cylindrical acoustic cavity modal diagram is shown in the present invention.

[0048] Figure 4 This is a diagram showing the iterative results of the layout optimization of porous sound-absorbing materials in the cylindrical example of this invention.

[0049] Figure 5The figure shows the iterative results of the characteristic frequencies of the acoustic cavity in the cylindrical example of this invention. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and specific analytical examples:

[0051] like Figure 1 As shown, the optimized design method for the layout of porous material layers for noise reduction on the surface of a acoustic cavity, as described in this invention, is carried out according to the following steps:

[0052] Step 1: Establish a three-dimensional geometric model of the cylindrical acoustic cavity, as follows: Figure 2 As shown, the cylindrical acoustic cavity model has a radius of 0.5m and a height of 2m. The boundary area S of the three-dimensional acoustic cavity geometry model is divided into 1440 two-dimensional quadrilateral elements, and each two-dimensional element contains four nodes. The interior of the three-dimensional acoustic cavity geometry model... The model is divided into 5500 three-dimensional hexahedral elements, each containing eight nodes, for a total of 6266 element nodes. Figure 2 As shown;

[0053] Step 2: Calculate the q-th three-dimensional unit in the three-dimensional acoustic cavity geometric model using equations (1) and (2). Acoustic element stiffness matrix and unit mass matrix Thus, the acoustic stiffness matrices of the Q three-dimensional units constitute a global acoustic stiffness matrix with dimensions of 6266×6266. The overall acoustic mass matrix, consisting of Q unit mass matrices of three-dimensional units, has a dimension of 6266×6266. ;

[0054] (1)

[0055] (2)

[0056] In equations (1) and (2), It is the Hamiltonian operator. Represents the q-th three-dimensional unit The volume of the infinitesimal element, Represents the transpose of a matrix; For the q-th three-dimensional unit The vector formed by the finite element shape functions of each node.

[0057] Step 3: Calculate the first equation in the three-dimensional acoustic cavity geometric model using equation (3). Two-dimensional unit Damping matrix :

[0058] C ′ h = ∫∫ S h [ Z h ] − 1 ( N h ) T N h d S h (3)

[0059] In equation (3), Let h represent the area of ​​the h-th two-dimensional unit; It is the Y-order diagonal matrix of the h-th two-dimensional unit, and Each diagonal element in the diagram represents the acoustic impedance at each node in the h-th two-dimensional element. [ ] − 1 Describes the inverse of a matrix. This represents the vector formed by the finite element shape functions of each node in the h-th two-dimensional element.

[0060] Step 4: Use equation (4) to obtain the first... The updated element damping matrix of the two-dimensional element Thus, the updated element damping matrices of H two-dimensional elements constitute a global element damping matrix with dimensions of 6266×6266. :

[0061] (4)

[0062] In equation (4), Indicates the first The artificial density of each two-dimensional unit, and ρ h ∈ [ ρ min , 1 ] , Here, n is the lower limit of artificial density, and n is the penalty factor, set to 3.

[0063] Step 5: Construct the acoustic finite element equations of the three-dimensional acoustic cavity geometric model using equation (5):

[0064] (5)

[0065] In equation (5), Let be the coefficient matrix of the acoustic finite element equation, and , where k is the wave number, and , Let the speed of sound wave propagation within the three-dimensional acoustic cavity geometry be set to... , It is the frequency of the sound wave. This represents the vector formed by the sound pressure at each node in the three-dimensional acoustic cavity finite element model.

[0066] Step 6: Substitute the variables in equation (5) to obtain the constraints of the topology optimization model using equation (6):

[0067] (6)

[0068] In equation (6), These are the eigenvalues ​​of the three-dimensional acoustic cavity geometric model; It is the feature vector of the three-dimensional acoustic cavity geometric model.

[0069] Step 7: The noise-reducing porous material attached to the boundary region area S of the three-dimensional acoustic cavity geometric model is equivalent to the impedance boundary condition, and the constraint conditions of the impedance boundary of the topology optimization model are obtained by using equation (7):

[0070] (7)

[0071] In equation (7), The acoustic impedance of the noise-reducing porous material over the boundary region area S is given by x; x represents the boundary region area. any point on; Indicates the direction of the outward normal at point x. This represents the sound pressure at point x, where i is the imaginary unit. The density of the material medium inside the three-dimensional acoustic cavity geometry model is set to... .

[0072] Step 8: Construct two constraints for the topology optimization model of the three-dimensional acoustic cavity geometric model using equation (8);

[0073] (8)

[0074] In equation (8), The number of two-dimensional units is set. , Area of ​​the boundary region The area of ​​the h-th two-dimensional unit. The area constraint ratio of the two-dimensional element is set to... .

[0075] Step 9: Construct the objective function F of the topology optimization model using equation (9):

[0076] (9)

[0077] In equation (9), The first-order characteristic frequency of the three-dimensional acoustic cavity geometric model. yes The imaginary part.

[0078] Step 10: Define the current iteration number as w, and initialize w=0. Initialize the artificial density of the h-th two-dimensional unit in the w-th iteration. The area of ​​the noise-reducing porous material laid in the wth iteration is ;

[0079] Step 11: According to The global element damping matrix under the w-th iteration is obtained using equation (4). Thus, the constraints of the topology optimization model under the w-th iteration can be obtained using equations (5) and (6);

[0080] Step 12: Solve the constraint conditions under the w-th iteration using the perimeter integral method to obtain the laying area of ​​the noise-reducing porous material in the w-th iteration. characteristic frequency of time and their corresponding mode shapes like Figure 3 As shown, and right Sensitivity information .

[0081] Step 13: Solve the topology optimization model for the (w+1)th time using the moving asymptote iterative optimization algorithm to obtain the artificial density of the h-th two-dimensional cell under the (w+1)-th iteration. and the area of ​​laying noise-reducing porous materials ;

[0082] Step 14: Determine whether equation (11) is true. If it is true, then it means... This is the optimal laying area of ​​the surface noise reduction porous material of the three-dimensional acoustic cavity geometric model; otherwise, assign w+1 to w and return to execute step 11 sequentially.

[0083] (11)

[0084] In equation (11), The allowable value is set to 1e-8.

[0085] The optimization ends when the above condition is met, and the optimization result is as follows: Figure 4 and Figure 5 As shown in the figure, with the progress of the optimization design, the coverage area of ​​the sound-absorbing material gradually reaches 40%, while the imaginary part of the first-order characteristic frequency tends to stabilize after a rapid increase. The results of 60 iterations are as follows. Figure 4 As shown in part (e), the sound-absorbing material distribution exhibits an ideal 0-1 distribution. At this point, the first-order characteristic frequency of the acoustic cavity is 1.17178 + 0.092i, and the imaginary part of the characteristic frequency reaches 104.97% of that when the sound-absorbing material is fully covered. Since the imaginary part of the characteristic frequency represents damping loss, it can be used to characterize the noise reduction performance of the sound-absorbing material. Therefore, the final results show that the material layout after topology optimization achieves better vibration reduction and noise reduction performance than the original material layout, using only 40% of the original material.

[0086] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0087] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for optimizing the layout of porous material layers for noise reduction on the surface of acoustic cavities, characterized in that, The procedure is as follows: Step 1: Establish a three-dimensional acoustic cavity geometric model and divide the boundary region area S of the three-dimensional acoustic cavity geometric model into H two-dimensional units, with each two-dimensional unit containing Y nodes; [The text then abruptly shifts to a different topic:] ...the interior of the three-dimensional acoustic cavity geometric model... It is divided into Q three-dimensional units, and each three-dimensional unit contains U nodes; Step 2: Calculate the q-th three-dimensional unit in the three-dimensional acoustic cavity geometric model using equations (1) and (2). Acoustic element stiffness matrix and unit mass matrix Thus, the acoustic stiffness matrices of the Q three-dimensional units constitute the overall acoustic stiffness matrix of dimension o×o. The overall acoustic mass matrix, consisting of the mass matrices of Q three-dimensional units, has a dimension of o×o. Where o represents the total number of nodes in the acoustic cavity finite element model; (1) (2) In equations (1) and (2), It is the Hamiltonian operator. Represents the q-th three-dimensional unit The volume of the infinitesimal element, Represents the transpose of a matrix; For the q-th three-dimensional unit The vector formed by the finite element shape functions of each node in the vector; Step 3: Calculate the first equation in the three-dimensional acoustic cavity geometric model using equation (3). Two-dimensional unit Damping matrix : (3) In equation (3), Let h represent the area of ​​the h-th two-dimensional unit; It is the Y-order diagonal matrix of the h-th two-dimensional unit, and Each diagonal element in the diagram represents the acoustic impedance at each node in the h-th two-dimensional element. Describes the inverse of a matrix. This represents the vector formed by the finite element shape functions of each node in the h-th two-dimensional element; Step 4: Use equation (4) to obtain the first... The updated element damping matrix of the two-dimensional element Thus, the updated element damping matrices of H two-dimensional elements constitute the global element damping matrix of dimension o×o. : (4) In equation (4), Indicates the first The artificial density of each two-dimensional unit, and , Here, n represents the lower limit of artificial density, and n is the penalty factor. Step 5: Construct the acoustic finite element equations of the three-dimensional acoustic cavity geometric model using equation (5): (5) In equation (5), Let be the coefficient matrix of the acoustic finite element equation, and , where k is the wave number, and , Let be the speed of sound wave propagation within the three-dimensional acoustic cavity geometry model. It is the frequency of the sound wave. This represents the vector formed by the sound pressure at each node in the three-dimensional acoustic cavity finite element model; Step 6: Substitute the variables in equation (5) to obtain the constraints of the topology optimization model using equation (6): (6) In equation (6), These are the eigenvalues ​​of the three-dimensional acoustic cavity geometric model; These are the feature vectors of the three-dimensional acoustic cavity geometric model; Step 7: The noise-reducing porous material attached to the boundary region area S of the three-dimensional acoustic cavity geometric model is equivalent to the impedance boundary condition, and the constraint conditions of the impedance boundary of the topology optimization model are obtained by using equation (7): (7) In equation (7), The acoustic impedance of the noise-reducing porous material over the boundary region area S is given by x; x represents the boundary region area. any point on; Indicates the direction of the outward normal at point x. This represents the sound pressure at point x, where i is the imaginary unit. The density of the material medium inside the three-dimensional acoustic cavity geometric model; Step 8: Construct two constraints for the topology optimization model of the three-dimensional acoustic cavity geometric model using equation (8); (8) In equation (8), The number of two-dimensional units is set. , Area of ​​the boundary region The area of ​​the h-th two-dimensional unit. This indicates the area constraint ratio of a two-dimensional element; Step 9: Construct the objective function F of the topology optimization model using equation (9): (9) In equation (9), The first-order characteristic frequency of the three-dimensional acoustic cavity geometric model. yes The imaginary part; Step 10: Define the current iteration number as w, and initialize w=0. Initialize the artificial density of the h-th two-dimensional unit in the w-th iteration. The area of ​​the noise-reducing porous material laid in the wth iteration is ; Step 11: According to The global element damping matrix under the w-th iteration is obtained using equation (4). Thus, the constraints of the topology optimization model under the w-th iteration can be obtained using equations (5) and (6); Step 12: Solve the constraint conditions under the w-th iteration using the perimeter integral method to obtain the laying area of ​​the noise-reducing porous material in the w-th iteration. characteristic frequency of time and their corresponding mode shapes ,as well as right Sensitivity information ; Step 13: Solve the topology optimization model for the (w+1)th time using the moving asymptote iterative optimization algorithm to obtain the artificial density of the h-th two-dimensional cell under the (w+1)-th iteration. and the area of ​​noise-reducing porous materials ; Step 14: Determine whether equation (11) is true. If it is true, then it means... This is the optimal laying area of ​​the surface noise reduction porous material of the three-dimensional acoustic cavity geometric model; otherwise, assign w+1 to w and return to execute step 11 sequentially. (11) In equation (11), This is the allowable value.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the porous material layer layout optimization method of claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program, when run by the processor, executes the steps of the porous material layer layout optimization method according to claim 1.

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