Porous material layer layout optimization method for sound cavity surface noise reduction

Abstract

The invention discloses a porous material layer layout optimization method for sound cavity surface noise reduction. The porous material layer layout optimization method comprises the following steps: 1, constructing a material interpolation model of a noise reduction porous material layer through a variable density method; 2, establishing a topological optimization model by taking the vocal cavity characteristic frequency as a target function; 3, establishing a sound cavity structure characteristic frequency solving method through a surrounding channel integration method; 4, calculating the characteristic frequency sensitivity through a direct differential method; and 5, performing iterative solution on the topological optimization mathematical model by using a moving asymptote algorithm to obtain the optimal laying layout of the noise reduction porous material layer on the surface of the vocal cavity. The layout of the noise reduction porous material layer on the surface of the acoustic cavity in any shape can be optimally designed, so that the noise reduction performance is improved, and meanwhile, the use amount of the porous sound absorption material is reduced.

Description

Technical Field

[0001] The invention relates to noise control, and more specifically to an optimization design method for the layout of a noise-reducing porous material layer on the surface of a sound cavity. Technical Background

[0002] In engineering, noise control of acoustic cavity structures has always been a research focus. For example, for automobiles, the whole vehicle acoustic cavity and tire acoustic cavity are hot spots in the study of automobile NVH performance. The acoustic cavity structure is similar to other structural systems, with modal frequencies and modal vibration shapes. When the external excitation frequency is close to the characteristic frequency of the acoustic cavity system, resonance will occur, exacerbating the noise problem of the acoustic cavity. Laying porous sound-absorbing materials or sound-absorbing structures on the boundary of the acoustic cavity is a commonly used method in engineering to suppress acoustic cavity noise. The traditional method is to completely lay sound-absorbing materials on the boundary of the entire acoustic cavity system. However, this method will not only increase the cost of noise reduction, but also bring significant additional weight to the structure. More importantly, this method often cannot achieve the best vibration reduction and noise reduction effect. Summary of the invention

[0003] In order to solve the deficiencies of the above-mentioned prior art, the present invention provides a method for optimizing the layout of a porous material layer for noise reduction on the surface of a sound cavity, in order to optimize the design of the distribution of sound-absorbing materials on the surface of a complex sound cavity system, while maintaining the sound absorption performance, it can also reduce the amount of sound-absorbing materials used, thereby saving material costs while ensuring the vibration reduction and noise reduction effects.

[0004] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0005] The porous material layer layout optimization method for reducing noise on the surface of a sound cavity of the present invention is characterized in that it is carried out according to the following steps:

[0006] Step 1: Establish a three-dimensional acoustic cavity geometry model and divide the boundary area S of the three-dimensional acoustic cavity geometry model into H two-dimensional units, and each two-dimensional unit contains Y nodes; divide the interior of the three-dimensional acoustic cavity geometry model into Divide into Q three-dimensional units, each of which contains U nodes;

[0007] Step 2: Use equations (1) and (2) to calculate the qth three-dimensional unit in the three-dimensional acoustic cavity geometry model: The acoustic element stiffness matrix and the element mass matrix , thus the acoustic unit stiffness matrix of Q three-dimensional units constitutes an overall acoustic stiffness matrix of dimension o×o , the unit mass matrices of Q three-dimensional units form an overall sound quality matrix with dimension 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), is the Hamiltonian operator, represents the volume element of the q-th three-dimensional element ; represents the transpose of the matrix; is the vector composed of the finite element shape functions of each node in the q-th three-dimensional element ;

[0011] Step 3: Calculate the damping matrix of the h-th two-dimensional element in the three-dimensional acoustic cavity geometric model using equation (3): :

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

[0013] In equation (3), represents the area element of the h-th two-dimensional element; is the Y-th diagonal matrix of the h-th two-dimensional element, and each diagonal element in represents the acoustic impedance at each node in the h-th two-dimensional element, [ ] − 1 represents the inverse matrix of the matrix, represents the vector composed of the finite element shape functions of each node in the h-th two-dimensional element;

[0014] Step 4: Obtain the updated element damping matrix of the h-th two-dimensional element using equation (4), and thus form the overall element damping matrix with dimension o×o from the updated element damping matrices of H two-dimensional elements: :

[0015] (4)

[0016] In equation (4), represents the artificial density of the -th two-dimensional element, and ρ h ∈ [ ρ min , 1 ] is the lower limit of the artificial density, and n is the penalty factor;

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

[0018] (5) ​

[0019] In Equation (5), is the coefficient matrix of the acoustic finite element equation, and , where k is the wave number, and , is the propagation speed of sound waves in the three-dimensional acoustic cavity geometric model, is the frequency of the sound wave, represents the vector composed of the sound pressure at each node in the three-dimensional acoustic cavity finite element model;

[0020] Step 6: Perform variable substitution on Equation (5) to obtain the constraint conditions of the topology optimization model using Equation (6):

[0021] (6)

[0022] In Equation (6), is the eigenvalue of the three-dimensional acoustic cavity geometric model; is the eigenvector of the three-dimensional acoustic cavity geometric model;

[0023] Step 7: Equivalent the noise-reducing porous material attached to the boundary region area S of the three-dimensional acoustic cavity geometric model to an impedance boundary condition, and use Equation (7) to obtain the constraint conditions of the impedance boundary of the topology optimization model:

[0024] (7)

[0025] In Equation (7), is the acoustic impedance of the noise-reducing porous material on the boundary region area S; x represents any point on the boundary region area ; represents the outer normal direction at point x, represents the sound pressure at point x, and i is the imaginary unit; is the material medium density inside the three-dimensional acoustic cavity geometric model;

[0026] Step 8: Use Equation (8) to construct two constraint conditions for the topology optimization model of the three-dimensional acoustic cavity geometric model;

[0027] (8)

[0028] In Equation (8), is the number of two-dimensional elements set, , is the boundary region area is the area of the h-th two-dimensional element on, represents the area constraint ratio of the two-dimensional element;

[0029] Step 9: Use Equation (9) to construct the objective function F of the topology optimization model:

[0030] (9)

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

[0032] Step 10: Define the current iteration number as w, initialize w = 0, and initialize the artificial density of the h-th two-dimensional unit at the w-th iteration and the laying area of the noise-reducing porous material at the w-th iteration as ;

[0033] Step 11: According to , use Equation (4) to obtain the overall unit damping matrix at the w-th iteration, and thus use Equations (5) and (6) to obtain the constraint conditions of the topology optimization model at the w-th iteration;

[0034] Step 12: Solve the constraint conditions at the w-th iteration by the contour integration method to obtain the characteristic frequency when the laying area of the noise-reducing porous material at the w-th iteration is and its corresponding modal vibration mode , as well as the sensitivity information of to ;

[0035] Step 13: Use the moving asymptote iterative optimization algorithm to perform the (w + 1)-th solution of the topology optimization model, and obtain the artificial density of the h-th two-dimensional unit and the laying area of the noise-reducing porous material at the (w + 1)-th iteration;

[0036] Step 14: Determine whether Equation (11) holds. If it holds, it means that is the optimal laying area of the surface noise-reducing porous material of the three-dimensional acoustic cavity geometric model. Otherwise, assign w + 1 to w and then return to execute Step 11 in sequence;

[0037] (11)

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

[0039] An electronic device according to the present invention includes a memory and a processor, characterized in that the memory is used to store a program for supporting the processor to execute the porous material layer layout optimization method, and the processor is configured to execute the program stored in the memory.

[0040] A computer-readable storage medium of the present invention, characterized in that a computer program is stored on the computer-readable storage medium, and when the computer program is run by a processor, it executes the steps of the method for optimizing the layout of the porous material layer.

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

[0042] 1. For the acoustic cavity structure with noise-reducing porous materials laid on the boundary, its characteristic frequency is a complex number, and the imaginary part of the characteristic frequency represents the damping loss, which can more truly reflect the damping loss characteristics of the acoustic cavity structure, can adapt to the design requirements of various complex acoustic cavity structures, makes the design of material distribution more flexible, and thus better meets the noise reduction requirements of different application scenarios. The present invention uses the imaginary part of the characteristic frequency as a quantitative index for the sound absorption effect of the noise-reducing porous material. This method avoids the possible simplifying assumptions or errors in the traditional evaluation method, making the evaluation of the sound absorption effect more scientific and accurate. Taking the imaginary part of the characteristic frequency as the objective function of topology optimization makes the optimization result more reliable and more in line with the actual requirements of sound absorption performance.

[0043] 2. The present invention transforms the non-linear eigenvalue problem, which is complex to calculate and difficult to solve, into a linear eigenvalue problem through the contour integration method, greatly simplifies the calculation process, improves the solution efficiency, and improves the accuracy and reliability of the solution result. The above optimization problem is iteratively solved by the moving asymptote method, combining the contour integration method and the moving asymptote method, providing a new idea for the optimal design of acoustic structures and enriching the theory and method system of acoustic design.

[0044] 3. The present invention can be applied to any complex acoustic cavity structure. While ensuring the sound absorption performance, it can reduce the usage amount of noise-reducing porous materials, which is beneficial to saving materials and reducing the weight of products, providing a new method for the layout optimization of attaching noise-reducing porous materials to the surface of the acoustic cavity. This optimized layout method is an innovative breakthrough in traditional acoustic design, can significantly improve the acoustic performance, and meets the higher standard noise reduction requirements. Description of the Drawings

[0045] Figure 1 It is a schematic flow chart of the method of the present invention;

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

[0047] Figure 3 It is a modal vibration mode diagram of the acoustic cavity of the cylindrical example of the present invention;

[0048] Figure 4 It is an iterative result diagram of the layout optimization of the porous sound-absorbing material of the cylindrical example of the present invention.

[0049] Figure 5Iteration result diagram of the characteristic frequency of the cylindrical example acoustic cavity of the present invention. Detailed implementation manners

[0050] The present invention will be further described below in conjunction with the accompanying drawings and specific analysis cases:

[0051] As Figure 1 shown, an optimization design method for the layout of a porous material layer for noise reduction on the surface of an acoustic cavity according to the present invention is carried out according to the following steps:

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

[0053] Step 2: Calculate the acoustic element stiffness matrix and the element mass matrix of the qth three-dimensional element in the three-dimensional acoustic cavity geometric model by using Equations (1) and (2), so as to form an overall acoustic stiffness matrix with a dimension of 6266×6266 from the acoustic element stiffness matrices of Q three-dimensional elements, and form an overall acoustic mass matrix with a dimension of 6266×6266 from the element mass matrices of Q three-dimensional elements; ;

[0054] (1)

[0055] (2)

[0056] In Equations (1) and (2), is the Hamiltonian operator, represents the volume element of the qth three-dimensional element , represents the transpose of the matrix; is the vector formed by the finite element shape functions of each node in the qth three-dimensional element .

[0057] Step 3: Calculate the damping matrix of the rth two-dimensional element in the three-dimensional acoustic cavity geometric model by using Equation (3): :

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

[0059] In Equation (3), represents the area differential of the h-th two-dimensional element; is the Y-th order diagonal matrix of the h-th two-dimensional element, and each diagonal element in represents the acoustic impedance at each node in the h-th two-dimensional element, [ ] − 1 represents the inverse matrix of the matrix, represents the vector composed of the finite element shape functions at each node in the h-th two-dimensional element.

[0060] Step 4: Use Equation (4) to obtain the updated element damping matrix of the th two-dimensional element , so that the updated element damping matrices of H two-dimensional elements form the overall element damping matrix of dimension 6266×6266 :

[0061] (4)

[0062] In Equation (4), represents the artificial density of the th two-dimensional element, and ρ h ∈ [ ρ min , 1 ] , is the lower limit of the artificial density, n is the penalty factor, set to 3.

[0063] Step 5: Use Equation (5) to construct the acoustic finite element equation of the three-dimensional acoustic cavity geometry model:

[0064] (5)

[0065] In Equation (5), is the coefficient matrix of the acoustic finite element equation, and , k is the wave number, and , is the propagation speed of sound waves in the three-dimensional acoustic cavity geometry model, set to , is the frequency of the sound wave, represents the vector composed of the sound pressures at each node in the three-dimensional acoustic cavity finite element model.

[0066] Step 6: Perform variable substitution on Equation (5), so as to obtain the constraint conditions of the topology optimization model using Equation (6):

[0067] (6)

[0068] In Equation (6), is the eigenvalue of the three-dimensional acoustic cavity geometry model; is the eigenvector of the three-dimensional acoustic cavity geometric model.

[0069] Step 7: Equivalent the noise-reducing porous material attached to the boundary region area S of the three-dimensional acoustic cavity geometric model to an impedance boundary condition, so as to obtain the constraint condition of the impedance boundary of the topology optimization model by using Equation (7):

[0070] (7)

[0071] In Equation (7), is the acoustic impedance of the noise-reducing porous material on the boundary region area S; x represents any point on the boundary region area ; represents the outer normal direction at point x, represents the sound pressure at point x, and i is the imaginary unit; is the material medium density inside the three-dimensional acoustic cavity geometric model, set to .

[0072] Step 8: Use Equation (8) to construct two constraint conditions of the topology optimization model of the three-dimensional acoustic cavity geometric model;

[0073] (8)

[0074] In Equation (8), is the number of two-dimensional elements set, , is the boundary region area of the h-th two-dimensional element on, represents the area constraint ratio of the two-dimensional element, set to .

[0075] Step 9: Use Equation (9) to construct the objective function F of the topology optimization model:

[0076] (9)

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

[0078] Step 10: Define the current iteration number as w, and initialize w = 0. Initialize the artificial density of the h-th two-dimensional element at the w-th iteration , the laying area of the noise-reducing porous material at the w-th iteration is ;

[0079] Step 11: According to , use Equation (4) to obtain the overall element damping matrix at the w-th iteration , so as to obtain the constraint condition of the topology optimization model at the \(w\)th iteration by using equations (5) and (6);

[0080] Step 12: Solve the constraint condition at the \(w\)th iteration by the contour integration method to obtain the laying area of the noise-reducing porous material at the \(w\)th iteration as the characteristic frequency at and its corresponding modal vibration mode as Figure 3 shown, and the sensitivity information of .

[0081] Step 13: Use the moving asymptote iterative optimization algorithm to perform the \((w + 1)\)th solution on the topology optimization model to obtain the artificial density of the \(h\)th two-dimensional unit at the \((w + 1)\)th iteration and the laying area of the noise-reducing porous material ;

[0082] Step 14: Judge whether equation (11) holds. If it holds, it means that is the optimal laying area of the noise-reducing porous material on the surface of the three-dimensional acoustic cavity model. Otherwise, after assigning \(w + 1\) to \(w\), return to execute Step 11 and execute sequentially;

[0083] (11)

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

[0085] When the above conditions are met, the optimization ends, and the optimization results are as Figure 4 and Figure 5 shown. It can be seen from the figure that as the optimization design progresses, the coverage area of the sound-absorbing material gradually reaches 40%, and the imaginary part of the first-order characteristic frequency increases rapidly and then tends to be stable. The result of 60 iterations is as Figure 4 shown in part (e) of . It can be seen that the distribution of the sound-absorbing material presents an ideal 0-1 distribution. At this time, 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 the damping loss and can be used to characterize the noise reduction performance of the sound-absorbing material, the final result shows that after the topology optimization of the material layout, better vibration and noise reduction performance is obtained with only 40% of the original material.

[0086] In this embodiment, an electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute the above 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 thereon, and when the computer program is run by a processor, it executes the steps of the above method.

Claims

1. A method for optimizing the layout of a porous material layer for noise reduction on a sound cavity surface, characterized in that: The steps are as follows: Step 1: Establish a three-dimensional acoustic cavity geometry model and divide the boundary area S of the three-dimensional acoustic cavity geometry model into H two-dimensional units, and each two-dimensional unit contains Y nodes; divide the interior of the three-dimensional acoustic cavity geometry model into Divide into Q three-dimensional units, each of which contains U nodes; Step 2: Use equations (1) and (2) to calculate the qth three-dimensional unit in the three-dimensional acoustic cavity geometry model: The acoustic element stiffness matrix and the element mass matrix , so that the acoustic unit stiffness matrix of Q three-dimensional units constitutes an overall acoustic stiffness matrix of dimension o×o , the unit mass matrices of Q three-dimensional units form an overall sound quality matrix with dimension o×o ; Wherein, o represents the total number of nodes in the acoustic cavity finite element model; (1) (2) In formula (1) and formula (2), is the Hamiltonian operator, represents the qth three-dimensional unit The volume element of Represents the transpose of a matrix; is the qth three-dimensional unit The vector formed by the finite element shape functions of each node in ; Step 3: Use equation (3) to calculate the first 2D cell The damping matrix : (3) In formula (3), represents the area element of the h-th two-dimensional unit; is the Y-order diagonal matrix of the h-th two-dimensional element, and Each diagonal element in represents the acoustic impedance at each node in the h-th two-dimensional element, represents the inverse matrix of a matrix, represents the vector of finite element shape functions for each node in the h-th two-dimensional element; Step 4: Use formula (4) to get The updated element damping matrix of a 2D element , so that the updated unit damping matrix of H two-dimensional units constitutes an overall unit damping matrix with dimension o×o : (4) In formula (4), Indicates The artificial density of two-dimensional cells, and , is the lower limit of artificial density, n is the penalty factor; Step 5: Use equation (5) to construct the acoustic finite element equation of the three-dimensional acoustic cavity geometry model: (5) In formula (5), is the coefficient matrix of the acoustic finite element equations, and , k is the wave number, and , is the propagation speed of sound waves in the three-dimensional acoustic cavity geometry model, is the frequency of the sound wave, A vector representing the sound pressure at each node in the three-dimensional acoustic cavity finite element model; Step 6: Replace the variables in formula (5) and use formula (6) to obtain the constraints of the topology optimization model: (6) In formula (6), is the eigenvalue of the three-dimensional acoustic cavity geometry model; is the characteristic vector of the three-dimensional acoustic cavity geometry model; Step 7: The noise reduction porous material attached to the boundary area S of the three-dimensional acoustic cavity geometric model is equivalent to the impedance boundary condition, so as to obtain the impedance boundary constraint condition of the topology optimization model using formula (7): (7) In formula (7), is the acoustic impedance of the noise-reducing porous material on the boundary area S; x represents the boundary area Any point on represents the direction of the external normal at point x, represents the sound pressure at point x, i is an imaginary unit; is the material medium density inside the three-dimensional acoustic cavity geometric model; Step 8: Use equation (8) to construct two constraint conditions of the topology optimization model of the three-dimensional acoustic cavity geometry model; (8) In formula (8), is the number of two-dimensional cells set, , The area of ​​the boundary region The area of ​​the h-th two-dimensional cell on represents the area constraint ratio of the two-dimensional element; Step 9: Use formula (9) to construct the objective function F of the topology optimization model: (9) In formula (9), is the first-order eigenfrequency of the three-dimensional acoustic cavity geometry model, yes The imaginary part of Step 10: Define the current number of iterations as w, and initialize w=0, and initialize the artificial density of the h-th two-dimensional unit under the w-th iteration , the paving area of ​​the denoising porous material in the wth iteration is ; Step 11: According to , using formula (4) to obtain the overall unit damping matrix at the wth iteration , and then use equations (5) and (6) to obtain the constraint conditions of the topology optimization model at the wth iteration; Step 12: Solve the constraint conditions under the w-th iteration by the contour integration method, and obtain the paving area of ​​the noise-reducing porous material under the w-th iteration: The characteristic frequency and its corresponding mode shape ,as well as right Sensitivity information ; Step 13: Use the moving asymptote iterative optimization algorithm to solve the topology optimization model for the w+1th time and obtain the artificial density of the hth two-dimensional unit under the w+1th iteration. and the paving area of ​​the noise reduction porous material ; Step 14: Determine whether equation (11) is true. If true, it means That is, the optimal paving area of ​​the surface noise reduction porous material of the three-dimensional acoustic cavity geometric model, otherwise, after assigning w+1 to w, return to execute step 11 sequentially; (11) In formula (11), 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 to execute the porous material layer layout optimization method according to claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the porous material layer layout optimization method according to claim 1 are executed.

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