Porous material sound absorption structure design method and device, electronic equipment and storage medium

Abstract

The invention relates to a porous material sound absorption structure design method and device, electronic equipment and a storage medium, and the method comprises the steps: building a sound absorption mathematical model based on a rubber material and a porous material, obtaining a target function for maximizing the acoustic performance, and adding constraint conditions for optimizing the target function, randomly generating an initial design meeting the target function and the constraint condition; carrying out optimization processing on design variables in the initial design based on density filtering and projection; a wave finite element method is adopted to calculate the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design; evaluating the sensitivity of the design variable to the objective function and the constraint condition based on the sound absorption coefficient; and updating the design variable based on a moving asymptote method, repeating the previous steps until a preset iteration requirement is met so as to output a result of the final optimized design variable, and outputting the porous material sound absorption structure based on the result.

Description

Technical Field

[0001] The present invention relates to the technical field of sound absorption and noise reduction, and particularly to a design method, device, electronic device and storage medium for a sound absorption structure of porous materials. Background Art

[0002] The underwater sound absorption performance of porous materials is closely related to their topological structures. The most mature and commonly used method for designing material structures relies on physical prior knowledge and manual experience, and verifies the material structure performance through finite element simulation. However, when it comes to complex internal structures and geometric shapes, such a design method is quite time-consuming and laborious.

[0003] Meanwhile, due to the limitations of manual experience, there is still a great deal of room for improvement in the acoustic performance of the currently designed underwater sound absorption material structures. A structure with excellent sound absorption effect, light weight and pressure resistance is the most ideal design goal.

[0004] So far, there is still a lack of an effective and relatively autonomous method to design a porous material structure that meets the expected acoustic and mechanical properties. For this reason, various increasingly powerful structure optimization design strategies may provide new methods for material property calculation and structure design. However, the work on studying acoustic metamaterials using the above strategies is still relatively limited, and the designed structures have poor effects. Summary of the Invention

[0005] The purpose of the present invention is to provide a design method, device, electronic device and storage medium for a sound absorption structure of porous materials.

[0006] To achieve the above invention purpose, the present invention provides a design method for a sound absorption structure of porous materials, including the following steps: S1. Establish an acoustic mathematical model based on rubber materials and porous materials, and obtain an objective function for maximizing acoustic performance, and add constraint conditions to optimize the objective function to randomly generate an initial design that meets the objective function and the constraint conditions; S2. Optimize the design variables in the initial design based on density filtering and projection; S3. Use the wave finite element method to calculate the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design; S4. Evaluate the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient; S5. Update the design variables based on the moving asymptote method to repeatedly execute steps S2 to S5 until the preset iteration requirements are met, to output the result of the finally optimized design variables, and output the porous material sound absorption structure based on the result.

[0007] According to one aspect of the present invention, in step S1, the acoustic mathematical model is an underwater acoustic mathematical model; The acoustic mathematical model includes: a scatterer made of a porous material, and a covering layer made of a rubber material and covering the outside of the scatterer.

[0008] According to one aspect of the present invention, in step S1, in the step of establishing an acoustic mathematical model based on a rubber material and a porous material, it includes: Set the area of the scatterer with a preset surface thickness as a constraint area, and set the remaining area surrounded by the constraint area as a design domain; Discretize the design domain into equal square units, and specify a variable to describe the material properties of each of the square units, where the variable describes a functional relationship between the square unit and the physical properties of the material, When it is 1, it means that the square unit is the matrix material, When it is 0, it means that the square unit is a pore region.

[0009] According to one aspect of the present invention, in step S1, in the step of establishing an acoustic mathematical model based on a rubber material and a porous material, obtaining an objective function for maximizing acoustic performance, and adding constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions, it includes: Based on the reflection coefficient calculation formula, calculate the reflection coefficients of the acoustic mathematical model when the sound waves are incident at the same incident angle with different incident frequencies, and use the minimization of the average reflection coefficient of the obtained multiple reflection coefficients as the objective function for maximizing acoustics; Obtain the constraint conditions to optimize the objective function based on the constraint conditions; wherein, the constraint conditions include volume constraint and deformation amount constraint.

[0010] According to one aspect of the present invention, the volume constraint is obtained by normalizing the amount of the matrix material used in the current design domain with the predefined maximum volume fraction, so that the actual amount of the matrix material used in the design domain has the same order of magnitude as the objective function, to control the equivalent density of the covering layer; The deformation amount constraint uses the surface average deformation rate to represent the hydrostatic bearing performance of the covering layer, and applies a constraint to the surface average deformation rate.

[0011] According to one aspect of the present invention, in step S2, in the step of optimizing the design variables in the initial design based on density filtering and projection, density filtering is performed by means of solid isotropic material penalization interpolation, and Heaviside projection operator is used for projection; wherein, the density filtering operator applied to density filtering is:

[0012] wherein, represents the filtering radius, represents the weight coefficient determined by the central positions of square element and square element such that the filtered variable corresponding to variable is the weighted average of variable and its neighboring variables , represents the central position vector of square element , represents the central position vector of square element ; The Heaviside projection operator applied to projection is:

[0013] wherein, and are the projection level and projection intensity respectively, is the final physical variable; In step S2, in the step of performing density filtering by means of solid isotropic material penalization interpolation, interpolation is performed based on the variable of the square element to convert the discrete variable into a continuous variable, which is expressed as:

[0014] wherein, and are the density and Young's modulus of square element respectively, and are the density and Young's modulus of the matrix material respectively, and represent the artificial material parameters of the hole domain respectively, and are the density and Young's modulus penalty coefficients.

[0015] According to one aspect of the present invention, in step S4, in the step of evaluating the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient, the gradients of the objective function and the constraint conditions with respect to the design variables are calculated, and the sensitivity is evaluated based on the gradients.

[0016] To achieve the above-mentioned invention purpose, the present invention provides an apparatus applied to the foregoing porous material sound absorption structure design method, including: An initial design module, which establishes an acoustic mathematical model based on rubber materials and porous materials, obtains an objective function for maximizing acoustic performance, and adds constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions; A density filtering and projection module, which optimizes the design variables in the initial design based on density filtering and projection; A wave finite element method calculation and sensitivity analysis module, which uses the wave finite element method to calculate the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design, and evaluates the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient; A solution calculation and structure determination module, which updates the design variables based on the moving asymptote method for the density filtering and projection module and the wave finite element method calculation and sensitivity analysis module to perform iterative optimization until a preset iteration requirement is met, outputs the result of the finally optimized design variables, and outputs the porous material sound absorption structure based on the result.

[0017] To achieve the above-mentioned invention purpose, the present invention provides an electronic device for the foregoing porous material sound absorption structure design method, including a memory and a processor, where the memory stores an acoustic mathematical model and a computer program, and the processor implements the porous material sound absorption structure design method when executing the computer program.

[0018] To achieve the above-mentioned invention purpose, the present invention provides a storage medium for the foregoing porous material sound absorption structure design method, on which a computer program is stored, and the computer program implements the porous material sound absorption structure design method when executed by a processor.

[0019] According to a solution of the present invention, the obtained sound absorption structure has excellent sound absorption performance while having lightweight and pressure-resistant mechanical properties; the present invention can design and optimize the porous material sound absorption structure in a time-saving and efficient manner, expands the richness of the structural style and realizes the intelligentization of the design process for the design method mainly relying on artificial experience. At the same time, due to the generality of the model and method, the present invention has a certain degree of migration in other material design optimization fields besides the design optimization of underwater acoustic porous material sound absorption structures. Description of the Drawings

[0020] Figure 1 is a schematic block diagram showing the steps of a method for designing a sound-absorbing structure of a porous material according to an embodiment of the present invention; Figure 2 is a schematic flow chart showing a method for designing a sound-absorbing structure of a porous material according to an embodiment of the present invention; Figure 3 is a schematic diagram showing a sound-absorbing mathematical model according to an embodiment of the present invention. Among them, (a) shows a schematic diagram of the simulation structure of the sound-absorbing mathematical model, (b) shows a schematic diagram of the parameter settings of the sound-absorbing mathematical model, and (c) shows a schematic diagram of the scatterer parameter settings of the sound-absorbing mathematical model; Figure 4 is a schematic diagram showing the verification result diagram of the implementation of the wave finite element method for an optimized sound-absorbing structure of a porous material in Example 1 according to an embodiment of the present invention. Among them, (a) shows a schematic diagram of the simulation structure of the sound-absorbing mathematical model of this example, (b) shows a comparison diagram of the calculation results of the wave finite element method and the direct simulation calculation using COMSOL under different harmonic orders when the incident wave is a normal plane wave for the sound-absorbing mathematical model shown in Figure (a), and (c) shows a comparison diagram of the calculation results of the wave finite element method and the COMSOL simulation calculation for plane waves with incident angles of 50° and 70° respectively when the incident wave is an oblique incidence as shown in Figure (a); Figure 5 is a schematic diagram showing the schematic diagram of the finally designed sound-absorbing structure of a porous material and the acoustic coefficient curve under different frequency ranges in Example 1 according to an embodiment of the present invention. Among them, (a) shows a schematic diagram of the simulation structure of the finally designed sound-absorbing mathematical model, (b) shows a front view of the finally designed sound-absorbing mathematical model, (c) shows a scatterer diagram of the finally designed sound-absorbing mathematical model, and (d) shows a schematic diagram of the sound-absorbing effect of the finally designed sound-absorbing mathematical model. Detailed Embodiments

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0022] When describing the embodiments of the present invention, the orientation or positional relationship expressed by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" is based on the orientation or positional relationship shown in the relevant drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting the present invention.

[0023] The present invention will be described in detail below with reference to the drawings and specific embodiments. The embodiments cannot be enumerated one by one here, but the embodiments of the present invention are not limited to the following embodiments.

[0024] Combined Figure 1 and Figure 2 As shown, according to an embodiment of the present invention, a method for designing an acoustic absorption structure of a porous material of the present invention includes the following steps: S1. Establish an acoustic absorption mathematical model based on rubber material and porous material, obtain the objective function for maximizing acoustic performance, and add constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and constraint conditions; S2. Optimize the design variables in the initial design based on density filtering and projection; S3. Use the wave finite element method to calculate the acoustic absorption coefficient of the porous material acoustic absorption structure corresponding to the optimized initial design; S4. Evaluate the sensitivity of the design variables to the objective function and constraint conditions based on the acoustic absorption coefficient; S5. Update the design variables based on the moving asymptote method to repeat steps S2 to S5 until the preset iteration requirements are met, output the results of the finally optimized design variables, and output the porous material acoustic absorption structure based on the results.

[0025] As Figure 3 shown, according to an embodiment of the present invention, in step S1, the acoustic absorption mathematical model is an underwater acoustic absorption mathematical model; in this embodiment, the acoustic absorption mathematical model includes: a scatterer made of a porous material, and a covering layer made of a rubber material coated on the outside of the scatterer.

[0026] As Figure 3 shown, according to an embodiment of the present invention, in the step of establishing an acoustic absorption mathematical model based on rubber material and porous material in step S1, it includes: Set the area with a preset thickness on the surface layer of the scatterer as the constraint area, and set the remaining area surrounded by the constraint area as the design domain; in this embodiment, the preset thickness of the constraint area = 1 mm.

[0027] Discretize the design domain into equal square units, and specify a variable to describe the material properties of each square unit, where the variable describes a functional relationship between the square unit and the physical properties of the material. When it is 1, it means the square unit is the matrix material. When it is 0, it means the square unit is the pore region. In this embodiment, the material properties of the constraint region are all set to 1, while the material properties in the design domain are optimized according to the subsequent steps.

[0028] According to an embodiment of the present invention, in step S1, based on the rubber material and the porous material, an acoustic absorption mathematical model is established, and an objective function for maximizing the acoustic performance is obtained. Moreover, in the step of adding constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions, it includes: Based on the reflection coefficient calculation formula, calculate the reflection coefficients of the acoustic absorption mathematical model incident at different incident frequencies at the same incident angle of the sound wave, and use the minimization of the average reflection coefficient of the obtained multiple reflection coefficients as the objective function for maximizing acoustics. In this embodiment, the reflection coefficient can be expressed as: , where represents the angular frequency of the incident sound wave, represents the incident angle of the sound wave.

[0029] Obtain constraint conditions to optimize the objective function based on the constraint conditions. Among them, the constraint conditions include volume constraint and deformation amount constraint. In this embodiment, the volume constraint is obtained by normalizing the ratio of the amount of matrix material used in the current design domain to the predefined maximum volume fraction, so that the actual amount of matrix material used in the design domain has the same order of magnitude as the objective function to control the equivalent density of the cover layer. The deformation amount constraint uses the surface average deformation rate to represent the hydrostatic bearing performance of the cover layer and applies a constraint to the surface average deformation rate. Based on this, the constraint conditions are expressed as:

[0030] Among them, for the optimization objective of minimizing the reflection coefficient, using the positive integer variable divide the reflection coefficient at all frequencies to ensure that as the optimization progresses, when the reflection coefficient continually decreases and approaches 0, the objective function can still be effectively iteratively optimized. The volume constraint is a normalization constraint function comparing the volume fraction of the amount of matrix material used in the current design domain with the predefined maximum volume fraction to ensure that it has the same order of magnitude as the objective function; The deformation amount constraint restricts the average surface deformation rate to ensure the hydrostatic load-bearing performance of the coating, which is expressed as the average deformation amount of the lateral displacement at the coating surface. And the coating thickness The ratio of, the predefined maximum value is , the optimized coating can have a smaller deformation amount under hydrostatic conditions, thus ensuring its certain mechanical load-bearing capacity. Due to the large hydrostatic pressure in the deep-water environment, the load-bearing performance of the structure cannot be ignored. The present invention considers the hydrostatic pressure acting on the plane of the coating surface. At this time, the surface will deform, and the average deformation rate of this surface is used as a constraint condition. See Figure 3 As shown, in the acoustic absorption mathematical model, a static pressure of is applied on the plane of the coating surface, and the direction is perpendicular to the plane, while the lower surface of the steel backing to which the coating is attached plane is a fixed constraint. The coating along the x direction is still a periodic boundary condition. Since the hydrostatic pressure is always perpendicular to the coating surface, so in the periodic boundary condition . Under the action of the hydrostatic pressure, at this time:

[0031] Among them, and are the stiffness matrix and the static force under the periodic boundary condition respectively, , , is the conjugate transpose of the transformation matrix containing the boundary condition information, represents the conjugate transpose, is the stiffness matrix, is the transformation matrix containing the boundary condition information, is the equivalent force vector under the static hydrostatic pressure, which has a non-zero value at the coating surface and a value of 0 at the remaining degrees of freedom, can be expressed as:

[0032] Among them, represents the number of square grid cells, represents the transpose of the displacement interpolation shape function matrix of the k th grid cell on the plane, represents the hydrostatic pressure applied on the plane; Furthermore, the average deformation amount of the lateral displacement at the coating surface is expressed as:

[0033] Among them, represents the number of lateral displacement degrees of freedom at the surface of the coating, is a dimensionless column vector with a value of 1 for the lateral displacement degree of freedom at the surface of the coating and 0 for the remaining values, and U is the deformation of the coating.

[0034] According to an embodiment of the present invention, the structural optimization design is carried out based on the gradient-based topology optimization framework. For this purpose, in step S2, in the step of optimizing the design variables in the initial design based on density filtering and projection, density filtering is performed in the manner of interpolation based on the solid isotropic material penalization method, and the Heaviside projection operator is used for projection to alleviate numerical instabilities (such as checkerboard and mesh dependence, etc.) during the optimization process, making the optimized structure more conducive to processing and manufacturing; among them, the density filtering operator applied to density filtering is:

[0035] Among them, represents the filtering radius, represents the weight coefficient determined by the central positions of the square element and the square element , which makes the filtering variable corresponding to the variable be the weighted average of the variable and its neighboring variables , represents the central position vector of the square element , represents the central position vector of the square element ; Furthermore, the Heaviside projection operator applied to projection is:

[0036] Among them, and are the projection level and projection intensity respectively, is the final physical variable; In this embodiment, in step S2, in the step of performing density filtering in the manner of interpolation based on the solid isotropic material penalization method, interpolation is performed based on the variable of the square element to convert the discrete variable into a continuous variable, which is expressed as:

[0037] Among them, and are the density and Young's modulus of the square element respectively, and are the density and Young's modulus of the matrix material, respectively, and represent the artificial material parameters of the pore domain, respectively, and are the density and Young's modulus penalty coefficients, and represent the variables of the square element Heaviside projection operators for density and Young's modulus.

[0038] According to an embodiment of the present invention, in step S3, in the step of calculating the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design by using the wave finite element method, the prerequisite for calculating the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design by using the wave finite element method is that the design domain in the sound absorption mathematical model is a periodic structure. Under the excitation of a plane wave, the transverse displacement on the fluid-structure coupling boundary satisfies Bloch's theorem, so it satisfies the Bloch-Floquet theory. Furthermore, the wave finite element method can be used to calculate the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design. See Figure 3 shown, the plane wave is incident from the water area to the covering layer domain along the y positive direction, and its incident elevation angle is , and finally transmits from the air domain. The bottom of the structure is excited by the sound pressure wave, and its amplitude is , and the wave number is , then it is expressed as:

[0039] where, represents the fluid-structure coupling action matrix, and the subscript i represents the label of the incident sound wave, represents the angular frequency of the incident sound wave, , , for simplicity, is omitted in the following text.

[0040] Furthermore, under the excitation of a plane incident wave, reflected sound waves and transmitted sound waves will be generated, which are the sum of finite-order harmonics, that is:

[0041]

[0042] where, represents the amplitude of the reflected sound wave, and the subscript represents the label of the reflected sound wave, represents the amplitude of the transmitted sound wave, and the subscript A tag indicating the transmitted acoustic wave, Indicating the order, Indicating the maximum order, Indicating the period length, Is the wave number in the air domain.

[0043] At this time, under the conditions of specific frequency, elevation angle, and deflection angle of the incident acoustic wave, the sound energy absorption coefficient of the structure Is:

[0044] Wherein, , Respectively represent the impedances of water and air, and the reflection coefficient And the transmission coefficient Are respectively:

[0045] Wherein, Represents a simplified writing of the relational expression related to the parameters , ; Furthermore, due to the large impedance difference between the steel backing of the covering layer and the air domain, usually the transmission coefficient The value is very small and can be ignored when calculating the absorption coefficient. At this time, the absorption coefficient is approximately:

[0046] For numerically calculating the sound absorption performance of the structure, the wave finite method is used for calculation. Refer to Figure 3 , and considering the finite element control equations of the covering layer and the steel backing domain are:

[0047] Wherein, , Are respectively the node degrees of freedom and the external node forces in the finite element equation. The external node force is the equivalent force generated by the excitation of the acoustic wave on the incident surface and the transmission surface, , Are respectively the stiffness matrix and the mass matrix, , , , . Is the displacement interpolation shape function matrix of the finite element, Is the strain matrix (i.e., the partial derivative of ), Is the elastic matrix. The present invention adopts two-dimensional bilinear quadrilateral elements.

[0048] Furthermore, for the periodic structure, under the excitation of plane waves, the transverse displacement on the fluid-structure coupling interface satisfies the Bloch theorem, that is , where represents the wave function, represents the original position matrix, represents the displacement matrix, represents the wave number; thus, it can be written as the sum of a series of harmonic functions through Fourier transform, is the surface of the transmitted sound wave or the incident sound wave, that is:

[0049] satisfies:

[0050] where is the node degree of freedom.

[0051] Furthermore, for the surface of the covering layer at, let: , , where represents the amplitude value of the reflected surface excitation when the order is m , represents the amplitude value of the incident surface excitation when the order is m , represents the fluid-structure coupling action matrix of the reflection surface when the order is m , represents the fluid-structure coupling action matrix of the incident surface when the order is, then the total sound pressure field is:

[0052] where , according to the continuity boundary condition between the fluid and the structure, the normal displacement (velocity) of the covering layer medium is continuous, which is expressed as:

[0053]

[0054] where is the density, . Similarly, at the surface of the covering layer at,

[0055] where , .

[0056] Furthermore, when the th-order harmonic When acting on the surface of the covering layer (subscript represents the incident acoustic wave , the reflected acoustic wave or the transmitted acoustic wave ), for the th grid cell, a consistent external nodal force is generated, which is:

[0057] where represents the transpose of the displacement interpolation shape function matrix of the th square cell, represents the surface domain. When on the surface of the covering layer or the backing layer, . When assembling the external nodal force in the finite element method, the total excitation external force of the covering layer structure containing grid cells is: .

[0058] Furthermore, when the incident acoustic wave, the reflected acoustic wave, and the transmitted acoustic wave all act on the covering layer, the excitation term generated on the surface of the covering layer structure is:

[0059] Let there is:

[0060] Let , , , , it can be obtained that:

[0061] Since the covering layer is composed of countless periodic unit cells extended along the x direction, according to the Bloch-Floquet theory, the nodal displacement on the left boundary interface of the structure and the nodal degree of freedom on the right boundary interface satisfy the boundary conditions , . Therefore, the nodal degrees of freedom of the structure can be divided into left boundary, right boundary, and internal nodal degrees of freedom, that is . Under the periodic boundary conditions, the nodal degrees of freedom can be simplified to . The degrees of freedom and the periodic degrees of freedom satisfy the following conditions:

[0062] Thus, a dynamic equation satisfying the Bloch-Floquet theory is obtained.

[0063] wherein, , , , denotes the conjugate transpose. When the dynamic equation is solved to obtain the periodic degrees of freedom afterwards, the full degrees of freedom and the reflection coefficient can be obtained, and are expressed as: .

[0064] According to an embodiment of the present invention, in step S4, in the step of evaluating the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient, the gradients of the objective function and the constraint conditions with respect to the design variables are calculated, and the sensitivity is evaluated based on the gradients. During the calculation process, after calculating the m th-order reflection coefficient, its sensitivity needs to be calculated according to the chain rule. First, according to the partial differential equations for calculating the objective function and the constraint function with respect to the final physical variable , that is: ; Let , the partial derivative of the th-order reflection coefficient with respect to the th physical variable is: ; The partial derivative of the calculated degrees of freedom with respect to the th physical variable is:

[0065] wherein, .

[0066] Furthermore, based on the adjoint method, the sensitivity of the objective function can be calculated by combining the above formulas; wherein, the sensitivity of the objective function includes: the volume sensitivity and the sensitivity of the average deformation of the lateral displacement at the surface of the covering layer, and is specifically expressed as: The volume sensitivity is: ; The sensitivity of the average deformation of the lateral displacement at the surface of the covering layer is: , wherein, .

[0067] Furthermore, calculate with respect to the initial variables according to the chain rule Sensitivity. Since density filtering and Heaviside projection are used in the optimization process, the function with respect to the initial variable partial derivatives satisfy the following chain rule:

[0068] where the differential terms introduced based on the density filtering operator and Heaviside projection are: .

[0069] According to an embodiment of the present invention, in step S5, the design variables are updated based on the moving asymptote method, and steps S2 to S5 are repeatedly executed until the preset iteration requirements are met, so as to output the result of the finally optimized design variables, and in the step of outputting the sound absorption structure of the porous material based on the result, the solution process of the moving asymptote method for the objective function with multiple constraint conditions is as follows: Step 1: Abstract the original problem as : Minimize

[0070] Constraint conditions

[0071] and

[0072] Select the initial point , iteration index .

[0073] Select the iteration point , calculate and the gradient .

[0074] Step 2: Based on the calculation results of step 1, replace the implicit function in the problem with the explicit function , and generate the sub-problem .

[0075] Step 3: Solve the sub-problem , and use it as the iteration point for the next loop. Let , and repeat step 1. Among them, when the solution obtained in a certain loop meets the requirements or reaches the maximum number of iterations, the loop is terminated and the current solution is output.

[0076] According to an embodiment of the present invention, the present invention provides an apparatus for the design method of the porous material sound absorption structure described above, including: an initial design module, a density filtering and projection module, a wave finite element method calculation and sensitivity analysis module, and a solution calculation and structure determination module; wherein, the initial design module establishes an acoustic mathematical model based on rubber materials and porous materials, and obtains an objective function for maximizing acoustic performance, and adds constraint conditions to the optimization objective function to randomly generate an initial design that satisfies the objective function and constraint conditions; the density filtering and projection module optimizes the design variables in the initial design based on density filtering and projection; the wave finite element method calculation and sensitivity analysis module calculates the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design by using the wave finite element method, and evaluates the sensitivity of the design variables to the objective function and constraint conditions based on the sound absorption coefficient; the solution calculation and structure determination module updates the design variables based on the moving asymptote method for the density filtering and projection module and the wave finite element method calculation and sensitivity analysis module to perform iterative optimization until the preset iteration requirements are met, so as to output the result of the finally optimized design variables, and output the porous material sound absorption structure based on the result.

[0077] According to an embodiment of the present invention, the present invention provides an electronic device for the design method of the porous material sound absorption structure described above, including a memory and a processor, where the memory stores a mathematical model and a computer program, and the porous material sound absorption structure design method is implemented when the processor executes the computer program.

[0078] In this embodiment, the memory may be, but is not limited to, a random access memory (RAM), a read only memory (ROM), a programmable read only memory (PROM), an erasable programmable read only memory (EPROM), an electrically erasable programmable read only memory (EEPROM), etc.

[0079] In this embodiment, the processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0080] In this embodiment, the electronic device provided by the present invention further includes: a network interface, a display screen, and an input device; wherein, the network interface of the electronic device is used to communicate with an external terminal through a network connection. The display screen of the electronic device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic device can be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the housing of the electronic device, or an external keyboard, touchpad, or mouse, etc.

[0081] According to an embodiment of the present invention, there is provided a storage medium for the aforementioned porous material sound absorption structure design method, on which a computer program is stored, and the porous material sound absorption structure design method is implemented when the computer program is executed by a processor.

[0082] To further illustrate the present solution, further examples are given for elaboration.

[0083] Example 1 For Figure 3 the model in, a commercial finite element software COMSOL Multiphysics is used to establish a sound-solid coupling model for simulating and calculating the sound absorption coefficient. In the simulation model, x on the boundary in the Figure 3 direction, the bloch-floquet boundary condition is applied, with one side of the covering layer being a semi-infinite water area and the back lining being a semi-infinite air area. At the same time, for

[0084] the covering layer structure model of Figure 4 as shown, based on the MATLAB language, the wave finite element method is implemented to calculate its sound absorption coefficient.

[0085] Figure 4In the results shown, when the incident wave is a normal plane wave, different harmonic orders have a certain influence on the calculation results of the wave finite element method. Among them, when the value is greater than or equal to 3, the calculation result of the sound absorption coefficient no longer changes with the increase of , and it is in good agreement with the COMSOL simulation results. When the incident wave is an oblique incident wave, for plane waves with incident angles of 50° and 70° respectively, the calculation results are in good agreement with the COMSOL simulation results, effectively verifying the accuracy of the wave finite element method.

[0086] In the optimized model (framework), the filtering radius r = 12q, and the projection level in the Heaviside projection operator , the projection intensity The initial value is 1, and then it is increased by 1.4 times every 50 generations. After 200 generations ( ), it is decreased to be increased by 1.2 times every 50 generations. Finally, when the projection intensity reaches the value of 1000, it no longer increases. The maximum number of iterations in the optimization process is 2000 times. In SIMP, the penalty coefficients of density and Young's modulus are and . The optimization problem of the sound absorption performance under this multi-constraint condition is solved by the MMA (Method of Moving Asymptotes) moving asymptote method. The parameters for updating the asymptotes in MMA are: the initial position parameter asyminit = 0.25, the attenuation factor asymdec = 0.7, the growth factor asyminc = 1.1, and the moving step limit move = 0.1. In addition, the parameters of the MMA optimization problem are: the initial value of the internal scaling factor , the corresponding to the reflection coefficient constraint, and the of the other constraints; the initial value of the external scaling factor ; the initial values of the other parameters . In the volume constraint, in order to achieve a lightweight covering layer to provide a weak positive buoyancy, the overall density of the constrained rubber and the embedded scatterer structure does not exceed water ( ), and the maximum volume fraction is . In the surface average deformation rate constraint, since only linear deformation is considered in this paper, in order to avoid large calculation errors caused by non-linear deformation under large hydrostatic pressure conditions, the surface average deformation rate is controlled at a small value, taking .

[0087] The sound absorption structure designed by this method and its acoustic performance are as Figure 5 shown.

[0088] It can be seen that the experimental results show that the method proposed in the present invention can successfully design a sound-absorbing structure of porous materials that meets the requirements of lightweight and pressure resistance.

[0089] The above content is only an example of the specific solution of the present invention. For the devices and structures not described in detail therein, it should be understood that the existing general devices and general methods in the art are adopted for implementation.

[0090] The above is only one solution of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for designing the sound absorption structure of a porous material, characterized in that It includes the following steps: S1. Establish an acoustic absorption mathematical model based on rubber materials and porous materials, obtain an objective function for maximizing acoustic performance, and add constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions; S2. Optimize the design variables in the initial design based on density filtering and projection; S3. Use the wave finite element method to calculate the acoustic absorption coefficient of the porous material acoustic absorption structure corresponding to the optimized initial design; S4. Evaluate the sensitivity of the design variables to the objective function and the constraint conditions based on the acoustic absorption coefficient; S5. Update the design variables based on the moving asymptote method to repeat steps S2 to S5 until the preset iteration requirements are met, output the result of the finally optimized design variables, and output the porous material acoustic absorption structure based on the result; 2. The design method of the sound absorption structure of the porous material according to claim 1, characterized in that, In step S1, the acoustic absorption mathematical model is an underwater acoustic absorption mathematical model; The acoustic absorption mathematical model includes: a scatterer made of a porous material, and a covering layer made of a rubber material coated on the outside of the scatterer; 3. The method for designing the sound absorption structure of the porous material according to claim 2, wherein In step S1, the steps of establishing an acoustic absorption mathematical model based on rubber materials and porous materials include: Set the area with a preset surface thickness of the scatterer as the constraint area, and set the remaining area surrounded by the constraint area as the design domain; Discretize the design domain into equal square elements and assign a variable to describe the material properties of each of the square elements, where the variable describes a functional relationship between the square element and the physical properties of the material, being 1 indicates that the square element is the matrix material, being 0 indicates that the square element is a hole region.

4. The method for designing the sound absorption structure of the porous material according to claim 3, characterized in that, In step S1, the steps of establishing an acoustic absorption mathematical model based on rubber materials and porous materials, obtaining an objective function for maximizing acoustic performance, and adding constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions include: Based on the reflection coefficient calculation formula, calculate the reflection coefficients of the acoustic absorption mathematical model incident at different incident frequencies at the same incident angle of the sound wave, and use the minimum average reflection coefficient of the obtained multiple reflection coefficients as the objective function for maximizing acoustics; Obtain the constraint conditions to optimize the objective function based on the constraint conditions; wherein, the constraint conditions include volume constraint and deformation amount constraint; 5. The method for designing the sound absorption structure of the porous material according to claim 4, wherein The volume constraint is obtained by normalizing the amount of matrix material used in the current design domain with the predefined maximum volume fraction, so that the actual amount of matrix material used in the design domain has the same order of magnitude as the objective function to control the equivalent density of the covering layer; The deformation amount constraint uses the surface average deformation rate to represent the hydrostatic bearing performance of the covering layer and applies a constraint to the surface average deformation rate; 6. The design method of the sound absorption structure of the porous material according to claim 5, characterized in that, In step S2, in the steps of optimizing the design variables in the initial design based on density filtering and projection, density filtering is performed by interpolation based on the solid isotropic material penalty method, and Heaviside projection operator is used for projection; wherein, the density filtering operator applied to density filtering is: Among them, represents the filtering radius, indicates that it is the weight coefficient determined by the central positions of the square unit and the square unit such that the filtering variable corresponding to the variable is the weighted average of the variable and its neighboring variables ; represents the central position vector of the square unit ; represents the central position vector of the square unit ;​ The Heaviside projection operator applied to projection is: Among them, and are the projection level and the projection intensity respectively, is the final physical variable; In step S2, in the step of performing density filtering by means of interpolation based on the solid isotropic material penalization method, based on the variables of the square element interpolation is performed to convert the discrete variable into a continuous variable, which is expressed as: Among them, and are the density and Young's modulus of the square unit respectively, and are the density and Young's modulus of the matrix material respectively, and represent the artificial material parameters of the hole domain respectively, and are the density and Young's modulus penalty coefficients.

7. The method for designing the sound absorption structure of the porous material according to claim 6, wherein In step S4, in the step of evaluating the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient, calculate the gradients of the objective function and the constraint conditions with respect to the design variables, and evaluate the sensitivity based on the gradients.

8. An apparatus for a method of designing a sound-absorbing structure of a porous material according to any one of claims 1 to 7, characterized in that, It includes: An initial design module, which establishes an acoustic absorption mathematical model based on rubber materials and porous materials, obtains an objective function for maximizing acoustic performance, and adds constraint conditions to optimize the objective function to randomly generate an initial design that satisfies the objective function and the constraint conditions; A density filtering and projection module, which optimizes the design variables in the initial design based on density filtering and projection; A wave finite element method calculation and sensitivity analysis module, which uses the wave finite element method to calculate the sound absorption coefficient of the porous material sound absorption structure corresponding to the optimized initial design, and evaluates the sensitivity of the design variables to the objective function and the constraint conditions based on the sound absorption coefficient; A solution calculation and structure determination module, which updates the design variables based on the moving asymptote method for the density filtering and projection module and the wave finite element method calculation and sensitivity analysis module to perform iterative optimization until the preset iteration requirements are met, to output the result of the finally optimized design variables, and output the porous material sound absorption structure based on the result; 9. An electronic device for the method of designing the sound absorption structure of the porous material according to any one of claims 1 to 7, characterized in that, It includes a memory and a processor, the memory stores a mathematical model and a computer program, and when the processor executes the computer program, it implements the porous material sound absorption structure design method described above.

10. A storage medium for the sound absorption structure design method of the porous material according to any one of claims 1 to 7, characterized in that A computer program is stored thereon, and when the computer program is executed by a processor, it implements the porous material sound absorption structure design method described above.

Images