Acoustic metamaterial with frequency-doubling filtering characteristics and shape optimization method thereof

Abstract

The application relates to an acoustic metamaterial with a frequency-doubling filtering characteristic and a shape optimization method thereof, the optimization method comprising the following steps: constructing a two-dimensional finite element simulation model, the two-dimensional finite element simulation model comprising a main plate, a thin adhesive layer and an acoustic metamaterial, the acoustic metamaterial having an initial structure, the initial structure being periodically arranged by an initial unit cell structure, and a free-shape boundary being arranged in the initial structure; constructing an optimization model according to a target that a fundamental frequency is a passband and a frequency double is a stopband; adjusting the free-shape boundary on the basis of the initial structure by using a moving asymptote method; and calculating to obtain an optimal structure of the acoustic metamaterial. Compared with the prior art, the application not only ensures that the optimization target can be achieved, but also reduces the complexity of the structure, facilitates processing and manufacturing, and the designed acoustic metamaterial has the frequency-doubling filtering characteristic, and can effectively filter the inevitable system nonlinearity in nonlinear ultrasonic Lamb wave detection.

Description

Technical Field

[0001] This invention relates to the field of acoustic metamaterial design technology, and in particular to an acoustic metamaterial with second harmonic filtering characteristics and its shape optimization method. Background Technology

[0002] Acoustic metamaterials, as artificial composite structures, exhibit extraordinary physical properties not found in natural materials, allowing for free control of sound wave transmission. Compared to natural materials, acoustic metamaterials can achieve many interesting sound field manipulation functions, such as acoustic cloaking, sound focusing, beam splitting, perfect sound absorption, and filtering. Among these, filtering, which removes specific frequency bands from a signal, is an effective measure to suppress and prevent interference. In nonlinear ultrasonic Lamb wave detection, system nonlinearity is unavoidable, severely affecting the accuracy of damage detection. To address this issue, acoustic metamaterials are introduced into nonlinear ultrasonic Lamb wave detection systems. Their filtering properties can reduce or even eliminate second harmonics generated by system nonlinearity, while simultaneously ensuring the fundamental wave can propagate smoothly to the damaged area, thereby improving the sensitivity and accuracy of damage detection. Acoustic metamaterials, with their unique filtering properties, have attracted widespread attention from scholars both domestically and internationally, and show broad application prospects in fields such as acoustic communication and nondestructive testing.

[0003] Currently, significant progress has been made in the research of acoustic metamaterials both domestically and internationally. However, research on metamaterials in filtering mainly focuses on achieving a single filtering function and cannot be used to eliminate system nonlinearity in nonlinear ultrasonic Lamb wave detection.

[0004] According to literature reports, existing studies on acoustic metamaterials typically employ size optimization or topology optimization for shape design. However, both methods have limitations: size optimization offers limited design freedom, often failing to achieve the final target and resulting in poor optimization effects; topology optimization generally produces complex geometries, posing high requirements and difficulties in fabrication. Furthermore, some studies have designed acoustic metamaterials that only filter at a specific frequency point, rather than targeting an entire frequency band. Therefore, further research into optimization design methods is necessary to broaden the stopband frequency range of acoustic metamaterials, allowing for more flexible selection of operating frequencies. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art by providing an acoustic metamaterial with second harmonic filtering characteristics and its shape optimization method, which can ensure the passage of fundamental frequency sound waves while suppressing the propagation of second harmonic sound waves, thereby solving the problem of the difficulty in eliminating system nonlinearity in nonlinear ultrasonic Lamb wave detection.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for optimizing the shape of acoustic metamaterials with second harmonic filtering characteristics includes the following steps:

[0008] A two-dimensional finite element simulation model is constructed, which includes a motherboard, a thin adhesive layer, and an acoustic metamaterial. The acoustic metamaterial is bonded to the motherboard through the thin adhesive layer. The acoustic metamaterial has an initial structure, which is formed by the periodic arrangement of initial unit cell structures. Free-shape boundaries are set in the initial structure.

[0009] Based on the objective of using the fundamental frequency as the passband and the second harmonic as the stopband, an optimization model is constructed. Using the moving asymptote method, the free-form boundary is adjusted on the basis of the initial structure, and the optimal structure of the acoustic metamaterial is calculated.

[0010] Furthermore, the initial unit cell structure is a T-shaped cross-section structure, comprising rectangular blocks and square blocks spliced ​​together to form a T shape, wherein the upper boundary and left and right boundaries of the square blocks are both set as the free shape boundaries.

[0011] Furthermore, the physical field of the two-dimensional finite element simulation model is set as follows: the upper and lower surfaces of the motherboard are set as free boundary conditions, a specified displacement is applied along the x-direction on the left boundary of the simulation model to simulate the excitation of the symmetric mode Lamb wave, and the right boundary is set as a low reflection boundary condition.

[0012] Furthermore, the step of calculating and obtaining the optimal structure of the acoustic metamaterial includes:

[0013] Network partitioning is performed on the two-dimensional finite element simulation model;

[0014] Based on the constructed optimization model, an optimization solver is selected, and calculations are performed within the selected frequency range based on the set maximum number of iterations and optimization tolerance to obtain the optimal structure.

[0015] Furthermore, in the network partitioning, the motherboard, thin adhesive layer, and rectangular blocks all use mapped meshes, while the rectangular blocks use free triangle meshes.

[0016] Furthermore, the maximum unit size of the free triangular mesh is 0.5 mm.

[0017] Furthermore, the objective function in the optimization model is expressed as:

[0018]

[0019] In the formula, obj is the objective function value, u in u out denoted as the in-plane displacements at the input and output ends, respectively, and f and 2f as the fundamental frequency and second harmonic, respectively.

[0020] Furthermore, when calculating the optimal structure of the acoustic metamaterial, the method of geometry creation includes:

[0021] Remesh the deformable configuration and create new geometry based on the mesh; or

[0022] The optimization results are exported in segments, interpolation curves are added to create new geometries, and the generated shape is adjusted by adjusting the relative tolerance.

[0023] Furthermore, the method also includes:

[0024] The optimal structure was imported into a two-dimensional finite element simulation model, and frequency domain and time domain analyses were performed to verify its performance.

[0025] The present invention also provides an acoustic metamaterial with second harmonic filtering characteristics, which is obtained by optimizing the shape of the acoustic metamaterial with second harmonic filtering characteristics as described above.

[0026] Compared with existing technologies, this invention, through optimized structural design, enables fundamental frequency sound waves to propagate within the flat plate while suppressing the propagation of second harmonic sound waves, thus offering the following beneficial effects:

[0027] (1) The acoustic metamaterial of the present invention is designed based on shape optimization, which overcomes the disadvantages of limited design freedom of size optimization and high manufacturing difficulty of topology optimization. It not only ensures that the optimization goal can be achieved, but also reduces the complexity of the structure and facilitates processing and manufacturing.

[0028] (2) The acoustic metamaterial designed in this invention has a second harmonic filtering characteristic, which ensures that the fundamental frequency sound wave can propagate while suppressing the propagation of the second harmonic sound wave. It can effectively filter out the unavoidable system nonlinearity in nonlinear ultrasonic Lamb wave detection and has great application value in the field of structural health monitoring.

[0029] (3) In the meshing of this invention, the square design domain adopts a free triangular mesh, and the maximum unit size is designed to be much smaller than the wavelength, which can save calculation time and ensure calculation accuracy. Attached Figure Description

[0030] Figure 1 Here is a schematic diagram of the acoustic metamaterial structure of the present invention, wherein (1a) is the shape optimization finite element model of the acoustic metamaterial with second harmonic filtering characteristics of the present invention, and (1b) is a schematic diagram of the initial unit structure of the acoustic metamaterial in (1a).

[0031] Figure 2 The present invention relates to the iterative change curve of the objective function during the shape optimization process and the geometric shape changes before and after optimization;

[0032] Figure 3These are the frequency response curves of the initial structure and the optimized structure in the range of 20-100kHz. The short dashed line in the figure is the frequency response curve of the initial structure, the solid line is the frequency response curve of the optimized structure, and the shaded area is the preset fundamental frequency range and second harmonic range.

[0033] Figure 4 These are in-plane displacement field distribution diagrams when Lamb waves of different frequencies are incident from the left side of the model, where (4a) has a frequency of 40kHz and (4b) has a frequency of 80kHz.

[0034] Figure 5 These are schematic diagrams of different geometric structures created based on shape optimization results. Among them, (5a) is a schematic diagram of a geometric structure created based on a mesh, (5b) is a schematic diagram of a geometric structure created based on an interpolation curve with a relative tolerance rt of 0.001, (5c) is a schematic diagram of a geometric structure created based on an interpolation curve with a relative tolerance rt of 0.05, and (5d) is a schematic diagram of a geometric structure created based on an interpolation curve with a relative tolerance rt of 0.1.

[0035] Figure 6 yes Figure 5 The frequency response curves of different geometric structures in the range of 20-100kHz are shown in the figure. The solid line is the frequency response curve of the geometric structure shown in (5a), the dashed line is the frequency response curve of the geometric structure shown in (5b), the dotted line is the frequency response curve of the geometric structure shown in (5c), the dotted line is the frequency response curve of the geometric structure shown in (5d), and the shaded area is the preset fundamental frequency range and second harmonic range.

[0036] Figure 7 The figure shows the frequency response curves of the acoustic metamaterial in the range of 20-100kHz under different adhesive layer thicknesses h2. The solid line in the figure is the frequency response curve when h2 = 0.01mm, the dashed line is the frequency response curve when h2 = 0.05mm, and the dotted line is the frequency response curve when h2 = 0.1mm.

[0037] Figure 8 These are the in-plane displacement signals received with and without metamaterial under different frequency excitations. Among them, the frequency of (8a) is 40kHz and the frequency of (8b) is 80kHz. The dashed line in the figure is the in-plane displacement signal received without metamaterial, and the solid line is the in-plane displacement signal received with metamaterial. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0039] There is limited research on acoustic metamaterials with a fundamental frequency passband and a second harmonic stopband in existing technologies, and there is currently no method for optimizing the design of acoustic metamaterials with second harmonic filtering characteristics based on shape optimization. To address the difficulty in eliminating system nonlinearity in nonlinear ultrasonic Lamb wave detection, and to overcome the drawbacks of limited design freedom in size optimization and high manufacturing difficulty in topology optimization, this invention provides a shape optimization method for acoustic metamaterials with second harmonic filtering characteristics. The method includes: constructing a two-dimensional finite element simulation model, comprising a main board, a thin adhesive layer, and an acoustic metamaterial, wherein the acoustic metamaterial is bonded to the main board via the thin adhesive layer. The acoustic metamaterial has an initial structure, which is formed by periodically arranging initial unit cell structures, and includes free-form boundaries within the initial structure; based on the objective of a fundamental frequency passband and a second harmonic stopband, an optimization model is constructed; using the moving asymptote method, the free-form boundaries are adjusted based on the initial structure to calculate the optimal structure of the acoustic metamaterial.

[0040] The acoustic metamaterial structure of the device, optimized by the above method, can be bonded to the test motherboard to achieve a filtering function, which can ensure that the fundamental frequency sound wave can pass smoothly while suppressing the propagation of the second harmonic sound wave.

[0041] This embodiment uses the finite element simulation software COMSOL Multiphysics to optimize the shape design of acoustic metamaterials. The specific steps include:

[0042] (1) Establishing the model environment

[0043] This embodiment selects a "two-dimensional" spatial dimension and a "solid mechanics" physical field, and selects "frequency domain" as the research type, which can be used to calculate the frequency response of the structure.

[0044] (2) Constructing a geometric model

[0045] Based on the filtering problem to be solved, a two-dimensional finite element simulation model is established, which includes a main board, an acoustic metamaterial, and a thin adhesive layer. To improve optimization efficiency, an initial metamaterial structure is designed first, which consists of a periodic arrangement of T-shaped sections, where the T-shaped sections include rectangular and square blocks. The required geometric parameters include the length and thickness of the main board, the thickness of the adhesive layer, the height of the rectangular blocks of the T-shaped sections, the side length of the square blocks, and the number of periods.

[0046] Figure 1 (1a) is the two-dimensional finite element simulation model constructed in this embodiment. The main board is 500mm long and 2mm thick. The initial unit cell structure is designed as follows: Figure 1As shown in (1b), it includes a T-shaped cross-section, which is combined with the main board through a thin adhesive layer. The T-shaped cross-section consists of a rectangular region and a square region. In the figure, h1 is the thickness of the main board, h2 is the thickness of the thin adhesive layer, h3 is the thickness of the rectangular region, and a is the side length of the square region. Specific dimensional parameters are shown in Table 1.

[0047] Table 1 Geometric Dimensions

[0048]

[0049] (3) Define material properties

[0050] The two-dimensional model consists of a main board, a periodic T-section, and a thin adhesive layer. The main board is made of aluminum, the periodic T-section is made of lead, and the adhesive used is "UHU PLUS ENDFEST 300" epoxy resin AB glue. Material parameters are shown in Table 2, where ρ is density, E is Young's modulus, and υ is Poisson's ratio. The significant difference in impedance between lead and aluminum is beneficial for creating a wider stopband.

[0051] Table 2 Material Parameters

[0052]

[0053] (4) Set physical fields and boundary conditions

[0054] An acoustic metamaterial shape optimization model was established using the finite element simulation software COMSOL, and the physical field was constructed based on the solid mechanics module of COMSOL software.

[0055] This embodiment employs a solid mechanics module, setting the upper and lower surfaces of the plate as free boundary conditions. A specified displacement u0 = 1 mm is applied along the x-direction on the left boundary of the model to simulate the generation of Lamb waves; the right boundary is set as a low-reflection boundary condition to reduce Lamb wave reflection. Furthermore, to optimize the structural design, a shape optimization interface is added to the software, allowing for free deformation of the geometry. Figure 1 As shown in (1b), the square domain is set as a free-shape domain, and the upper boundary and left and right boundaries of the square domain are both set as free-shape boundaries. The maximum displacement of the boundary deformation is a / 2.

[0056] (5) Grid division

[0057] Based on the established two-dimensional finite element simulation model, mesh generation is performed. This invention employs shape optimization for structural design, a method achieved by deforming the mesh. Reasonable mesh generation helps improve optimization efficiency.

[0058] In this embodiment, the motherboard, thin adhesive layer, and T-shaped cross-section rectangular domain all use mapped meshes, with 5, 2, and 3 mesh layers respectively along the thickness direction (z direction). The square design domain uses a free triangular mesh, with a maximum cell size of 0.5 mm (much smaller than the wavelength), which saves computation time while ensuring computational accuracy.

[0059] (6) Solving the model

[0060] Set up the "Shape Optimization" study step and select the optimization solver. Employ the Moving Asymptote (MMA) method and set the objective function, constraints, maximum number of iterations, and optimization tolerance. During optimization, it's necessary to consider that the shapes of the design domains will not intersect; therefore, a constraint is added: the displacement d of the mesh nodes in the design domain does not exceed a / 2, i.e., d... max = a / 2. Then add a "frequency domain" study, set the selected frequency range for calculation, and find the optimal value.

[0061] Before optimization, the objective function needs to be determined, as its value guides the direction in which the structural shape changes. The objective function in this invention aims to achieve two objectives: first, to ensure the smooth passage of the fundamental frequency sound wave; and second, to suppress the propagation of the second harmonic sound wave, meaning the fundamental frequency response should be as large as possible, and the second harmonic frequency response as small as possible. Therefore, the optimization problem is transformed into a minimization problem, and the objective function is expressed as:

[0062]

[0063] In the formula, obj is the objective function value, u in u out Let be the in-plane displacements at the input and output terminals, respectively, and f and 2f be the fundamental frequency and second harmonic, respectively. For the fundamental frequency f, when u in ≤u out When the objective function value obj is 0, optimization stops; when u in >u out To increase the frequency response, u out / u in As the frequency response gradually approaches 1, the objective function value obj gradually approaches 0. For the second harmonic 2f, to reduce the frequency response, u... out / u in The value gradually approaches 0, meaning the objective function value obj also gradually approaches 0. In this embodiment, the fundamental frequency range is preset to 35-45kHz, corresponding to a second harmonic range of 70-90kHz, and the optimization tolerance is set to 10. -3 The maximum number of iterations is 100. After all settings are completed, the solution will begin until the final optimization result is output.

[0064] (7) Post-processing of results

[0065] The final optimized shape of the acoustic metamaterial is output, and the performance of the results is verified. Figure 2 The final optimization model of the acoustic metamaterial and the iterative change curve of the objective function are presented.

[0066] In this embodiment, the filtering performance of the designed acoustic metamaterial is verified from both frequency and time domain perspectives. A corresponding two-dimensional model is established in the finite element simulation software COMSOL. The optimized structure of the final design is imported into the new model to replace the initial metamaterial structure. Frequency and time domain analyses are performed using the solid mechanics module. During the analysis, the upper and lower surfaces of the plate are set as free boundary conditions, and the right boundary is set as a low-reflection boundary condition to reduce Lamb wave reflection.

[0067] 1) Frequency domain verification

[0068] During frequency domain analysis, a specified displacement is applied along the x-direction on the left boundary of the model to simulate the generation of S-mode Lamb waves. A frequency domain solver is then selected for frequency sweep calculation to obtain the frequency response of the structure. Furthermore, the effects of minute variations in the metamaterial structure and the thickness of the adhesive layer on the filtering performance are considered. Minor structural variations can be achieved using different methods of constructing geometric models in COMSOL software, while variations in the adhesive layer thickness can be achieved through parametric sweeps.

[0069] This embodiment utilizes the solid mechanics module of the finite element software COMSOL to calculate the frequency response of the structure. The optimized structure, as shown in the previous example, is imported into a new model, replacing the initially designed acoustic metamaterial, while other settings remain unchanged. In the study settings, a frequency domain solver is selected, and a frequency sweep calculation is performed within the 20-100kHz frequency range with a step size of 1kHz. The frequency response function is defined as FR = 20log(u out / u in ), where u out and u in These are the in-plane displacements at the output and input ends, respectively. This index can be used to quantify the degree of wave attenuation.

[0070] Figure 3 The frequency responses of the initial and optimized structures under different frequency excitations are presented, where negative values ​​indicate wave attenuation within the corresponding frequency range. The figures show that, compared to the initial structure, the optimized structure exhibits almost no wave attenuation in the fundamental frequency range, indicating that fundamental frequency sound waves can pass smoothly through the optimized structure. However, the corresponding second harmonic range shows some attenuation, indicating that second harmonic sound waves are suppressed from propagating within the structure. The in-plane displacement fields under 40kHz (fundamental frequency) and 80kHz (second harmonic) excitations are calculated, as follows: Figure 4 As shown in (4a) and (4b), it is clear that a 40kHz wave can pass smoothly through the acoustic filtering metamaterial and continue to propagate along the plate, while an 80kHz wave cannot pass through the optimized metamaterial structure.

[0071] Because the fabrication process of metamaterials may involve certain manufacturing errors, minor dimensional changes were made to the designed metamaterial structure to verify the impact of these minor dimensional changes on filtering performance. In COMSOL software, there are two methods for creating geometry based on shape optimization results. The first is "re-meshing for deformable configurations," which creates geometry based on the mesh, such as... Figure 5 As shown in (5a); the second method is to export the optimization results in "segments" and then add "interpolation curves" to create new geometry, and the generated shape can be adjusted by adjusting the relative tolerance rt, such as Figure 5 As shown in (5b), (5c), and (5d), a smaller tolerance rt results in a more realistic curve that reflects the data, but may generate complex or "wobbly" geometry. Conversely, a larger tolerance rt may result in an oversimplified curve that does not faithfully reflect the optimization results. In this embodiment, relative tolerances of 0.001, 0.05, and 0.1 are selected to construct different metamaterial structures. For the four different structures, frequency analysis is performed using the finite element numerical simulation method to calculate the frequency response function of each structure. Figure 6 Frequency response curves for four structures are presented. As shown in the figures, within the 35-45kHz (fundamental frequency) range, the frequency response functions of different geometries are not significantly different, with almost no attenuation, indicating that the fundamental wave passes smoothly. Within the 70-90kHz (second harmonic) range, the wave exhibits some attenuation, although the amount of attenuation varies, it still provides suppression. Therefore, minor changes in the metamaterial structure do not affect its filtering performance, and the geometry created based on the interpolation curve exhibits the best filtering performance when the relative tolerance rt is 0.05.

[0072] Furthermore, it is difficult to precisely control the thickness of the adhesive layer in practical situations. This embodiment also analyzes the impact of the adhesive layer thickness on the filtering performance. Figure 7 Frequency response curves of the acoustic metamaterial with different adhesive layer thicknesses are presented. When the adhesive layer thickness h3 varies between 0.01-0.1 mm, the frequency response in the 35-45 kHz frequency range does not change significantly, indicating that the adhesive layer thickness has no effect on the fundamental frequency sound wave, which can pass smoothly. While the attenuation in the 70-90 kHz frequency range changes somewhat, overall attenuation still occurs, indicating that the second harmonic sound wave is still suppressed. Therefore, the adhesive layer thickness has little impact on the filtering performance of the acoustic metamaterial of this invention.

[0073] 2) Time-domain verification

[0074] For time-domain analysis, a sinusoidal pulse displacement signal with 7 cycles of Hanning window modulation was applied to the left boundary of the model. The excitation frequencies were 40 kHz and 80 kHz, respectively, and the displacement amplitude was 1 μm. A transient solver was selected, and the time step was 6 × 10⁻⁶. -7 s, receives the in-plane displacement signal of the upper surface of the plate on the right side of the model.

[0075] This embodiment utilizes COMSOL software to perform time-domain analysis of acoustic metamaterials. First, a geometric model is established, and the optimized structure, derived from the previous optimization, is imported into the new model, replacing the initially designed acoustic metamaterial. This embodiment still employs the solid mechanics module, setting the upper and lower surfaces of the plate as free boundary conditions, and setting a low-reflection boundary condition on the right boundary to avoid end-face reflection of Lamb waves. An in-plane displacement signal u = u0A(t) is applied to the left boundary, where the excitation displacement amplitude u0 = 1 μm, which is typically the order of magnitude for Lamb waves propagating in solids; A(t) is a 7-cycle Hanning window modulated sinusoidal signal with excitation frequencies of 40 kHz and 80 kHz, i.e., the fundamental frequency and second harmonic. A symmetrical excitation method is used to generate symmetrical mode Lamb waves in the simulation. The mesh generation is consistent with the previous method; the main plate, adhesive layer, and T-shaped rectangular domain are meshed using a mapped mesh, while other parts use a free triangular mesh. The maximum element size is 0.5 mm (much smaller than the wavelength), resulting in a total of 28,947 domain elements and 12,683 boundary elements. The solver type is selected as transient solver, and the time step is 6 × 10⁻⁶. -7 After calculation, the in-plane displacement signals received before and after the installation of the acoustic metamaterial under excitation at 40kHz and 80kHz are as follows: Figure 8 As shown in (8a) and (8b), the signal amplitude decreases slightly under 40kHz excitation, but remains relatively large, indicating that the wave can pass through smoothly; the signal amplitude decreases significantly under 80kHz excitation, indicating that the propagation of the second harmonic sound wave can be suppressed. Furthermore, in... Figure 8 In (8a), it can be observed that the signal lags after the acoustic metamaterial is installed. However, the filtering performance is based on the signal amplitude rather than the signal phase, and the same applies to the subsequent application of the nonlinear ultrasonic Lamb wave detection method.

[0076] This invention first optimizes the shape of the acoustic metamaterial structure to obtain an acoustic metamaterial with second-harmonic filtering characteristics. Then, the filtering performance of the acoustic metamaterial is verified from both frequency and time domain perspectives, demonstrating that the designed acoustic metamaterial not only ensures the smooth passage of fundamental frequency sound waves but also suppresses the propagation of second-harmonic sound waves, and possesses a certain stopband width, indicating that the excitation frequency can be flexibly selected. This invention can be used for nonlinear ultrasonic Lamb wave detection, solving the problem of difficulty in filtering out system nonlinearity during the detection process, and has broad application prospects in the field of structural health monitoring.

[0077] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for optimizing the shape of acoustic metamaterials with second-harmonic filtering characteristics, characterized in that, Includes the following steps: A two-dimensional finite element simulation model is constructed, which includes a motherboard, a thin adhesive layer, and an acoustic metamaterial. The acoustic metamaterial is bonded to the motherboard through the thin adhesive layer. The acoustic metamaterial has an initial structure, which is formed by the periodic arrangement of initial unit cell structures. Free-shape boundaries are set in the initial structure. Based on the objective of using the fundamental frequency as the passband and the second harmonic as the stopband, an optimization model is constructed. Using the moving asymptote method, the free-shape boundary is adjusted on the basis of the initial structure, and the optimal structure of the acoustic metamaterial is calculated. The initial unit cell structure is a T-shaped cross-section structure, including rectangular blocks and square blocks spliced ​​into a T shape, wherein the upper boundary and left and right boundaries of the square blocks are set as the free shape boundary; The steps for calculating the optimal structure of the acoustic metamaterial include: Network partitioning is performed on the two-dimensional finite element simulation model; Based on the constructed optimization model, an optimization solver is selected, and calculations are performed within the selected frequency range based on the set maximum number of iterations and optimization tolerance to obtain the optimal structure. The objective function in the optimization model is expressed as: In the formula, The objective function value, , These represent the in-plane displacements at the input and output ends, respectively. f 2 f These are the fundamental frequency and the second harmonic, respectively. When calculating and obtaining the optimal structure of the acoustic metamaterial, the methods for geometry creation include: Remesh the deformable configuration and create new geometry based on the mesh; or The optimization results are exported in segments, interpolation curves are added to create new geometries, and the generated shape is adjusted by adjusting the relative tolerance.

2. The method for optimizing the shape of acoustic metamaterials with second harmonic filtering characteristics according to claim 1, characterized in that, The physical field settings of the two-dimensional finite element simulation model are as follows: the upper and lower surfaces of the motherboard are set as free boundary conditions, and along the left boundary of the simulation model... x A specified displacement is applied in the direction to simulate the excitation of a symmetric mode Lamb wave, with the right boundary set as a low-reflection boundary condition.

3. The method for optimizing the shape of acoustic metamaterials with second-harmonic filtering characteristics according to claim 1, characterized in that, In the network partitioning, the motherboard, thin adhesive layer and rectangular blocks all use mapped meshes, while the rectangular blocks use free triangle meshes.

4. The method for optimizing the shape of acoustic metamaterials with second harmonic filtering characteristics according to claim 3, characterized in that, The maximum cell size of the free triangular mesh is 0.5 mm.

5. The method for optimizing the shape of acoustic metamaterials with second harmonic filtering characteristics according to claim 1, characterized in that, The method also includes: The optimal structure was imported into a two-dimensional finite element simulation model, and frequency domain and time domain analyses were performed to verify its performance.

6. An acoustic metamaterial with second harmonic filtering characteristics, characterized in that, The shape of the acoustic metamaterial with second harmonic filtering characteristics was optimized using the method described in any one of claims 1-5.

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