Double-frequency filtering metasurface design method based on topological optimization

Abstract

The invention relates to a double-frequency filtering metasurface design method based on topological optimization. The method comprises the following steps: establishing a two-dimensional simulation model comprising a double-frequency filtering metasurface matrix and a scatterer; according to a preset target forbidden band, taking a forbidden band frequency covering frequency doubling target interval as a fitness function, coding the binary matrix representing material distribution as a chromosome to perform optimization iteration of the chromosome, and obtaining the chromosome with the maximum fitness function value; in optimization iteration, material distribution corresponding to chromosomes is constructed on a two-dimensional simulation model, an energy band structure of the two-dimensional simulation model is obtained, and a fitness function value is calculated; and according to the binary matrix of the chromosome with the maximum fitness function value, outputting final optimized material distribution of the double-frequency filtering metasurface, and performing performance verification on a result through simulation to obtain the double-frequency filtering metasurface of which a fundamental frequency wave can be blocked through a double-frequency wave. Compared with the prior art, systematic optimization of the frequency doubled sound filtering scene is realized.

Description

Technical Field

[0001] This invention relates to the field of acoustics, and in particular to a design method for a second harmonic filtering metasurface based on topology optimization. Background Technology

[0002] Acoustic metamaterials are a class of artificial acoustic materials that achieve special acoustic properties through the careful design of their internal microstructures, and have attracted much attention in the field of sound wave manipulation in recent years. Elastic metasurfaces, as an important branch of acoustic metamaterials, can effectively control the reflection, refraction, scattering, and absorption of sound waves by precisely designing their microstructural units, thereby achieving interesting acoustic functions such as perfect sound absorption, sound focusing, sound cloaking, beam splitting, and filtering.

[0003] Filtering, which removes specific frequency components from a signal, is an effective measure to suppress and prevent interference. Second harmonic filtering metasurfaces can form a bandgap at the second harmonic of the fundamental frequency signal, effectively blocking the second harmonic. This technology is significant in the field of nonlinear ultrasonic testing. Nonlinear ultrasonic testing typically uses the finite amplitude method to observe harmonic generation. However, besides the nonlinear effects caused by the material and defects themselves, the signal generator, power amplifier, and ultrasonic transducer in the testing system inevitably introduce certain system nonlinearities. Liquid coupling agents also exhibit nonlinearity, and these non-defect-related nonlinearities may overwhelm the nonlinear response caused by damage. Second harmonic filtering metasurfaces, by precisely constructing a strong bandgap at the second harmonic, can not only effectively improve the signal-to-noise ratio and suppress harmful harmonics, but also achieve highly selective and sensitive filtering functions while ensuring lossless transmission of the fundamental frequency signal. This method of controlling second harmonic filtering is currently difficult for traditional elastic filters and conventional metamaterials to simultaneously achieve wide bandwidth, high control precision, and engineerability.

[0004] Currently, significant progress has been made in the research of elastic metasurfaces both domestically and internationally. However, research on elastic metasurfaces for filtering mainly focuses on achieving single filtering functions, with limited research on elastic metasurfaces with a fundamental frequency passband and a second harmonic stopband. According to literature reports, existing elastic metasurfaces largely rely on empirical or parametric shape optimization. For example, Chinese patent application CN118366584A discloses an acoustic metamaterial with second harmonic filtering characteristics and its shape optimization method. However, due to limitations in design freedom and manufacturability, it often struggles to achieve precise bandgap control for specific frequency bands (such as the second harmonic range). Topology optimization methods, especially their integration with genetic algorithms, provide a theoretical and practical foundation for the reverse design of complex geometries and multi-frequency band targets, but a systematic optimization method specifically for second harmonic acoustic filtering scenarios is still lacking.

[0005] In summary, the proposal of an elastic metasurface structure for second harmonic acoustic filtering and its topology optimization design method based on genetic algorithm is of great significance. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a second harmonic filtering metasurface design method based on topology optimization. The scatterer design domain is discretized into a binary matrix, and topology optimization is performed by encoding the binary matrix into chromosomes. This breaks through the limitations of traditional parametric shape optimization and allows for flexible control of material distribution.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A method for designing a second-harmonic filtering metasurface based on topology optimization, the method comprising:

[0009] A two-dimensional simulation model including a second-harmonic filtering metasurface substrate and a scatterer was established.

[0010] Based on the preset target bandgap, and using the bandgap frequency covering the second harmonic target range as the fitness function, the binary matrix representing the material distribution is encoded into a chromosome for chromosome optimization iteration. The iteration continues until the preset maximum number of iterations is reached, and the chromosome with the largest fitness function value is obtained. In the optimization iteration, the material distribution corresponding to the chromosome is constructed on the two-dimensional simulation model, and its band structure is obtained, and the fitness function value is calculated.

[0011] The final optimized material distribution of the second harmonic filtering metasurface is output based on the binary matrix of the chromosome with the largest fitness function value. The performance of the results is verified by frequency domain / time domain simulation. Finally, the second harmonic filtering metasurface in which the fundamental frequency wave can be blocked by the second harmonic wave is obtained.

[0012] Furthermore, the second harmonic filtering metasurface substrate is an initial unit structure containing a second harmonic filtering metasurface scatterer design domain. The initial unit structure has a T-shaped cross section and includes rectangular blocks and square blocks representing the second harmonic filtering metasurface design domain.

[0013] Furthermore, the design domain of the second harmonic filter metasurface scatterer is discretized into a binary matrix, in which 1 represents solid material filling the corresponding pixel point, and 0 represents vacuum region not filling the corresponding pixel point.

[0014] Furthermore, the process of obtaining the band structure includes:

[0015] Floquet periodic conditions are set on the parallel boundaries in the x-direction of the second harmonic filtering metasurface substrate, and all other boundaries are set as free boundaries; a parameterized scan is performed along the x-direction to scan the wave vector k, and the curve of the intrinsic frequency as a function of the wave vector k is obtained, i.e., the band structure; the intrinsic frequency is the acoustic frequency that the current material is allowed to propagate.

[0016] Furthermore, the expression for the fitness function is:

[0017] F=(Ω stop ∩Ω target-stop )-(Ω stop ∩Ω target-pass )

[0018] Among them, Ω stop Ω represents the bandgap range calculated by the current model. target-stop Indicates the target no-band area, Ω target-pass Indicates the target passband range.

[0019] Furthermore, the performance verification process includes:

[0020] A performance verification model is established, and the final optimized material distribution is imported into the performance verification model. The material distribution is constructed on the performance verification model. The upper and lower surfaces of the performance verification model are set as free boundary conditions, and a perfect matching layer is added to the right boundary. Frequency domain analysis and time domain analysis are performed on the performance verification model to determine whether the final optimized material achieves the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

[0021] Furthermore, the frequency domain analysis process includes:

[0022] A specified displacement is applied along the x-direction to the left boundary of the performance verification model to simulate the generation of S-mode Lamb waves. By frequency sweep calculation, the frequency response values ​​of the structure of the performance verification model under different frequency waves are obtained. The attenuation of waves at different frequencies is judged by the frequency response values. If the frequency response value under the fundamental frequency wave is non-negative and the frequency response value under the second harmonic wave is negative, it is determined that the final optimized material achieves the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

[0023] If the frequency response is negative, the wave in the corresponding frequency band will experience wave attenuation; if the frequency response is non-negative, the wave in the corresponding frequency band can propagate smoothly.

[0024] Furthermore, in the frequency sweep calculation, the frequency response function is:

[0025] TL = 20log(u out / u in )

[0026] Among them, uout and u in These represent the in-plane displacements at the output and input ends, respectively.

[0027] Furthermore, the time-domain process includes:

[0028] An in-plane displacement signal is applied to the left boundary of the performance verification model, and the in-plane displacement signal on the right side of the model is received. The amplitude of the in-plane displacement signal received on the right side of the model before and after the final optimized material distribution is compared. If the amplitude of the received fundamental wave remains unchanged and the amplitude of the second harmonic wave decreases, it is determined that the final optimized material achieves the effect of allowing the fundamental wave to pass through while blocking the second harmonic wave.

[0029] Furthermore, the displacement signal is:

[0030] u=u0A(t)

[0031] Where u0 is the magnitude of the general displacement amplitude of Lamb wave propagation in a solid, and A(t) is a sinusoidal signal modulated by a Hanning window for 10 periods.

[0032] Compared with the prior art, the beneficial effects of the present invention include:

[0033] 1. This invention proposes a topology-optimized design scheme for a second harmonic filtering metasurface. By integrating binary mesh and discrete genetic algorithm for inverse design, the elastic metasurface structure for second harmonic acoustic filtering is optimized. Through iterative optimization with the bandgap frequency covering the second harmonic target range as the fitness function, combined with band structure analysis, this invention can design a metasurface that allows the fundamental frequency wave to pass through smoothly while effectively blocking the second harmonic wave. This achieves precise filtering in the fundamental passband and second harmonic stopband, meeting the needs of specific frequency control in scenarios such as nonlinear ultrasonic testing.

[0034] 2. This invention uses a T-shaped cross-section initial unit structure as the surface substrate of a two-dimensional simulation model, and discretizes the scatterer design domain into a binary matrix. It then uses binary matrix encoding to encode chromosomes for topology optimization, breaking through the limitations of traditional parametric shape optimization. This allows for flexible control of material distribution and provides theoretical and engineering tools for high-degree-of-freedom, reverse design in complex application scenarios.

[0035] 3. The second harmonic filtering metasurface designed in this invention has second harmonic filtering characteristics, ensuring the fundamental frequency passes through while suppressing second harmonic propagation. 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.

[0036] 4. This invention obtains the band structure by setting Floquet periodic conditions and wave vector k-scanning, which can accurately identify the passband and bandgap ranges of metasurfaces, providing a reliable basis for optimization iteration; at the same time, dual performance verification through frequency domain analysis and time domain analysis can fully confirm the stability and accuracy of the design effect. Attached Figure Description

[0037] Figure 1 This is a flowchart of the overall method of the present invention;

[0038] Figure 2 Part (a) of the present invention is the finite element model of an elastic metasurface with second harmonic filtering characteristics. Figure 2 Part (b) is Figure 2 The initial unit structure model of the elastic metasurface in part (a);

[0039] Figure 3 This is a flowchart of the topology optimization process based on genetic algorithms in this invention;

[0040] Figure 4 This invention relates to the iterative change curve of the optimal fitness value during the topology optimization process, as well as some representative intermediate topologies.

[0041] Figure 5 Part (a) is the final second-harmonic filtering metasurface cell model and its mesh generation after topology optimization; Figure 5 Part (b) is Figure 5 The band structure obtained from simulation calculations for part (a);

[0042] Figure 6 The frequency response function of the second harmonic filtering metasurface system designed for this invention;

[0043] Figure 7 Part (a) is the in-plane displacement field distribution diagram when a Lamb wave with a frequency of 250 kHz is excited from the left side of the model; Figure 7 Part (b) is the in-plane displacement field distribution diagram when a 500kHz Lamb wave is excited from the left side of the model;

[0044] Figure 8 Part (a) is the in-plane displacement signal received with / without a second harmonic filter on the metasurface under excitation at a frequency of 250 kHz; Figure 8 Part (b) is the in-plane displacement signal received with / without second harmonic filtering on the metasurface under 500kHz excitation;

[0045] Figure 9 Part (a) is the frequency domain signal obtained by fast Fourier transforming the in-plane displacement signal received under 250kHz excitation with / without a second harmonic filtered metasurface. Figure 9 Part (b) is the frequency domain signal obtained by fast Fourier transforming the in-plane displacement signal received under 500kHz excitation with / without a second harmonic filtered metasurface. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0047] Example 1

[0048] This embodiment discloses a second-harmonic filtering metasurface design method based on topology optimization, the method as follows: Figure 1 As shown, the process includes steps S1-S4, and the specific steps are as follows:

[0049] Step S1: Establish a two-dimensional simulation model including the second harmonic filter metasurface substrate and the scatterer;

[0050] Step S2: Based on the preset target bandgap, using the bandgap frequency covering the second harmonic target range as the fitness function, the binary matrix representing the material distribution is encoded into a chromosome for chromosome optimization iteration. The iteration continues until the preset maximum number of iterations is reached, and the chromosome with the largest fitness function value is obtained.

[0051] Step S3: Output the final optimized material distribution of the frequency-doubled filtered metasurface based on the binary matrix of the chromosome with the largest fitness function value;

[0052] Step S4: The performance of the results is verified by frequency domain / time domain simulation, and finally the second harmonic filtering metasurface that can block the second harmonic wave through the fundamental frequency wave is obtained.

[0053] In step S1, the second harmonic filtering metasurface substrate is an initial unit structure containing the second harmonic filtering metasurface scatterer design domain. The initial unit structure is a T-shaped cross section, including rectangular blocks and square blocks representing the second harmonic filtering metasurface design domain.

[0054] The design domain of the second-harmonic filtering metasurface scatterer is discretized into a binary matrix. In the binary matrix, 1 represents solid material filling the corresponding pixel, and 0 represents vacuum region without material filling the corresponding pixel.

[0055] In step S2, where the binary matrix representing the material distribution is encoded into chromosomes for chromosome optimization iteration, the topology optimization process based on the genetic algorithm is as follows: Figure 3The diagram shows the iterative process of an existing genetic algorithm. Its variables are binary matrices representing the material distribution, and its objective function is a fitness function that covers the second harmonic target range of the bandgap frequency. Other aspects of the genetic algorithm will not be elaborated upon here.

[0056] In step S2, during the optimization iteration, the material distribution corresponding to the chromosome is constructed on a two-dimensional simulation model, and its band structure is obtained, and the fitness function value is calculated.

[0057] The process of obtaining the band structure includes:

[0058] Floquet periodic conditions are set on the parallel boundaries in the x direction of the second harmonic filtering metasurface substrate, and the other boundaries are set as free boundaries; a parameterized scan is performed along the x direction to scan the wave vector k, and the curve of the eigenfrequency as a function of the wave vector k is obtained, i.e., the band structure.

[0059] The intrinsic frequency is the frequency of sound waves that are allowed to propagate in the current material.

[0060] The fitness function is expressed as follows:

[0061] F=(Ω stop ∩Ω target-stop )-(Ω stop ∩Ω target-pass )

[0062] Among them, Ω stop Ω represents the bandgap range calculated by the current model. target-stop Indicates the target no-band area, Ω target-pass Indicates the target passband range.

[0063] The specific process of performance verification in step S4 includes:

[0064] A performance verification model was established, and the final optimized material distribution was imported into the performance verification model. The material distribution was constructed on the performance verification model, and the upper and lower surfaces of the performance verification model were set as free boundary conditions. A perfect matching layer was added to the right boundary. Frequency domain analysis and time domain analysis were performed on the performance verification model to determine whether the final optimized material achieved the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

[0065] The process of frequency domain analysis includes:

[0066] A specified displacement is applied along the x-direction on the left boundary of the performance verification model to simulate the generation of S-mode Lamb waves. The frequency response values ​​of the performance verification model structure under different frequency waves are obtained by frequency sweep calculation. The attenuation of waves at different frequencies is judged by the frequency response values. If the frequency response is negative, the wave in the corresponding frequency band has wave attenuation. If the frequency response is non-negative, the wave in the corresponding frequency band can propagate smoothly.

[0067] If the frequency response value under the fundamental frequency wave is non-negative and the frequency response value under the second harmonic wave is negative, then it is determined that the final optimized material achieves the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

[0068] In frequency sweep calculation, the frequency response function is:

[0069] TL = 20log(u out / u in )

[0070] Among them, u out and u in These represent the in-plane displacements at the output and input ends, respectively.

[0071] The time-domain process includes:

[0072] An in-plane displacement signal is applied to the left boundary of the performance verification model, and the in-plane displacement signal on the right side of the model is received. The amplitude of the in-plane displacement signal received on the right side of the model before and after importing the final optimized material distribution is compared. If the amplitude of the received fundamental wave remains unchanged and the amplitude of the second harmonic wave decreases, it is determined that the final optimized material achieves the effect of allowing the fundamental wave to pass through while blocking the second harmonic wave.

[0073] The displacement signal is:

[0074] u=u0A(t)

[0075] Where u0 is the magnitude of the general displacement amplitude of Lamb wave propagation in a solid, and A(t) is a sinusoidal signal modulated by a Hanning window for 10 periods.

[0076] Example 2

[0077] This embodiment is based on the above embodiment 1, and uses the above topology optimization-based design method for second harmonic filtering metasurfaces to perform topology design on the shape of the second harmonic filtering metasurface.

[0078] In this embodiment, a second-harmonic filtering metasurface design method based on topology optimization is implemented using a finite element simulation software and data processing software, specifically including the following steps:

[0079] (1) Establishing a model

[0080] This embodiment proposes a... Figure 2 The second harmonic filtering metasurface shown in (a) can be bonded to an aluminum plate to achieve the second harmonic filtering function, which can ensure that the fundamental frequency can pass smoothly while suppressing the propagation of the second harmonic.

[0081] A two-dimensional planar model was established using the solid mechanics module of a finite element simulation software to study its characteristic frequencies. Figure 2(b) is the two-dimensional planar model constructed in this embodiment, consisting of additional short piles and a substrate. It is the initial unit structure of the elastic metasurface. This structure has a T-shaped cross-section and includes a rectangular substrate (aluminum plate) and a square block (elastic metasurface design domain). In the figure, H is the height of the rectangular substrate, a is the width of the rectangular substrate, and h is the side length of the square block. Specific dimensional parameters are shown in Table 1.

[0082] Table 1 Geometric Dimensions

[0083]

[0084] (2) Define material properties

[0085] In the T-section of the two-dimensional planar model, the rectangular substrate represents the main board, which is made of aluminum. The square blocks represent elastic metasurface units made of lead. The material parameters are shown in Table 2, where ρ is the density and λ and μ are Lamé parameters. Because lead and aluminum have significantly different impedances, this is beneficial for producing a wider bandgap.

[0086] Table 2 Material Parameters

[0087]

[0088] (3) Set boundary conditions and mesh the calculation:

[0089] Floquet periodic boundary conditions are applied to the left and right boundaries of the model unit structure, while the remaining boundaries are left free. The wavenumber scan range is 0–π / a, with a step size of 0.1π / a. The substrate plate is meshed using a mapped mesh: the maximum mesh element size is 0.1 mm; the design domain uses a free triangular mesh with a maximum size of 0.1 mm (much smaller than the wavelength) (e.g., Figure 5 As shown in (a), a good balance is achieved between computation time and accuracy, and the band diagram of the current model can be obtained through calculation.

[0090] (4) Define the objective function:

[0091] To achieve the goal of allowing the fundamental frequency to pass while suppressing the second harmonic, we extended the functionality of the elastic metasurface to obtain the desired bandgap position and width, thus allowing for more flexible selection of the excitation frequency. In this embodiment, the target fundamental frequency passband is preset to 230-280kHz, and the corresponding target second harmonic bandgap range is 460-560kHz, resulting in the objective function expressed in the following mathematical form:

[0092] F=(Ω stop ∩Ω target-stop )-(Ω stop ∩Ω target-pass )

[0093] In the formula, Ω stopΩ represents the bandgap range calculated by the current model. target-stop Indicates the target no-band area, Ω target-pass Indicates the target passband range.

[0094] (5) Optimization iteration based on genetic algorithm:

[0095] In a certain finite element simulation software and data processing software, the design domain is discretized into... Figure 2 (b) shows a binary matrix that facilitates the representation of chromosome genes in a genetic algorithm, where "1" represents material filling the corresponding pixel and "0" represents no material filling the corresponding pixel in a vacuum region. After generating the initial population in the data processing software, the fitness value of each chromosome is obtained through finite element simulation using the aforementioned two-dimensional planar model. Subsequently, the fitness is evaluated, and selection, crossover, and mutation operations are performed to achieve iterative optimization until the preset termination condition is reached.

[0096] (6) Output the final optimization results:

[0097] Figure 4 The final optimization model and iterative change curve of the objective function for the second harmonic filtering elastic metasurface are presented. The chromosome with the highest fitness after meeting the preset conditions is obtained, and the corresponding second harmonic filtering metasurface model is constructed as the final optimization result model.

[0098] (7) Result verification:

[0099] The band structure diagram obtained by performing the above band calculation on the optimized second harmonic filter metasurface model in a certain finite element simulation software is shown below. Figure 5 As shown in (b), observing the band structure reveals that the complete bandgap lies between the 5th and 6th bands, as indicated by the gray area in the figure. The bandgap range is 454.06-567.03 kHz, encompassing the target bandgap of 460-560 kHz, and also exhibiting corresponding characteristic frequencies within the target passband of 230-280 kHz. This result demonstrates that the aforementioned topology optimization method based on a genetic algorithm can meet our requirements for second-harmonic bandgap control.

[0100] Example 3

[0101] This embodiment, based on Embodiments 1 and 2 above, discloses the evaluation process of the filtering performance of the designed second harmonic filtering metasurface. In this embodiment, the filtering performance of the second harmonic filtering metasurface designed in Embodiment 2 is evaluated from the frequency domain perspective. The frequency response of the structure is calculated using the solid mechanics module of a certain finite element simulation software.

[0102] The second harmonic filtering metasurface, the final output of Example 1, is imported into the new model, replacing... Figure 2(a) shows the initially designed elastic metasurface, with a transmission model comprising 10 cycles, attached to a 60 mm long, 1 mm thick aluminum plate. A specified displacement load along the x-direction is applied at the excitation end, and perfectly matched layers are added to the left and right boundaries of the model to reduce boundary reflections. A frequency domain solver is selected, with the scan frequency range set to 5-900 kHz and a step size of 5 kHz. The frequency response function, i.e., the transmittance TL = 20log(u... out / u in ), where u out and u in These represent the in-plane displacements at the output and input ends, respectively.

[0103] Figure 6 The frequency response function of the optimized second harmonic filtering metasurface is given, where a negative TL value indicates wave attenuation in the corresponding frequency band. It can be seen that the attenuation band and... Figure 5 The bandgap ranges in (b) are highly consistent. There is almost no wave attenuation in the fundamental frequency range, indicating that the fundamental frequency can pass smoothly through the optimized structure. However, some wave attenuation occurs in the corresponding second harmonic range, indicating that the second harmonic propagation is suppressed within the structure. It can be seen that there are still many wave attenuation segments above the designed bandgap range, due to the existence of other bandgap ranges. Furthermore, the displacement field distributions under 250kHz excitation (fundamental frequency) and 500kHz excitation (second harmonic) were calculated, as follows: Figure 7 As shown in (a) and (b), it can be clearly observed that a 250 kHz wave can propagate through the second harmonic filtering metasurface in the plate, while the 500 kHz wave is significantly suppressed.

[0104] Example 4

[0105] Based on the above embodiments 1-3, this embodiment discloses another evaluation process for the filtering performance of the designed second harmonic filtering metasurface. In order to further evaluate the filtering performance of the second harmonic filtering metasurface designed in embodiment 2, a finite element simulation software is used to perform time-domain analysis on the second harmonic filtering metasurface.

[0106] First, a geometric model is established, and the optimized structure output from Example 2 is imported into the new model to replace the initially designed elastic metasurface.

[0107] This embodiment still uses the solid mechanics module, setting the upper and lower surfaces of the plate as free boundary conditions and the right boundary as a low-reflection boundary condition to avoid end-face reflection of Lamb waves.

[0108] An in-plane displacement signal u = u0A(t) is applied to the left boundary, where the excitation displacement amplitude u0 = 1 μm. The amplitude of the Lamb wave displacement propagating in the solid is usually on this order of magnitude. A(t) is a sinusoidal signal modulated by a Hanning window for 10 periods, with excitation frequencies of 250 kHz and 500 kHz, i.e., the fundamental frequency and the second harmonic.

[0109] When meshing, the substrate uses a mapped mesh with a maximum cell size of 0.5 mm, while the second harmonic filtering metasurface uses a free triangular mesh with a maximum cell size of 0.1 mm. The complete mesh contains 3360 domain cells and 3364 boundary cells. This setting ensures both computational accuracy and saves computation time.

[0110] In the transient solver, the time range is set to [0, 150] and the time step to 0.02 μs at 250 kHz; the time range is set to [0, 100] and the time step to 0.02 μs at 500 kHz. After calculation, the in-plane displacement signals received before and after installing the second-harmonic filtering metasurface under 250 kHz and 500 kHz excitation can be obtained, such as... Figure 8 As shown in (a) and (b). Figure 8 In (a), the solid line represents the in-plane displacement signal received without a second harmonic filter metasurface, and the dashed line represents the in-plane displacement signal received with a second harmonic filter metasurface. Figure 8 (b) The solid line represents the in-plane displacement signal received without a second harmonic filter metasurface, and the dashed line represents the in-plane displacement signal received with a second harmonic filter metasurface.

[0111] By observation, we can see that Figure 8 In (a), the signal amplitude after passing through the second harmonic filter metasurface under 250kHz excitation is almost unchanged compared to the signal after passing through the plate, with only a certain time delay, indicating that the fundamental frequency elastic wave can pass smoothly; while the signal amplitude after passing through the second harmonic filter metasurface under 500kHz excitation is significantly reduced, indicating that the elastic wave at this frequency is suppressed.

[0112] Performing a Fast Fourier Transform on a time-domain signal yields its spectrum, such as... Figure 9 As shown in (a) and (b), Figure 9 As can be seen in (a), the amplitude of the signal at 250kHz does not change significantly, while the amplitude of the signal after the second harmonic filtering metasurface decreases significantly at 500kHz. This proves that the second harmonic filtering metasurface can filter out the second harmonic 500kHz signal while maintaining the smooth propagation of the fundamental frequency 250kHz signal.

[0113] In summary, this invention first performs topology optimization design on a second-harmonic filtering metasurface to obtain an elastic metasurface structure with second-harmonic filtering characteristics. Then, the filtering performance of the second-harmonic filtering metasurface is verified in both the frequency and time domains, demonstrating that the designed second-harmonic filtering metasurface not only ensures the smooth passage of the fundamental frequency but also suppresses second-harmonic propagation and possesses a certain bandgap, indicating that the excitation frequency can be flexibly selected. This invention can be used for nonlinear ultrasonic Lamb wave detection, solving the problem of difficult filtering of system nonlinearity and interference during the detection process, and has broad application prospects in the field of structural health monitoring.

[0114] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing a second-harmonic filtering metasurface based on topology optimization, characterized in that, The method includes: A two-dimensional simulation model including a second-harmonic filtering metasurface substrate and a scatterer was established. Based on the preset target bandgap, and using the bandgap frequency covering the second harmonic target range as the fitness function, the binary matrix representing the material distribution is encoded into a chromosome for chromosome optimization iteration. The iteration continues until the preset maximum number of iterations is reached, and the chromosome with the largest fitness function value is obtained. In the optimization iteration, the material distribution corresponding to the chromosome is constructed on the two-dimensional simulation model, and its band structure is obtained, and the fitness function value is calculated. The final optimized material distribution of the second harmonic filtering metasurface is output based on the binary matrix of the chromosome with the largest fitness function value. The performance of the results is verified by frequency domain / time domain simulation. Finally, the second harmonic filtering metasurface in which the fundamental frequency wave can be blocked by the second harmonic wave is obtained.

2. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 1, characterized in that, The second harmonic filtering metasurface substrate is an initial unit structure containing a second harmonic filtering metasurface scatterer design domain. The initial unit structure has a T-shaped cross section and includes rectangular blocks and square blocks representing the second harmonic filtering metasurface design domain.

3. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 2, characterized in that, The design domain of the second harmonic filter metasurface scatterer is discretized into a binary matrix. In the binary matrix, 1 represents solid material filling the corresponding pixel, and 0 represents vacuum region not filling the corresponding pixel.

4. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 1, characterized in that, The process of obtaining the band structure includes: Floquet periodic conditions are set on the parallel boundaries in the x-direction of the second harmonic filtering metasurface substrate, and all other boundaries are set as free boundaries; a parameterized scan is performed along the x-direction to scan the wave vector k, and the curve of the intrinsic frequency as a function of the wave vector k is obtained, i.e., the band structure; the intrinsic frequency is the acoustic frequency that the current material is allowed to propagate.

5. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 1, characterized in that, The expression for the fitness function is: F=(Ω stop ∩Oh target-stop )-(Oh stop ∩Oh target-pass ) Among them, Ω stop Ω represents the bandgap range calculated by the current model. target-stop Indicates the target no-band area, Ω target-pass Indicates the target passband range.

6. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 1, characterized in that, The performance verification process includes: A performance verification model is established, and the final optimized material distribution is imported into the performance verification model. The material distribution is constructed on the performance verification model. The upper and lower surfaces of the performance verification model are set as free boundary conditions, and a perfect matching layer is added to the right boundary. Frequency domain analysis and time domain analysis are performed on the performance verification model to determine whether the final optimized material achieves the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

7. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 6, characterized in that, The frequency domain analysis process includes: A specified displacement is applied along the x-direction to the left boundary of the performance verification model to simulate the generation of S-mode Lamb waves. By frequency sweep calculation, the frequency response values ​​of the structure of the performance verification model under different frequency waves are obtained. The attenuation of waves at different frequencies is judged by the frequency response values. If the frequency response value under the fundamental frequency wave is non-negative and the frequency response value under the second harmonic wave is negative, it is determined that the final optimized material achieves the effect of allowing the fundamental frequency wave to pass through while blocking the second harmonic wave.

8. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 7, characterized in that, In the frequency sweep calculation, the frequency response function is: TL=20log(u out / u in ) Among them, u out and u in These represent the in-plane displacements at the output and input ends, respectively.

9. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 6, characterized in that, The time-domain process includes: An in-plane displacement signal is applied to the left boundary of the performance verification model, and the in-plane displacement signal on the right side of the model is received. The amplitude of the in-plane displacement signal received on the right side of the model before and after the final optimized material distribution is compared. If the amplitude of the received fundamental wave remains unchanged and the amplitude of the second harmonic wave decreases, it is determined that the final optimized material achieves the effect of allowing the fundamental wave to pass through while blocking the second harmonic wave.

10. The method for designing a second-harmonic filtering metasurface based on topology optimization according to claim 9, characterized in that, The displacement signal is: u=u0A(t) Where u0 is the magnitude of the general displacement amplitude of Lamb wave propagation in a solid, and A(t) is a sinusoidal signal modulated by a Hanning window for 10 periods.

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