Radial filter with double filtering of double frequency and guided wave mode and its topology optimization design method

Abstract

The application relates to a radial filter with double filtering of frequency doubling and waveguide mode and a topological optimization design method thereof, and comprises the following steps: based on a set physical field condition, a material distribution topology of a scatterer design domain is iteratively optimized by adopting a finite element model construction and a genetic algorithm, and an optimal material distribution topology of the scatterer design domain is obtained; in the iterative optimization process, a fitness function is constructed by jointly considering a passband coverage range of an S0 mode energy band at a target base frequency, a forbidden band coverage range of an A0 mode energy band at the target base frequency, and a joint forbidden band coverage range of S0 mode and A0 mode energy bands at a target frequency doubling. Compared with the prior art, the radial metamaterial unit scatterer shape is automatically designed by combining finite element band analysis and genetic algorithm topological optimization, so that a radial filter structure with single mode filtering and frequency doubling filtering capacity is obtained.

Description

Technical Field

[0001] This invention belongs to the field of acoustic metamaterials and elastic wave modulation, and in particular relates to a radial filter with dual filtering of second harmonic and guided wave modes and its topology optimization design method. Background Technology

[0002] Lamb waves are widely used in structural health monitoring and non-destructive testing in aerospace, machinery, rail transportation, and energy engineering due to their long propagation distance, sensitivity to damage in plate structures, and high detection efficiency. For thin plate structures, Lamb waves typically exhibit multimodal and dispersion characteristics, with symmetrical modes (such as the S0 mode) and antisymmetric modes (such as the A0 mode) potentially existing simultaneously within the same frequency range. Multimodal propagation complicates the received signal, increasing the difficulty of damage identification and signal interpretation. Therefore, achieving single-mode propagation within a specific frequency band and suppressing non-target modes are crucial for improving the accuracy and reliability of Lamb wave detection.

[0003] On the other hand, in nonlinear ultrasonic Lamb wave detection, second harmonic signals are often used to characterize nonlinear features such as micro-damage, contact nonlinearity, and early fatigue damage in materials. However, in actual detection systems, due to the influence of factors such as excitation equipment, sensors, coupling layers, and structural boundaries, nonlinear second harmonic components often arise. These non-target second harmonic signals can overlap with the nonlinear response induced by structural damage, affecting the accuracy of the detection results. Therefore, effectively suppressing the system interference second harmonic signals generated by the testing system itself while ensuring the effective propagation of the fundamental frequency target mode has significant engineering application value.

[0004] Phononic crystals, as a typical class of acoustic metamaterials, can modulate the propagation of elastic waves through periodic structures or local resonant units, forming band gaps within specific frequency bands to achieve functions such as filtering, vibration isolation, beam modulation, and mode conversion. Traditional phononic crystal filters mostly rely on the optimization of dimensional parameters of regular geometric structures, which limits their design freedom and makes it difficult to simultaneously meet multiple constraints such as "fundamental frequency target mode passage, fundamental frequency non-target mode suppression, and second harmonic multimode suppression".

[0005] Currently, there are few reported design methods for radial filters that simultaneously possess guided wave mode filtering and second harmonic filtering functions in Lamb wave radial propagation scenarios. In particular, how to adjust the band structure of the radial periodic structure to ensure that the fundamental operating frequency is within the passband of the S0 mode, while simultaneously ensuring that the A0 mode is within the bandgap of the fundamental operating frequency, and further, ensuring that both the S0 and A0 modes are within the bandgap of the second harmonic operating frequency, is a crucial technical problem that urgently needs to be solved to achieve high-performance Lamb wave filtering.

[0006] Existing patent CN122021208B discloses a topology optimization method for a mode filter. It evaluates mode purity and energy transmittance through frequency domain transmission simulation, achieving a single-mode filtering function that suppresses the A0 mode while maintaining high transmittance of the S0 mode in a linear propagation scenario. This method is then applied to artifact suppression in damage imaging. However, this prior art can only achieve mode filtering at a single frequency, lacks second-harmonic suppression capability, and is designed for one-dimensional linear propagation scenarios.

[0007] Therefore, it is necessary to propose a new design method to obtain a radial filter structure that combines single-mode filtering and second-harmonic filtering capabilities. Summary of the Invention

[0008] The purpose of this invention is to overcome the above-mentioned problems in the prior art by providing a radial filter with dual filtering of second harmonic and guided wave mode and its topology optimization design method, so as to allow the propagation of S0 mode and suppress the propagation of A0 mode at the fundamental operating frequency, and simultaneously suppress the propagation of S0 mode and A0 mode at the second harmonic operating frequency, thereby realizing the dual functions of guided wave mode filtering and second harmonic filtering.

[0009] The objective of this invention can be achieved through the following technical solutions: A topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes, wherein the radial filter includes radial filter units, each radial filter unit including a main plate and a scattering design domain disposed on the main plate, and the design method includes the following steps: Based on the set physical field conditions, the material distribution topology of the scatterer design domain is iteratively optimized using a finite element model and a genetic algorithm to obtain the optimal material distribution topology of the scatterer design domain. In the iterative optimization process, the fitness function is constructed by jointly considering the passband coverage of the S0 mode band at the target fundamental frequency, the bandgap coverage of the A0 mode band at the target fundamental frequency, and the joint bandgap coverage of the S0 and A0 mode bands at the target second harmonic.

[0010] Furthermore, the fitness function is expressed as: in, F For the fitness function, This indicates the coverage range of the S0 mode band within the baseband target range. This indicates the coverage range of the A0 mode band within the target baseband frequency range. This indicates the coverage range of the joint bandgap of S0 mode and A0 mode within the second harmonic target range. These are the weighting coefficients.

[0011] Furthermore, the weighting coefficients satisfy:w 1=2 w 3, w 2 =-2 w 3, w 3 is a positive number.

[0012] Furthermore, during the iterative optimization, the mode type is identified by the polarization factor, and then the fitness value is calculated. The polarization factor is the ratio of the in-plane displacement component to the out-of-plane displacement component in the modal displacement field.

[0013] Furthermore, the polarization factor is expressed as: in, var Polarization factor u for x In-plane displacement in direction 、w for z Out-of-plane displacement in the direction of S This indicates the cross-section of the transmission end.

[0014] Furthermore, during the iterative optimization, the scatterer design domain is divided into array-type pixel units, each pixel unit corresponding to a binary design variable. When the design variable is 1, it indicates that the corresponding area is filled with solid material; when the design variable is 0, it indicates that the corresponding area is empty. All design variables form a binary matrix, which is further encoded as chromosomes in the genetic algorithm.

[0015] Furthermore, the physical field conditions are: the unit structure along... x Set Floquet periodicity conditions on the parallel boundaries of the direction, and set all other boundaries as free boundaries.

[0016] Furthermore, this design method also includes: The designed radial filter is subjected to filtering performance verification, which includes at least frequency domain verification and displacement field verification.

[0017] Furthermore, in the frequency domain verification, a frequency sweep calculation is performed using a frequency domain solver, wherein... For S0 mode, the frequency response function of the frequency domain solver is: , and These represent the in-plane displacements at the output and input ends, respectively. For A0 mode, the frequency response function of the frequency domain solver is: , and These represent the out-of-plane displacements at the output and input ends, respectively.

[0018] The present invention also provides a radial filter with dual filtering of second harmonic and guided wave mode, which is designed using the topology optimization design method of the radial filter with dual filtering of second harmonic and guided wave mode as described above.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. When optimizing the material distribution in the scatterer design domain, this invention constructs a fitness function by jointly considering the passband coverage of the S0 mode band at the target fundamental frequency, the bandgap coverage of the A0 mode band at the target fundamental frequency, and the joint bandgap coverage of the S0 and A0 mode bands at the target second harmonic. This enables the dual functions of fundamental frequency single-mode filtering and second harmonic spurious signal suppression to be achieved through the collaborative structure of a single metamaterial unit.

[0020] 2. This invention sets the weight coefficients in the fitness function, which can more accurately obtain radial filter design results that meet the preset requirements.

[0021] 3. Based on band structure calculation and modal polarization factor identification, this invention designs the fundamental frequency S0 passband, fundamental frequency A0 bandgap, and second harmonic joint bandgap at the band level to construct a fitness function for optimization evaluation, thereby effectively realizing band control.

[0022] 4. The radial filter designed in this invention is suitable for engineering scenarios such as nonlinear ultrasonic testing, Lamb wave structure health monitoring, and elastic wave mode control. It can effectively reduce the interference of non-target modes and system stray second harmonic signals on the detection results. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the radial filter of the present invention; Figure 2 Here are unit structure diagrams of the radial filter of the present invention, wherein (2a) is a two-dimensional axisymmetric diagram of the radial filter unit structure, and (2b) is a three-dimensional structural diagram of the radial filter unit structure; Figure 3 This is a flowchart of the radial filter topology optimization design method of the present invention; Figure 4 It is the band diagram of the final target structure with polarization factor. When the polarization factor is 0, it is a pure S0 mode, and when the polarization factor is 1, it is a pure A0 mode. There is only the S0 mode band at the fundamental frequency of 300 kHz, and there is a wide band gap at the second harmonic of 600 kHz. Figure 5 It is the frequency response function of the target structure in the range of 10-1000 kHz when the S0 mode excitation signal is used. A negative TL value indicates that there is wave attenuation in the corresponding frequency band. Figure 6It is the frequency response function of the target structure in the range of 10-1000 kHz when the A0 mode excitation signal is used. A negative TL value indicates that there is wave attenuation in the corresponding frequency band. Figure 7 These are in-plane displacement field distribution diagrams when excited by S0 Lamb waves at different frequencies, where (7a) has a frequency of 300 kHz and (7b) has a frequency of 600 kHz. Figure 8 These are in-plane displacement field distribution diagrams when excited by A0 Lamb waves at different frequencies, where (8a) has a frequency of 300 kHz and (8b) has a frequency of 600 kHz. Detailed Implementation

[0024] 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.

[0025] Example 1 This embodiment provides a topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes for Lamb wave radial propagation scenarios. The radial filter designed by this method includes periodic radial filter units. Each radial filter unit includes a main plate and a scatterer design domain disposed on the main plate. Based on the set physical field conditions, a finite element model is used to construct and a genetic algorithm is used to iteratively optimize the material distribution topology of the scatterer design domain to obtain the optimal material distribution topology of the scatterer design domain.

[0026] In this embodiment, the scatterer design domain is used as the topology optimization region. Different topological configurations are formed by the distribution and combination of solid materials and spatial domains, thereby controlling the band structure characteristics of the unit structure. In the iterative optimization of the genetic algorithm, the scatterer design domain is divided into array-type pixel units. Each pixel unit corresponds to a binary design variable. When the design variable is 1, it indicates that the corresponding region is filled with solid material. When the design variable is 0, it indicates that the corresponding region is a spatial domain. All design variables form a binary matrix, which is further encoded as chromosomes in the genetic algorithm.

[0027] This embodiment uses COMSOL Multiphysics finite element software and MATLAB co-simulation platform to perform topology optimization design on a radial filter unit with dual filtering functions of second harmonic and guided wave modes. The optimization objective is to allow only S0 mode propagation and suppress A0 mode propagation near the fundamental frequency of 300 kHz, while simultaneously suppressing both S0 and A0 mode propagation near the second harmonic of 600 kHz. Figure 1 As shown.

[0028] like Figure 3 As shown, the method specifically includes the following steps: S1. Construct the finite element model of the radial filter.

[0029] Using the MATLAB platform to call the COMSOL finite element software to construct a radial filter element model, such as... Figure 2 As shown.

[0030] S2. Define the dual filtering objectives and process constraints.

[0031] In this embodiment, the defined optimization objective is a dual filtering objective of maximizing the second-order bandgap and purifying specific guided wave modes. Process constraints include 3D printing self-support constraints, minimum thickness constraints, etc.

[0032] In this embodiment, the genetic algorithm parameters are set as follows: population size is set to 20, crossover probability is 0.8, mutation probability is 0.3, and maximum number of iterations is set to 30 generations.

[0033] S3. Generate the initial population for the genetic algorithm.

[0034] In this embodiment, the scatterer design domain is divided into 10×10 pixel units, with each pixel unit corresponding to a binary design variable. A design variable of 1 indicates that the corresponding region is filled with solid material, while a design variable of 0 indicates that the corresponding region is empty. All design variables form a binary matrix, which is further encoded into chromosomes in a genetic algorithm to generate an initial population. Each chromosome represents a possible scatterer topology.

[0035] S4. The dispersion curves of the individual structure of the population are solved using the finite element method.

[0036] In COMSOL, set material parameters and physics conditions: The model's main body and scatterers are both made of aluminum, with the following parameters: density ρ= 2700 kg / m 3 Lamé parameters λ= 51.1 GPa μ= The pressure is 26.3 GPa, and Floquent periodic boundary conditions are applied at the boundary. The eigenfrequency of the structure under different wave vectors is calculated through characteristic frequency studies, thereby obtaining the band structure of the radial filter unit. Furthermore, the mode type is identified by the ratio of in-plane displacement components to out-of-plane displacement components in the modal displacement field (i.e., the polarization factor). The polarization factor is defined as follows: (1) in, var Polarization factor u for x In-plane displacement in direction、w for z Out-of-plane displacement in the direction of S Indicates the cross-section of the transmission end 。 The S0 mode is dominated by in-plane displacement (polarization factor). var Approaching 0), the A0 mode is dominated by out-of-plane displacement (polarization factor). var The value approaches 1, which is used to determine the propagation state of each mode at different frequencies.

[0037] In this embodiment, the physical field conditions are set as follows: using the solid mechanics module of COMSOL software, along the metasurface unit structure... x Floquet periodicity conditions are set on the parallel boundaries of the direction, while all other boundaries are set as free boundaries. A parametric scan is set up in the characteristic frequency study, along... x Directional scanning wave vector k (π / ) a , a (where is the lattice constant), the intrinsic frequency is obtained as a function of the wave vector. k The change curve of the band structure.

[0038] MATLAB decodes individual chromosomes into a geometric model recognizable by COMSOL and then calls COMSOL to perform band structure calculations.

[0039] S5. Perform a comprehensive fitness assessment of dual filtering.

[0040] To achieve effective propagation of the S0 mode and effective suppression of the A0 mode at the fundamental operating frequency, as well as effective suppression of both the S0 and A0 modes at the second harmonic operating frequency, this embodiment constructs a fitness function by jointly considering the passband coverage of the S0 mode at the target fundamental frequency, the bandgap coverage of the A0 mode at the target fundamental frequency, and the joint bandgap coverage of the S0 and A0 modes at the target second harmonic. The final objective function adopted is as follows: (2) in, F For the fitness function, This indicates the coverage range of the S0 mode band within the baseband target range. This indicates the coverage range of the A0 mode band within the target baseband frequency range. This indicates the coverage range of the joint bandgap of S0 mode and A0 mode within the second harmonic target range. Let be the weighting coefficients, and let the weighting coefficients satisfy . w 1=2 w 3. w 2 =-2 w 3. Among them, w1 is a positive weight, the purpose of which is to make the S0 band as wide as possible in the target fundamental frequency range and to give it a reward; w The negative weight 2 is intended to penalize the A0 band when it appears within the target fundamental frequency range. w 3 is a positive weight, the purpose of which is to maximize the amount of bandgap within the target second harmonic and to reward this maximization. In this embodiment, the target fundamental frequency passband is preset to 280-320 kHz, corresponding to a target second harmonic bandgap range of 560-640 kHz, and the weight value is: w 1 = 2, w 2 =- 2, w 3 = 1.

[0041] S6. Determine whether the termination condition is met. If the maximum number of iterations is reached, output the optimal dual-filter radial topology based on the fitness value. If not, proceed to step S7.

[0042] S7. Perform a selection operation on the current population.

[0043] S8. Select individuals with high fitness as parents, and generate new offspring structures through crossover and mutation operations. In this embodiment, the crossover operation uses column-directed truncated crossover, and the mutation operation uses surface-level fine-tuning mutation.

[0044] S9. Generate a new generation of population and return to step S4.

[0045] After iterative optimization using the genetic algorithm described above, the two-dimensional axisymmetric diagram of the final target radial filter unit structure is obtained as follows: Figure 2 As shown in (2a), Figure 2 (2b) is its three-dimensional structure diagram, and its band structure diagram with polarization factor annotations is as follows: Figure 4 As shown. Figure 4 In the diagram, the color on the right represents the polarization factor. (From...) Figure 4 It can be seen that the polarization factor near 300 kHz var The value approaching 0 indicates that the mode is dominated by in-plane displacement and has an S0 mode band, while the A0 mode band does not appear at this frequency. This suggests that the structure can achieve single S0 mode propagation at the fundamental operating frequency. Simultaneously, the absence of any band around 600 kHz indicates a wide bandgap, preventing effective propagation of both S0 and A0 modes. This demonstrates that the structure possesses a second harmonic filtering function. The 415.3–471.1 kHz and 552.5–642.3 kHz values ​​in the figure represent the frequency ranges of these two bandgaps.

[0046] Example 2 The topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes provided in this embodiment further includes: verifying the filtering performance of the designed radial filter, wherein the filtering performance verification includes at least frequency domain verification and displacement field verification.

[0047] 1. Frequency Domain Verification To verify the frequency domain filtering performance of the obtained radial filter unit, this embodiment establishes a finite element frequency domain analysis model containing the target structure, and applies S0 mode and A0 mode excitation respectively, performing frequency sweep calculations in the range of 10kHz-1000kHz with a step size of 5 kHz.

[0048] Under S0 mode excitation conditions, the frequency response function of the target structure was calculated, and the results are as follows: Figure 5 As shown. The frequency response function, expressed as the ratio of the transmission coefficient magnitudes, is defined as follows. ,in and These represent the in-plane displacements at the output and input ends, respectively. TL A high value indicates high transmission efficiency. TL A low value indicates low transmission efficiency. (From...) Figure 5 It can be seen that around 300 kHz, A value close to 0 indicates that the S0 mode can propagate effectively through the target structure; while around 600 kHz, The significant decrease in the value indicates that the target structure can effectively suppress the second harmonic component of the S0 mode.

[0049] Furthermore, under A0 mode excitation conditions, the frequency response function of the target structure is calculated, defined as follows: ,in and These represent the out-of-plane displacements at the output and input terminals, respectively. Figure 6 It can be seen that around 300 kHz and 600 kHz, The values ​​are all significantly reduced, indicating that the radial filter unit can simultaneously suppress the propagation of A0 mode in the fundamental frequency and second harmonic range.

[0050] In summary, the frequency domain verification results show that the radial filter unit designed in this invention can selectively allow S0 mode propagation and suppress A0 mode propagation near the fundamental frequency of 300 kHz, while simultaneously suppressing both S0 and A0 modes near the second harmonic of 600 kHz, thus possessing the dual functions of guided wave mode filtering and second harmonic filtering.

[0051] 2. Displacement field verification To further illustrate the filtering mechanism of the target structure, this embodiment applies S0 mode and A0 mode excitation at 300 kHz and 600 kHz respectively, and calculates the in-plane displacement field distribution in the target structure.

[0052] Under S0 mode excitation conditions, the in-plane displacement field distribution at 300 kHz is as follows: Figure 7 As shown in (7a), the S0 mode can propagate effectively in the target structure, indicating that there is no bandgap for the S0 mode at this frequency. The in-plane displacement field distribution at 600 kHz is shown in Figure 7a. Figure 7 As shown in (7b), the S0 mode exhibits significant amplitude attenuation in the target structure, indicating that the structure has a filtering effect on the S0 mode at the second harmonic operating frequency.

[0053] Under A0 mode excitation conditions, the in-plane displacement field distribution at 300 kHz is as follows: Figure 8 As shown in (8a), the propagation of the A0 mode in the target structure is significantly suppressed, indicating that the structure can filter out non-target A0 modes at the fundamental operating frequency. The in-plane displacement field distribution at 600 kHz is shown in Figure 8a. Figure 8 As shown in (8b), the A0 mode also shows significant attenuation in the target structure, indicating that the structure also has a good suppression effect on the A0 mode at the second harmonic operating frequency.

[0054] The displacement field results are consistent with the band analysis and frequency response results, further verifying that the radial filter unit designed by the method of the present invention can achieve single S0 mode propagation at the fundamental frequency of 300 kHz and can simultaneously suppress the propagation of both S0 and A0 modes at the second harmonic of 600 kHz, which fully demonstrates the effectiveness of the method of the present invention.

[0055] The above verification results demonstrate that the designed radial filter can not only achieve single-mode filtering, but also suppress second harmonic propagation and has a certain stopband width, indicating that the excitation frequency can be flexibly selected.

[0056] 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.

[0057] 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 topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes, wherein the radial filter includes radial filter units, each radial filter unit including a main plate and a scattering design domain disposed on the main plate, characterized in that, The design method includes the following steps: Based on the set physical field conditions, a finite element model and a genetic algorithm are used to iteratively optimize the material distribution topology of the scatterer design domain to obtain the optimal material distribution topology of the scatterer design domain. During the iterative optimization, the eigenfrequency of the structure under different wave vectors is calculated through characteristic frequency research, thereby obtaining the band structure of the radial filter unit. The S0 and A0 modes in the band structure are identified by the polarization factor, which is the ratio of in-plane displacement components to out-of-plane displacement components in the modal displacement field. A fitness function is constructed by jointly considering the passband coverage of the S0 mode band at the target fundamental frequency, the bandgap coverage of the A0 mode band at the target fundamental frequency, and the joint bandgap coverage of the S0 and A0 mode bands at the target second harmonic. The fitness function is expressed as follows: in, F For the fitness function, This indicates the coverage range of the S0 mode band within the baseband target range. This indicates the coverage range of the A0 mode band within the target baseband frequency range. This indicates the coverage range of the joint bandgap of S0 mode and A0 mode within the second harmonic target range. Let be the weighting coefficient, and the weighting coefficient satisfies: w 1=2 w 3, w 2 =-2 w 3, w 3 is a positive number; The polarization factor is expressed as: in, var Polarization factor u for x In-plane displacement in direction 、w for z Out-of-plane displacement in the direction of S This indicates the cross-section of the transmission end.

2. The topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes according to claim 1, characterized in that, During the iterative optimization, the scatterer design domain is divided into array-type pixel units. Each pixel unit corresponds to a binary design variable. When the design variable is 1, it means that the corresponding area is filled with solid material. When the design variable is 0, it means that the corresponding area is empty. All design variables form a binary matrix, which is further encoded as chromosomes in the genetic algorithm.

3. The topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes according to claim 1, characterized in that, The physical field conditions are: the unit structure along... x Set Floquet periodic conditions on the parallel boundaries of the direction, and set all other boundaries as free boundaries.

4. The topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes according to claim 1, characterized in that, This design approach also includes: The designed radial filter is subjected to filtering performance verification, which includes at least frequency domain verification and displacement field verification.

5. The topology optimization design method for a radial filter with dual filtering of second harmonic and guided wave modes according to claim 4, characterized in that, In the frequency domain verification, a frequency sweep calculation is performed using a frequency domain solver, wherein... For S0 mode, the frequency response function of the frequency domain solver is: , and These represent the in-plane displacements at the output and input ends, respectively. For A0 mode, the frequency response function of the frequency domain solver is: , and These represent the out-of-plane displacements at the output and input ends, respectively.

6. A radial filter with dual filtering capabilities of second harmonic and guided wave mode, characterized in that, The radial filter with dual filtering of second harmonic and guided wave modes, as described in any one of claims 1-5, was designed using the topology optimization design method.

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