Elastic wave field regulation and control model based on broadband reflective mode conversion

Abstract

The invention relates to the technical field of regulation and control models, and particularly discloses an elastic wave field regulation and control model based on broadband reflection type mode conversion. The elastic wave mode converter is used for solving the problems that most of existing elastic wave mode converters based on metamaterials or phononic crystals are transmission-type, narrow in working bandwidth and sensitive to processing errors, a reflection system is difficult to achieve accurate and controllable emergent wave front phase, and broadband efficient reflection-type mode conversion and flexible wave field regulation and control are difficult to achieve. The model can realize an achromatic function of a superstructure, so that focusing and abnormal reflection effects are kept stable in a broadband.

Description

Technical Field

[0001] This invention relates to the field of control model technology, and in particular to an elastic wavefield control model based on broadband reflective mode conversion. Background Technology

[0002] Phononic crystals, as artificial structural materials composed of periodic units at the subwavelength scale, can expand band gaps and shape dispersion relations by utilizing Bragg scattering and local resonance mechanisms, thereby enabling the engineered control of the propagation direction, group velocity, and energy flow of elastic waves. In elastic wave field manipulation, phononic crystals can achieve broadband vibration isolation and noise suppression, selective wave guiding and bending, anomalous refraction / reflection and focusing, superlensing and super-resolution imaging, energy orientation and beamforming, mode conversion and filtering, and can be coupled with braking / sensing to form functionally reconfigurable metasurfaces.

[0003] Elastic wave mode conversion plays a crucial role in fields such as ultrasonic nondestructive testing, acoustic sensing, and signal processing. Currently, research on mode converters based on metamaterials or phononic crystals mainly focuses on transmissive structures, whose designs largely rely on theories such as FP resonance and dual-mode impedance matching. These methods typically achieve efficient conversion only at a single frequency point, exhibiting inherent drawbacks such as narrow operating bandwidth and extreme sensitivity to fabrication errors in mode conversion efficiency. Furthermore, research on reflective mode conversion units is insufficient, particularly regarding the active control of the emitted wave field phase, which remains a challenge. Existing technologies struggle to achieve precise control of the reflected wavefront across a wide bandwidth and lack the integration of intelligent algorithms to optimize structural geometric parameters, thus limiting the development of reflective functional devices (such as focusing lenses and deflectors). Therefore, there is an urgent need to develop a scheme capable of achieving broadband, efficient reflective mode conversion and flexible control of the elastic wave field. Summary of the Invention

[0004] The technical problem this invention aims to solve is to provide an elastic wave field control model based on broadband reflective mode conversion, which can achieve efficient reflective elastic wave mode conversion over a wide bandwidth. It also constructs a broadband mode conversion focusing and anomalous reflection superstructure, and optimizes geometric parameters using a Kriging surrogate model and Q-learning algorithm. and The model enables the superstructure to achieve achromatic functionality, keeping focusing and anomalous reflection effects stable over a wide frequency band.

[0005] To achieve the above objectives, the present invention provides the following technical solution: An elastic wave field manipulation model based on broadband reflective mode conversion includes a plate-shaped elastic substrate and a periodic scatterer array arranged on one side of the substrate, with the scatterer array along the elastic wave propagation direction. In cycles Arranged to form an elastic phononic crystal, wherein: the unit geometry of the scatterer array is determined by two adjustable geometric parameters. and Characterization, and The geometric feature dimensions with a length dimension are obtained through a Kriging surrogate model and a Q-learning optimization framework; the scatterer array geometrically preserves the slip symmetry of the propagation direction while violating the relationship between the length dimension and the length dimension. Mirror symmetry of the axis; Through the above symmetry constraints and geometric parameters , The selection of the parameters allows the elastic phonon crystal to form a hybrid Bragg bandgap within the target operating frequency band, generated by the coupling of symmetric SO Lamb wave modes and antisymmetric AO Lamb wave modes. The characteristic modes on both sides of the hybrid Bragg bandgap simultaneously contain symmetric and antisymmetric displacement components. When an SO mode plane wave is incident perpendicularly from one side of the substrate, the incident energy is reflected back to the substrate in the form of an AO mode elastic wave within the frequency band corresponding to the hybrid Bragg bandgap, thus achieving broadband incident mode conversion.

[0006] It should be noted that the design and verification method of the model includes the following steps: (1) Symmetry Analysis and Initial Structural Design: By analyzing the energy band of the periodic scatterer array constructed on the surface of the plate-shaped elastomer and analyzing its structural symmetry, it is found that the element geometry satisfies: preserving the glide symmetry along the propagation direction; and breaking the symmetry about the propagation direction. Based on the mirror symmetry of the axis, the initial structure of the phonon crystal was designed.

[0007] (2) Parametric modeling: Establish a two-dimensional model and express the bandgap width and bandgap center frequency as geometric parameters. and Bivariate functions: and .

[0008] (3) Parameter scan optimization: The geometric parameters of the maximum band gap point are found by traversal. The parameter scan traverses the parameter space composed of two geometric parameters. Maximize the bandgap and center frequency It falls within the target frequency band. The reflection spectrum is calculated using a hybrid WFEM / SAFEM method to verify that the bandgap is a "mode conversion bandgap".

[0009] (4) Determine the number of units: First, set the operating frequency of the phonon crystal to 130kHz-190kHz, and define the attenuation of incident sound waves as exceeding 60 dB to determine the number of phonon crystals. Therefore, the number of phonon crystals can be determined as follows: ; In the formula: This refers to the number of phonon crystal periodic units required to be arranged along the propagation direction, i.e., the number of units in the scattering section. This is the rounding operator. This represents the complex Bloch wavenumber of the phonon crystal on the branch corresponding to the target mode conversion bandgap at the lower boundary of the operating frequency band of 130 kHz. This refers to the complex Bloch wavenumber of the phononic crystal on the same bandgap branch at the upper boundary of the operating frequency band of 130 kHz. The operator for taking the imaginary part of the complex wavenumber, i.e., the spatial attenuation constant, The period length (lattice constant) of the phononic crystal along the propagation direction is the distance between the centers of two adjacent scattering units.

[0010] The final number of phonon crystals was determined to be eight.

[0011] (5) Frequency domain simulation verification of the reflection spectrum and transmission characteristics of the phononic crystal: A scatterer was constructed using eight phononic crystal units designed above, and a model was established. Under the condition of S0 mode incident wave radiation, the reflection spectrum was obtained by WFEM method. After setting a perfectly matched layer on the left side of the model, characteristic frequency analysis was performed to obtain the frequency domain simulation of the phononic crystal transmission characteristics.

[0012] As one aspect of the present invention, the plate-shaped elastomer is an aluminum plate with a thickness of 2 mm, and the period of the scatterer array along the propagation direction is... It is on the order of millimeters; The geometric parameters , The value range satisfies 0.2mm≤ ≤4.5mm, 0.2mm≤ ≤4.8mm, and through different , The combined band structure calculations determine the geometric parameter combination that maximizes the band gap width and ensures the band gap center frequency falls within the target operating frequency band of 130kHz to 190kHz, and serves as the final geometric parameter for the scatterer unit.

[0013] As one aspect of the present invention, the scatterer array includes, in the direction of elastic wave propagation, A phonon crystal periodic unit The propagation constant of the minimum imaginary part within the band gap of the elastic phonon crystal is determined to ensure that the amplitude attenuation of the incident S0 mode elastic wave after passing through the scatterer array is greater than 60 dB within the target operating frequency band.

[0014] As one aspect of the present invention, in the frequency range of 125kHz to 220kHz, in the reflection of the incident SO mode elastic wave by the unit, the ratio of the mode conversion reflection energy composed of AO modes to the total reflection energy is not less than 0.75 within a set range except near a single narrow-frequency failure region, and there is a local mode conversion failure narrow-frequency region at a frequency close to 191kHz, which corresponds to the SO / AO hybrid localized mode of the elastic phonon crystal.

[0015] As one aspect of the present invention, the method for modulating the elastic wave field in a plate-shaped elastic body using the model includes: Step 1: Establish a solid mechanics model for the plate-shaped elastic body, and use the wave finite element method to obtain the Lamb wave band structure in the absence of a scatterer, and identify the degenerate crossover point formed by the symmetric S0 mode and the antisymmetric A0 mode; Step 2: Constrain the geometry of the scatterer unit according to the symmetry characteristics of the degenerate intersection, so that the scatterer array arranged on the plate surface retains the slip symmetry along the propagation direction and destroys the mirror symmetry about the propagation axis, thereby constructing an elastic wave field modulation model based on broadband reflective mode conversion with a hybrid Bragg bandgap. Step 3, in structural geometric parameters , Within the set value range, parameterization and discretization sampling are performed, and simulation results based on the sampling points are used to construct a... The Kriging surrogate model, taking the bandgap center frequency and bandgap width as input, is embedded as an environment evaluator within a Q-learning optimization framework. Candidate models are iteratively selected within the discrete parameter domain. It predicts the corresponding bandgap center frequency and bandgap width, takes the bandgap width falling into the target operating frequency band as a constraint, and imposes a penalty if it does not meet the constraint. It updates the Q value with the maximum bandgap width as the reward objective until convergence, and outputs the geometric parameter combination that satisfies the constraint and has the maximum bandgap width. Step 4: Determine the number of elements required to make the amplitude attenuation of the elastic wave within the bandgap greater than 60 dB based on wave finite element complex energy band calculation. and according to the determined The mode conversion unit is arranged along the propagation direction to obtain a broadband reflective mode conversion scattering section for elastic wave field modulation.

[0016] As one aspect of this invention, the method for designing a broadband mode conversion focusing superstructure includes: Step S1: Arrange multiple broadband reflective mode conversion scattering segments as metasurface units on the surface of the plate-shaped elastic body along the array direction, and assume that the incident elastic wave is a normally incident S0 mode plane wave, and set the spatial position of the focal point of the target A0 mode reflected wave. Step S2: Based on the geometric path difference of the incident wave from different units of the metasurface to the focal point, derive the phase distribution of the ideal reflecting surface, and superimpose the reflection dynamic phase generated by the mode conversion scattering segment with the propagation phase introduced by the free propagation plate segment between each unit to construct the actual surface phase; Step S3: Within the operating frequency band of 125kHz to 220kHz, an objective function for chromatic aberration optimization across multiple frequency points is established, approximating the square root relationship of the A0 mode wavenumber with respect to frequency and the linear relationship of the S0 mode wavenumber with respect to frequency. The distribution of the free propagation segment length between each metasurface unit is obtained through analytical solution or numerical optimization, so that the effective surface phase at different frequencies fits the ideal surface phase, thereby obtaining a mode conversion superstructure that achieves broadband focusing.

[0017] As one aspect of the present invention, the method for designing a broadband mode-conversion anomalous reflection superstructure includes: Step A1: Set the emission angle of the reflected wave of the target A0 mode. And based on the generalized law of reflection, determine the relationship with The corresponding surface phase gradient; Step A2: Replace the surface phase distribution used for focusing design with a linear phase distribution along the array direction, and use the reflection dynamics phase of the mode conversion scattering section and the propagation phase introduced by the free propagation plate section between each mode conversion unit as design variables to establish a color difference optimization function for the error between the target phase and the actual phase under multiple frequency points. Step A3: Solve the chromatic difference optimization function to obtain the length distribution of the free propagation plate segments between each mode conversion unit, so that the main energy beam of the A0 mode reflected wave generated by the S0 mode incident within the 125kHz to 220kHz operating frequency band propagates stably near the emission angle, realizing broadband anomalous reflection.

[0018] As one aspect of the present invention, the method for numerically simulating the designed focusing or anomalous reflection superstructure using the model includes: establishing a model containing a plate-like elastic body, an elastic wave field control model array based on broadband reflective mode conversion, and a perfectly matched layer boundary using the finite element method; exciting with a Gaussian S0 mode incident wave; extracting the out-of-plane displacement component on the plate thickness neutral surface within the working frequency band; analyzing the focal position, emission angle, and energy distribution of the A0 mode reflected wave field at different frequencies; and using whether the deviation between the measured focal position and the target focal position, and between the measured emission angle and the target emission angle, meets a preset threshold as a criterion for whether the design passes.

[0019] It should be noted that the numerical simulation method of the model was verified using COMSOL Multiphysics software. A linear array model consisting of 30 phonon crystal units was constructed, with each unit having a width of 3mm and a unit spacing of 1mm. The parameters were set to 62mm. Based on theoretical calculations and the spatial arrangement characteristics of phonon crystal units, a geometric model of a broadband focusing superstructure was established. A perfectly matched layer (PML) was used as the boundary condition to simulate an infinitely large propagation field. The incident sound field was set to a Gaussian beam distribution. Four characteristic frequencies of 125kHz, 160kHz, 185kHz, and 220kHz were selected for numerical simulation analysis. In the post-processing stage, to obtain a pure A0 mode wave field, the out-of-plane displacement component at the mid-surface position of the plate structure was specifically extracted. In the broadband mode-conversion anomalous reflection superstructure and frequency domain full-wave simulation, the exit angle was set to 30°. The anomalous reflection superstructure based on dynamic phase consisted of 30 phonon crystals uniformly arranged, targeting the theoretically obtained broadband anomalous reflection superstructure. The remaining settings remained the same, with the S0 mode positive incident Gaussian beam wave field generated by the boundary load after placing a perfectly matched layer around it.

[0020] As one aspect of the present invention, when constructing the surface phase of the mode-transformation superstructure in the model, the center positions of two adjacent mode-transformation scattering segments are respectively denoted as... and Let the wavenumbers of the S0 mode and A0 mode propagating in the plate be denoted as follows: and By representing the reflection dynamics phase during mode switching as a phase factor In this way, the relative positions of the scatterers and the length of the free propagation plate between the scatterers are uniformly mapped as the control variables of the phase of the reflected wave field of the outgoing A0 mode, so as to achieve continuous phase adjustment in the range of 0 to 2π.

[0021] As one aspect of the present invention, after determining the geometric parameters of the mode conversion unit, the number of units, and the length of the free propagation plate segment, the model also includes a broadband performance evaluation of the design results. The performance evaluation includes: statistically analyzing the ratio of the A0 mode reflected energy generated by the S0 mode incident to the total reflected energy within the 125kHz to 220kHz operating frequency band, and calculating the change in the focal position or exit angle in the corresponding wave field with frequency, so that the ratio is not less than 0.75 at most frequency points and the focal position offset or exit angle change does not exceed a preset threshold.

[0022] Compared with existing technologies, the technical effects of this invention are as follows: (1) Broadband and high efficiency: Through the mode conversion bandgap designed with symmetry, high-efficiency mode conversion within a bandwidth of nearly 100 kHz is achieved, overcoming the shortcomings of narrow bandwidth in traditional methods. (2) Adjustable phase: A dynamic phase mechanism in a reflective system is proposed, providing an effective means for phase control of the reflected wave field. (3) Achromatic design: The achromatic function of the superstructure is realized through optimization algorithms, so that the focusing and anomalous reflection effects remain stable within a wide frequency band, improving device performance. (4) Wide application: The designed focusing and anomalous reflection superstructure provides core theoretical and technical support for the development of new acoustic devices (such as ultrasonic focusing probes, acoustic deflectors, acoustic cloaks, etc.). The model of this invention can be used on Internet platforms and can realize the achromatic function of the superstructure, so that the focusing and anomalous reflection effects remain stable within a wide frequency band. Attached Figure Description

[0023] Figure 1 Here are schematic diagrams of the broadband reflective mode conversion and elastic wave field control of the present invention: (a) a focusing schematic diagram of S0 mode incident and A0 mode exit; (b) a schematic diagram of abnormal reflection of S0 mode incident and A0 mode exit. Figure 2 This invention relates to an energy band structure for the propagation of elastic Lamb waves using an aluminum plate structure with a period of 1cm and a thickness of 2mm. Figure 3 This invention relates to the band structure of elastic phonon crystals after breaking two different symmetries: (a) breaking Glide symmetry; (b) breaking along... Band structure after axisymmetric flip; Figure 4 The optimized propagation behavior of elastic waves in a phonon crystal obtained by the WFEM algorithm of this invention is as follows: (a) propagation constant; (b) attenuation constant; Figure 5 The reflection spectrum and reflection phase response curves of the elastic phononic crystal of the present invention under the excitation of S0 mode incident wave: (a) A0 mode (i.e. mode conversion) in the scattered field; (b) S0 mode in the scattered field; Figure 6 The phonon crystal structure of this invention exhibits the following 191.5kHz localized modes: (a) normalized displacement amplitude distribution and deformation mode; (b) in-plane displacement distribution; and (c) out-of-plane displacement distribution. Figure 7 This invention is based on a broadband focusing superstructure with dynamic phase. The frequency domain simulation model shows the out-of-plane displacement distribution on the neutral plane of the propagation part. The simulation frequencies include: (a) 125kHz; (b) 160kHz; (c) 185kHz; (d) 220kHz. Figure 8The results of the out-of-plane displacement distribution on the neutral plane of the propagation part at different frequencies in the frequency domain simulation model of the broadband focusing superstructure based on dynamic phase of this invention are as follows: (a) longitudinal distribution (propagation direction); (b) transverse distribution (perpendicular to the propagation direction). Figure 9 The results of the out-of-plane displacement distribution on the neutral plane of the propagation part of the broadband anomalous reflection superstructure based on dynamic phase of this invention are as follows: (a) 125kHz; (b) 160kHz; (c) 185kHz; (d) 220kHz; (e) the relationship between the wave field exit angle and frequency. Detailed Implementation

[0024] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Example 1

[0026] This embodiment provides a detailed description of the design and functional verification of an elastic wavefield modulation model based on broadband reflective mode conversion according to the present invention.

[0027] like Figure 1 As shown, the operating conditions of the elastic wavefield modulation model based on broadband reflective mode conversion proposed in this invention include: Figure 1 (a) Indicates the focusing condition: In a thin plate, the S0 Lamb wave travels along the plane wave. The incident S0 mode is efficiently converted into the A0 mode in the reflection channel through the mode-converting phonon crystal array arranged in the gray area in the center of the plate. The emitted A0 wavefront is arc-shaped and converges to a certain spatial focal point on the plate surface, realizing reflective mode conversion focusing. Figure 1 (b) Indicates the abnormal reflection condition: the S0 mode also follows... When incident on the gray mode-converting metasurface in the normal direction, the main energy is converted into the A0 mode after reflection and emitted in a direction that makes a specific angle with the normal, forming an anomalous reflected beam that deviates from the direction of specular reflection. The dashed line indicates the location of the mode-converting metasurface.

[0028] In this invention, the design and functional verification of an elastic wavefield modulation model based on broadband reflective mode conversion includes: (1) Plate band structure analysis: A solid mechanical plane strain model of the aluminum plate was established. After assembling the element mass matrix and stiffness matrix, the band structure was calculated using the WFEM method. The S0 and A0 modes were distinguished by the boundary conditions of the semi-model. The band structure results are shown in the figure below. Figure 2As shown, light-colored lines represent symmetric modes, and dark-colored lines represent antisymmetric modes. The band structure shows four crossover points. The first set of crossover points consists of two bands representing symmetric and antisymmetric modes, respectively. Therefore, we can conclude that this set of band crossover points is protected by symmetry along the x-axis. The other set of band crossover points consists of two degenerate modes of the same mode but with opposite propagation directions, protected by so-called Glide symmetry. This means that when a periodic structure can overlap with the original structure after being flipped along the x-axis and translated along the propagation direction by half an integer period, this degeneracy will not be disrupted. Disrupting this symmetry can produce a single-mode bandgap, which exhibits mode-selective characteristics when other modes exist within it.

[0029] (2) Structure and materials: A 2mm thick aluminum plate was selected as the base, along... Surface microstructure elements with a directional setting period of 6 mm. Element geometry is determined by parameters. , Characterization, as shown by the band structure analysis and symmetry criterion analysis below, shows that independent modes should satisfy "preserving glide symmetry and breaking..." "Axial mirror symmetry".

[0030] (3) Band structure analysis and symmetry criterion: The influence of symmetry on the elastic phonon crystal was further explored by calculating the band structure after breaking the two symmetries respectively. The band structure calculation results are as follows: Figure 3 As shown, to better distinguish different modes, the color of each feature mode in the figure represents the polarization factor. , expressed as: ; In the formula: Polarization factor For this intrinsic mode in the out-of-plane direction (i.e., the plate thickness direction) Displacement components in the direction) For this intrinsic mode in the in-plane direction (inside the plate plane, i.e., the propagation direction) Or orthogonal to it Displacement components on the composite () The integration region comprises the geometric region of a periodic unit cell (i.e., the substrate and the scattering structure on it).

[0031] As can be seen from the band structure diagram, when the Glide symmetry is broken, as... Figure 3 (a) The A0 single-mode bandgap appears at approximately 108 kHz, indicating a mode-selective bandgap; it preserves Glide symmetry and breaks along the bandgap. When axially symmetric, such as Figure 3As shown in (b), the bandgap opens at approximately 205 kHz, and the modes on both sides of the bandgap have P≈0.5, indicating a mixed S0 / A0 bandgap. The purpose of this invention is to design a mode-switching bandgap that improves mode-switching efficiency while reducing reflections of the same mode. Therefore, the design concept is to preserve the Glide symmetry of the phononic crystal while disrupting the structure along... Symmetry of the axis.

[0032] (4) Bandgap optimization and parameter domain: in the structural geometric parameters , Within the set value range, parameterization and discretization sampling are performed, and simulation results based on the sampling points are used to construct a... The Kriging surrogate model, taking the bandgap center frequency and bandgap width as input, is embedded as an environment evaluator within a Q-learning optimization framework. Candidate models are iteratively selected within the discrete parameter domain. It predicts the corresponding bandgap center frequency and bandgap width, using the constraint that the bandgap width falls within the target operating frequency band. If this constraint is not met, a penalty is imposed. The Q-value is updated with the objective of maximizing the bandgap width as the reward, until convergence. The output is the geometric parameter combination that satisfies the constraints and maximizes the bandgap width. The bandgap width and bandgap center frequency are expressed as geometric parameters. and Bivariate functions: and The geometric parameters of the maximum bandgap point are found by traversing the parameter space composed of two geometric parameters. Maximize the bandgap and center frequency It fell into the target frequency band.

[0033] (5) Complex band and number of units: For the obtained phononic crystal with the largest band gap, in order to ensure the mode conversion function of the phononic crystal, the phononic crystal should be used as few as possible. The complex band is calculated by WFEM method, where the minimum imaginary part propagation constant in the band gap represents the minimum attenuation characteristic of elastic waves in the band gap. Figure 4 The result is the complex band calculation result of the WFEM method. The operating frequency of the phonon crystal is set to 130kHz-190kHz, and the number of phonon crystals is determined by defining the attenuation of the incident sound wave as exceeding 60 dB. Therefore, the number of phonon crystals can be calculated by equation (1) as N=8.

[0034] (6) Frequency domain reflection spectrum and phase calculation of the 8-unit scatterer using WFEM / SAFEM: A model was established using 8 phonon crystal units designed above. Under the condition of S0 mode incident wave radiation, the reflection spectrum was obtained by WFEM method. Figure 5As shown, the results indicate that within the frequency range of 125kHz-220kHz, except for a very small frequency band near 183kHz, the mode conversion efficiency of this phononic crystal functional device is higher than 0.75, confirming the viewpoint in band analysis that the hybrid Bragg bandgap has mode conversion functionality. It should be noted that a very small mode conversion failure region exists near 191kHz. After setting a perfectly matched layer on the left side of the model, characteristic frequency analysis was performed to obtain the frequency domain simulation of the phononic crystal's transmission characteristics. Figure 6 As shown, Figure 6 (a) represents the modal normalized amplitude and deformation mode. Figure 6 (b) and Figure 6 (c) shows the in-plane and out-of-plane displacement distributions, respectively. The analysis indicates that this state is a mixed mode of symmetric and antisymmetric modes.

[0035] Example 2

[0036] The difference between Embodiment 2 and Embodiment 1 is that this embodiment introduces a broadband mode conversion and focusing performance verification method based on a broadband reflective mode conversion elastic wave field modulation model.

[0037] In this invention, the broadband mode conversion and focusing performance verification method includes: (1) Dynamic phase derivation: Considering that the two scatterers are located at , Introducing a phase factor in the mode conversion reflection channel By changing the relative positions of the scatterers or inserting free propagation sections between elements, continuous control of the outgoing A0 phase within the range of 0–2π can be achieved.

[0038] (2) Surface phase and achromatic optimization: Normally incident S0 plane wave, target A0 reflected and focused at the specified focal point; ideal surface phase Determined by the geometric path difference, where, For operating frequency, The lateral coordinates are along the direction of the metasurface array. In frequency Below, the phase of the ideal reflecting surface located at the metasurface coordinates, In frequency The wavenumber of the target emission mode is, in this invention, the propagation wavenumber of the AO mode in the plate. The focal length is the geometric distance between the target focus and the metasurface plane, i.e., the distance from the center of the array to the focal point along the normal direction. This is a frequency-dependent phase constant (path constant) used to set the phase zero or eliminate overall unrelated constant phase. Within the operating frequency range of 125kHz-220kHz, it is set... , , , All A0. To minimize chromatic difference across the entire operating frequency range, the following optimization problem is defined to solve for the optimal propagation length. To ensure that the calculated free propagation segment length is greater than 0, the maximum width of the metasurface is used. Zero-phase reference point: ; In the formula: To be at a given position Given the length of free propagation Under the given conditions, the weighted square integral of the phase error at the inner surface of the frequency band is the objective function of the optimization problem. , These are the lower and upper limits of the operating frequency band, respectively. The comprehensive phase coefficient, related to the wavenumber and phase normalization of the target's emitted A0 mode, is used to convert the geometric path difference into a frequency-dependent ideal phase difference term. For position The corresponding free propagation segment length, i.e. the length of the unstructured plate segment reserved between the mode conversion unit and the reference plane, is a design variable that needs to be solved through optimization.

[0039] Analyze the above system of equations and find Achieve minimal color difference.

[0040] (3) Geometric and simulation settings: Numerical simulation verification was performed in COMSOL Multiphysics software. For example... Figure 1 As shown in (a), a linear array model consisting of 30 phonon crystal units is constructed, with each unit having a width of 3 mm and a spacing of 1 mm. Based on this, the xmax parameter is set to 62 mm. According to theoretical calculations and considering the spatial arrangement characteristics of the phonon crystal units, a geometric model of a broadband focusing superstructure is established. A perfectly matched layer (PML) is used as the boundary condition to simulate an infinitely large propagation field, and the incident sound field is set to a Gaussian beam distribution. This invention selects four characteristic frequencies—125 kHz, 160 kHz, 185 kHz, and 220 kHz—for numerical simulation analysis.

[0041] (4) Simulation results: In the post-processing stage, in order to obtain a pure A0 mode wave field, the out-of-plane displacement component of the mid-surface position of the plate structure was specifically extracted. Figure 7The simulation results at four frequencies (125kHz, 160kHz, 18kHz, and 220kHz) shown in the figure demonstrate that when S0 mode plane waves of different frequencies are incident on the metasurface, the A0 mode wave field generated after mode conversion can be accurately focused at the theoretically predicted position (the intersection of the dashed lines in the figure). Notably, at the four characteristic frequencies studied, the measured focal positions maintain good consistency with the theoretical predictions, which fully verifies the stable focusing performance of the superstructure over a wide frequency range. Figure 8 Images (a) and (b) show the distribution of out-of-plane displacement on the neutral plane at different frequencies along the longitudinal and transverse dashed lines, respectively. It can be seen that due to the model's symmetry along the zoy plane, the focal spot distribution along the transverse line is concentrated near 0, and the focal spot diameter gradually decreases with increasing frequency. The longitudinal distribution results show that the focal spot is distributed between 0.08 ± 0.004, and the focusing effect is inconsistent at different frequencies. This indicates that although the model achieves good broadband focusing performance, it cannot completely eliminate the influence of chromatic aberration.

[0042] Example 3

[0043] The difference between this embodiment and Embodiments 1 and 2 is that this embodiment specifically describes the implementation of a broadband mode conversion and anomalous reflection performance verification of an elastic wave field modulation model based on broadband reflective mode conversion.

[0044] In this invention, the verification of broadband mode conversion and abnormal reflection performance includes: (1) Phase gradient and target angle: Set the surface phase gradient to achieve the target launch angle. =30°, incorporate dynamic phase into achromatic design, and replace the coefficient in the focusing design with Calculate the length of the free propagation segment of each unit. .

[0045] (2) Array and simulation settings: Construct a geometric model of a 30-element equally spaced linear array as follows Figure 1 As shown in (b) (consistent with Example 2), the PML and S0 are set to be positively incident Gaussian beams, and the numerical simulation analysis is performed using four characteristic frequencies of 125kHz, 160kHz, 185kHz and 220kHz, consistent with Example 2.

[0046] (3) Simulation results: Figure 9Images (a), (b), (c), and (d) show wavefield results at four frequencies: 125kHz, 160kHz, 185kHz, and 220kHz, respectively. It can be seen that most of the energy in the emitted wavefield is concentrated in the same direction, and the emission angles exhibit good consistency. Further investigation of the emission angle is conducted by using spatial Fourier transform to estimate the propagation direction of the emitted wave on a 150mm long horizontal line 80mm from the superstructure on the neutral surface. Wavenumber analysis then determines the reflection angle as follows: ; In the formula, The angle of reflection, This represents the tangential wavenumber component of the reflected wave along the intercepted transverse direction.

[0047] from Figure 9 (e) The processing results show that the emitted wave field is around 30° in the frequency range of 125kHz-220kHz. However, since the chromatic aberration cannot be completely eliminated, the emission angle has a slight decreasing trend with frequency.

[0048] In summary, this invention first optimizes and verifies the function of the reflective elastic wave mode conversion unit through Example 1, enabling it to have a certain mode conversion function; then, through Example 2, it verifies the broadband focusing performance of the designed phononic crystal; and finally, through Example 3, it designs an abnormal reflection mode conversion metasurface and frequency domain full-wave simulation for both normal and oblique incidence cases. This invention solves the problems of narrow working bandwidth, sensitivity to processing tolerance, and difficulty in controlling the phase of the reflection system in the prior art.

[0049] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0050] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An elastic wavefield modulation model based on broadband reflective mode conversion, characterized in that, It includes a plate-shaped elastic substrate and a periodic array of scatterers arranged on one side of the substrate, with the scatterer array along the direction of elastic wave propagation. In cycles Arranged to form an elastic phononic crystal, wherein: the unit geometry of the scatterer array is determined by two adjustable geometric parameters. and Characterization, and The geometric feature dimensions with a length dimension are obtained through a Kriging surrogate model and a Q-learning optimization framework; the scatterer array geometrically preserves the slip symmetry of the propagation direction while violating the relationship between the length dimension and the length dimension. Mirror symmetry of the axis; Through the above symmetry constraints and geometric parameters , The selection of the parameters allows the elastic phonon crystal to form a hybrid Bragg bandgap within the target operating frequency band, generated by the coupling of symmetric SO Lamb wave modes and antisymmetric AO Lamb wave modes. The characteristic modes on both sides of the hybrid Bragg bandgap simultaneously contain symmetric and antisymmetric displacement components. When an SO mode plane wave is incident perpendicularly from one side of the substrate, the incident energy is reflected back to the substrate in the form of an AO mode elastic wave within the frequency band corresponding to the hybrid Bragg bandgap, thus achieving broadband incident mode conversion.

2. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, The plate-shaped elastomer is an aluminum plate with a thickness of 2 mm, and the period of the scatterer array along the propagation direction is... It is on the order of millimeters; The geometric parameters , The value range satisfies 0.2mm≤ ≤4.5mm, 0.2mm≤ ≤4.8mm, and through different , The combined band structure calculations determine the geometric parameter combination that maximizes the band gap width and ensures the band gap center frequency falls within the target operating frequency band of 130kHz to 190kHz, and serves as the final geometric parameter for the scatterer unit.

3. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, The scatterer array includes, in the direction of elastic wave propagation A phonon crystal periodic unit The propagation constant of the minimum imaginary part within the band gap of the elastic phonon crystal is determined to ensure that the amplitude attenuation of the incident S0 mode elastic wave after passing through the scatterer array is greater than 60 dB within the target operating frequency band.

4. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, In the frequency range of 125kHz to 220kHz, the ratio of mode conversion reflected energy composed of AO modes to the total reflected energy in the reflection of incident SO mode elastic waves by the model is not less than 0.75 in a set range except near a single narrow-frequency failure region. Furthermore, there is a local mode conversion failure narrow-frequency region at a frequency close to 191kHz, which corresponds to the SO / AO hybrid localized mode of the elastic phonon crystal.

5. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, In the model, the method for controlling the elastic wave field in the plate-shaped elastic body includes: Step 1: Establish a solid mechanics model for the plate-shaped elastic body, and use the wave finite element method to obtain the Lamb wave band structure in the absence of a scatterer, and identify the degenerate crossover point formed by the symmetric S0 mode and the antisymmetric A0 mode; Step 2: Constrain the geometry of the scatterer unit according to the symmetry characteristics of the degenerate intersection, so that the scatterer array arranged on the plate surface retains the slip symmetry along the propagation direction and destroys the mirror symmetry about the propagation axis, and constructs an elastic wave field control model based on broadband reflective mode conversion with a hybrid Bragg bandgap. Step 3, in structural geometric parameters , Within the set value range, parameterization and discretization sampling are performed, and simulation results based on the sampling points are used to construct a... The Kriging surrogate model, taking the bandgap center frequency and bandgap width as input, is embedded as an environment evaluator within a Q-learning optimization framework. Candidate models are iteratively selected within the discrete parameter domain. It predicts the corresponding bandgap center frequency and bandgap width, takes the bandgap width falling into the target operating frequency band as a constraint, and imposes a penalty if it does not meet the constraint. It updates the Q value with the maximum bandgap width as the reward objective until convergence, and outputs the geometric parameter combination that satisfies the constraint and has the maximum bandgap width. Step 4: Determine the number of elements required to make the amplitude attenuation of the elastic wave within the bandgap greater than 60 dB based on wave finite element complex energy band calculation. and according to the determined The model is arranged along the propagation direction to obtain a broadband reflective mode conversion scattering section for elastic wave field manipulation.

6. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, In the model described, the method for designing a broadband mode-conversion focusing superstructure includes: Step S1: Arrange multiple broadband reflective mode conversion scattering segments as metasurface units on the surface of the plate-shaped elastic body along the array direction, and assume that the incident elastic wave is a normally incident S0 mode plane wave, and set the spatial position of the focal point of the target A0 mode reflected wave. Step S2: Based on the geometric path difference of the incident wave from different units of the metasurface to the focal point, derive the phase distribution of the ideal reflecting surface, and superimpose the reflection dynamic phase generated by the mode conversion scattering segment with the propagation phase introduced by the free propagation plate segment between each unit to construct the actual surface phase; Step S3: Within the operating frequency band of 125kHz to 220kHz, an objective function for chromatic aberration optimization across multiple frequency points is established, approximating the square root relationship of the A0 mode wavenumber with respect to frequency and the linear relationship of the S0 mode wavenumber with respect to frequency. The distribution of the free propagation segment length between each metasurface unit is obtained through analytical solution or numerical optimization, so that the effective surface phase at different frequencies fits the ideal surface phase, thereby obtaining a mode conversion superstructure that achieves broadband focusing.

7. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 1, characterized in that, In the model, the method for designing a broadband mode-conversion anomalous reflection superstructure includes: Step A1: Set the emission angle of the reflected wave of the target A0 mode. And based on the generalized law of reflection, determine the relationship with The corresponding surface phase gradient; Step A2: Replace the surface phase distribution used for focusing design with a linear phase distribution along the array direction, and use the reflection dynamics phase of the mode conversion scattering section and the propagation phase introduced by the free propagation plate section between each mode conversion unit as design variables to establish a color difference optimization function for the error between the target phase and the actual phase under multiple frequency points. Step A3: Solve the chromatic difference optimization function to obtain the length distribution of the free propagation plate segments between each mode conversion unit, so that the main energy beam of the A0 mode reflected wave generated by the S0 mode incident within the 125kHz to 220kHz operating frequency band propagates stably near the emission angle, realizing broadband anomalous reflection.

8. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 7, characterized in that, In step A2 of the above-described method for designing a broadband mode-conversion anomalous reflection superstructure, the method for numerically simulating the designed focusing or anomalous reflection superstructure includes: establishing a model using the finite element method, which includes a plate-like elastic body, an elastic wave field control model array based on broadband reflective mode conversion, and a perfectly matched layer boundary; using a Gaussian S0 mode incident wave for excitation; extracting the out-of-plane displacement component on the plate thickness neutral surface within the working frequency band; analyzing the focal position, emission angle, and energy distribution of the A0 mode reflected wave field at different frequencies; and using whether the deviation between the measured focal position and the target focal position, and between the measured emission angle and the target emission angle, meets the preset threshold as the criterion for whether the design passes.

9. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 8, characterized in that, In the model described above, when constructing the surface phase of the mode-conversion superstructure, the center positions of two adjacent mode-conversion scattering segments are respectively denoted as... and Let the wavenumbers of the S0 mode and A0 mode propagating in the plate be denoted as follows: and By representing the reflection dynamics phase during mode switching as a phase factor In this way, the relative positions of the scatterers and the length of the free propagation plate between the scatterers are uniformly mapped as the control variables of the phase of the reflected wave field of the outgoing A0 mode, so as to achieve continuous phase adjustment in the range of 0 to 2π.

10. The elastic wavefield modulation model based on broadband reflective mode conversion according to claim 5, characterized in that, After determining the model mode conversion geometric parameters, number of elements, and length of the free propagation plate segment, the design results are further evaluated in a broadband manner. The performance evaluation includes: statistically analyzing the ratio of A0 mode reflected energy generated by S0 mode incident to total reflected energy within the 125kHz to 220kHz operating frequency band, and calculating the change in focal position or exit angle in the corresponding wavefield with frequency, so that the ratio is not less than 0.75 at most frequency points and the focal position offset or exit angle change does not exceed a preset threshold.

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