A method and system for designing a multiplexed non-local acoustic metasurface considering dual-wave cooperative regulation

Abstract

A kind of multiplexing non-local acoustic metasurface design method and system considering double-wave cooperative regulation belongs to the front cross field of acoustic wave fluctuation control and multidisciplinary optimization design. With the whole supercell as the optimization design object, the non-local coupling and transverse energy exchange between adjacent unit cells are utilized. At the same time, the local sound power intensity vector direction in the reflection target domain and the transmission target domain is taken as the cooperative optimization index, the energy balance penalty and adaptive weight are introduced, and the unified regulation of the transmission / reflection sound field direction and energy distribution is realized. The flexible substrate stretching regulation mode is introduced, the initial state and the target after stretching are included in the same optimization model, and the multiplexing non-local acoustic metasurface can realize continuous adjustment by stretching the flexible substrate, which can improve the solving efficiency of complex double-wave coupling problems. The present application can cooperatively control the multiplexing non-local acoustic metasurface of the transmission wave field and the reflection wave field, realize the precise acoustic wave control of fusion dynamic tuning and multi-functional characteristics.

Description

Technical Field

[0001] This invention belongs to the cutting-edge interdisciplinary field of acoustic wave control and multidisciplinary optimization design, and relates to a design method and system for multiplexed nonlocal acoustic metasurfaces that consider dual-wave synergistic control. Background Technology

[0002] Acoustic metasurfaces are typically composed of subwavelength-scale artificial microstructure arrays, characterized by their small thickness, ease of integration, and strong wavefront manipulation capabilities, making them promising for applications in noise control, underwater communication, and ultrasonic testing. Traditional acoustic metasurfaces are mostly designed based on the generalized Snell's law, achieving functions such as anomalous reflection and anomalous transmission through localized manipulation of the unit phase. For example, Chinese invention patent CN111489732A proposes an acoustic metasurface design method and acoustic device based on a cavity-back structure. Chinese invention patent CN121237073A proposes a reflective acoustic coding metasurface design method based on a genetic algorithm. Most of these methods target unilateral wavefield manipulation; however, in practical applications, incident sound waves simultaneously create usable sound fields on both the reflection and transmission sides of the metasurface. Controlling only one side can easily lead to insufficient spatial utilization of acoustic energy and low functional integration of the device.

[0003] To improve functional integration, existing research has attempted to achieve dual-sided manipulation of transmitted and reflected waves by setting different local phase gradients. However, such designs still mainly rely on the phase gradient distribution of individual unit cells, typically neglecting nonlocal interactions, parasitic scattering, and near-field coupling effects between adjacent and next-nearest unit cells. When the target deflection angle is large, or when simultaneous synergistic manipulation of transmitted and reflected waves is required, the phase distribution formed by splicing local unit cells is easily affected by strong scattering and higher-order diffraction, leading to target orientation deviation or decreased manipulation efficiency. Simultaneously, there are mutual constraints on energy distribution and target orientation between the transmission and reflection sides, easily resulting in improved manipulation performance on one side but decreased performance on the other. Therefore, coordinating the energy flow and distribution of reflected and transmitted waves within the same structure is a key bottleneck in dual-wave synergistic manipulation design. On the other hand, existing research on transmission / reflection synergistic manipulation is mostly focused on static structures, and tunable multiplexed metasurface designs remain relatively scarce. Existing tunable solutions often rely on empirical configurations, mechanical rotation, liquid filling, or external field control of smart materials, which have problems such as limited degrees of freedom, complex responses, and difficulty in obtaining better topological configurations in a systematic manner.

[0004] In summary, how to develop a design method for multiplexed nonlocal acoustic metasurfaces that considers the coordinated control of transmitted / reflected waves, so that the acoustic metasurface structure has both customized dynamic tuning capability and multiplexing characteristics, thereby improving its space utilization efficiency and functional integration, has become a key problem that urgently needs to be solved. Summary of the Invention

[0005] To address the problems in existing dual-wave synergistic acoustic metasurface designs, which rely on unit cell phase gradient distribution, leading to near-field coupling, parasitic scattering, mutual constraints between dual-wave targets, underutilization of nonlocal coupling, and the inability of static structures to adapt to wavefield manipulation requirements after mechanical deformation, this invention provides a multiplexed nonlocal acoustic metasurface design method and system that considers dual-wave synergistic manipulation. This invention uses a supercell containing the coupling relationship between adjacent units as the overall design object, directly using the direction of the local acoustic power intensity vector in the reflection and transmission target domains as the optimization basis. When dynamic manipulation is required, the tensile deformation of the flexible substrate and the dual-wave targets in the initial and post-stretched states are incorporated into the same optimization framework, thereby obtaining a manufacturable structure that can achieve customized synergistic manipulation of transmitted / reflected acoustic waves under multiple operating states.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A design method for multiplexed nonlocal acoustic metasurfaces considering dual-wavelength coordinated modulation includes the following steps: The first step is to collect the acoustic functional target parameters, material parameters, and geometric constraint parameters of the metasurface, as follows: Step 1.1: Obtain or set the acoustic function target parameters, including the operating frequency. f Background medium density Background medium sound velocity Angle of incidence Incident sound pressure amplitude Metasurface thickness h Supersurface and supercellular periodic boundary conditions. Set dual-wavelength coordinated control targets as needed, including the target reflection angle in the initial state. and target transmission angle Determine if dynamic adjustment is needed; if so, further set the target reflection angle after stretching. and target transmission angle .

[0007] Step 1.2: Set the acoustic and mechanical parameters of the metasurface candidate solid scatterer material, the air medium, and the optional flexible substrate material; wherein, the parameters of the flexible substrate material include at least the hyperelastic constitutive parameters, density, and allowable deformation range, and the acoustic impedance of the candidate solid scatterer material is approximately an acoustically rigid boundary when it is significantly greater than that of the background medium.

[0008] Step 1.3 sets manufacturing constraints and evaluation requirements, including minimum structural feature size, air channel connectivity, supercell periodic continuity, upper limit of solid material volume fraction, energy balance range of reflected and transmitted waves, and plane wave or Gaussian wave incident conditions for verification.

[0009] The second step involves constructing a nonlocal dual-wave propagation and deformation analysis model based on the acoustic functional objectives, and evaluating the energy flow direction based on the acoustic power intensity vector, as detailed below: Step 2.1, based on the operating frequency and initial target transmission angle set in Step 1.1. Determining the supercell period of a metasurface Let the background medium wavelength be... sound wave number Under normal incidence conditions, the metasurface supercell periodicity Determined based on the initial target transmission angle .

[0010] Step 2.2, using metasurface supercell periodicity An initial-state nonlocal dual-wave propagation acoustic model is constructed, utilizing nonlocal coupling and lateral energy exchange between adjacent unit cells to overcome the limitations of traditional independent unit cell phase stitching. Specifically, a reflection target domain is set above the supercell. A transmission target domain is set below the supercell. A pressure acoustic model with periodic boundaries is established as the initial state nonlocal two-wave propagation acoustic model. The sound pressure fields of the incident wave, reflected wave, and transmitted wave are denoted as follows: , and , represented as: (1) in, The incident wave acoustic pressure field; The sound pressure field of the reflected wave; This represents the acoustic pressure field of the transmitted wave. , and These represent the amplitudes of the incident wave, reflected wave, and transmitted wave, respectively. x Let be the lateral coordinate of any point in the sound pressure field; y Let be the longitudinal coordinate of any point in the sound pressure field; j This refers to the imaginary part in numerical computation. k It is the wavenumber in the background medium at the operating frequency; , and These are the angle of incidence, the angle of reflection, and the angle of transmission, respectively.

[0011] Step 2.3: Calculate the velocity vector based on the sound pressure field in Formula 1. Harmony power intensity vector The velocity vector satisfies The sound power intensity vector is defined as follows: (2) in, To calculate the real part in "[]"; For sound pressure field, this is an option. , and ; This is the velocity vector; superscript " "Represents complex conjugation; The sound power intensity vector along x Component of direction; The sound power intensity vector along y Component of direction; It is a defined metasurface structure x The normal vector of the direction; It is a defined metasurface structure y The normal vector of the direction.

[0012] Step 2.4: Calculate the sound power intensity vector using formula (2). The sound power intensity vector direction of each node in the reflection target domain and the transmission target domain is obtained by formula (3). The local sound power intensity vector direction is used to characterize the actual deflection direction of the sound wave, thereby avoiding the use of the unit cell phase gradient as the design basis.

[0013] (3) in, and These represent the directions of the acoustic power intensity vectors at each node within the reflection and transmission target domains, respectively. i Represents the first target within the reflection target domain and the transmission target domain. i One node; and For the first in the reflection target domain i The sound power intensity vector of each node along x and y Component of direction; and For the first in the transmission target domain i The sound power intensity vector of each node along x and y The directional component.

[0014] Step 2.5, when the dynamic adjustment function is required as set in step 1.1, i.e. Based on the target transmission angle of the stretched metasurface structure. Determine the supercell period of the metasurface after stretching Then the target tensile strain Should meet: (4) Step 2.6: Based on the initial nonlocal dual-wave propagation acoustic model constructed in Step 2.2, establish a large deformation analysis model for the flexible substrate. The flexible substrate is described using reference configuration coordinates D and current configuration coordinates d, and the deformation gradient F and Cauchy-Green tensor are calculated. , represented as Cauchy-Green tensor The flexible substrate is described using a hyperelastic strain energy function, and the nonlinear equilibrium equations are solved under given boundary displacement and periodic boundary conditions. The spatial position of the stretched solid scatterer is obtained. Here, R represents the residual stress; u is the displacement vector in the finite element analysis considering large deformation.

[0015] Step 2.7: After obtaining the acoustic metasurface structure after large deformation stretching in step 2.6, construct the nonlocal dual-wave propagation acoustic model in the stretched state, and calculate the acoustic power intensity vector of the acoustic metasurface structure in the stretched state and the local acoustic power intensity vector direction of each node in the reflection target domain and the transmission target domain.

[0016] Step 2.8: In cases requiring dynamic control, construct nonlocal dual-wave propagation acoustic models for the initial state and the stretched state respectively; in static design, omit steps 2.5-2.7, and directly use the initial state nonlocal dual-wave propagation model as the physical basis for the next optimization model.

[0017] The third step involves constructing a topology optimization model for a multiplexed nonlocal acoustic metasurface that considers dual-wavelength co-modulation. Here, "nonlocal" refers to the interaction between adjacent and next-nearest unit cells; the acoustic response of the metasurface is determined by the overall metacell mode, rather than by the simple superposition of scattering from individual unit cells. The constructed topology optimization model for a multiplexed nonlocal acoustic metasurface considering dual-wavelength co-modulation uses the deviation between the local acoustic power intensity vector direction and the target direction within the target domain as the objective function. Specifically: Step 3.1: For the case where dynamic control is not considered and only the initial state is taken into account, calculate the direction of the acoustic power intensity vector of each node in the reflection target domain. With the target reflection angle The deviation, and the direction of the acoustic power intensity vector of the nodes within the transmission target domain. With the target transmission angle The deviation is defined by the initial state dual-wave cooperative deviation function. for: (5) in, and An adaptive weighting factor is used to address the target conflict problem in dual-wave modulation. The first adaptive weighting factor, This is the second adaptive weighting factor; n This represents the number of nodes within the reflection target domain and the transmission target domain.

[0018] Step 3.2: When considering the dynamic control scenario, i.e., including the stretched state model, calculate the direction deviation of the acoustic power intensity vector between the reflected and transmitted target domains in the stretched state in the same way (using the method in Step 3.1), and define the dual-wave cooperative deviation function in the stretched state. : (6) Step 3.3: To avoid significant energy dominance on the reflection or transmission side, a transmission / reflection sound pressure amplitude ratio is defined. And construct an energy balance penalty function. ,make Located in the preset range It takes a smaller value when the value is within the preset range, and increases rapidly when the value exceeds the preset range. Specifically, it is expressed as follows: (7) Step 3.4, based on steps 3.1 to 3.3, construct a multiplexed nonlocal acoustic metasurface topology optimization model considering dual-wavelength coordinated modulation: (8) in, Represents the chain material field function, used to describe the nonlocal acoustic metasurface topology with predetermined spatial correlation; The unknown coefficients represent the field function of the chain material, and are also the design variables for optimization; This represents the objective function of the optimization model; This represents the energy balance penalty function between the reflecting and transmitting sides in the initial state; This represents the energy balance penalty function between the reflection and transmission sides under stretched conditions. Representation of tensile strain A related step coefficient, when hour, ,when hour, ; Represents the sound pressure field; Indicates the density of the material; Represents angular frequency, and frequency f The relationship is ; Indicates the speed of sound; The equations are nonlinear equilibrium equations. This is the volume constraint value. Design domain for acoustic metasurfaces.

[0019] When tensile deformation is not considered, i.e. At that time, with the initial state objective function To optimize the objective; when considering tensile deformation, i.e. At that time, the joint objective function of the initial state and the stretched state. To optimize the objective, the adaptive weighting factor in the objective function... and It is used to balance the competition between reflected and transmitted wave targets.

[0020] Step 3.5: Apply constraints to the topology optimization model constructed in Step 3.4, including the pressure acoustic control equations. Optional flexible substrate nonlinear equilibrium equation Material field constraints Solid material volume fraction constraint And the periodic continuity constraints of the left and right boundaries of the supercell.

[0021] The fourth step involves using a chain-like material field series expansion that maintains periodic continuity and an adaptive sequence Kriging gradient-free optimization algorithm to solve the topology optimization model of a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation, as detailed below: Step 4.1: To address the supercell periodicity continuity constraint, arrange material field observation points within the design domain, and align the observation points within the left and right adjacent periodic domains. Calculate the observation points for any two points within the design domain. and Relevant distance The distance between it and the adjacent periodic domain pairs needs to be included in the relevant distance calculation, defined as: (9) in, Represents any two observation points and The relevant distance; This represents the set of distances between periodic pairs of points in the adjacent design domain. For any observation point in the design domain; For the design domain The corresponding sites are the same; In the left adjacent domain The corresponding site; In the right adjacent domain The corresponding site.

[0022] Step 4.2, using the exponential correlation function Constructing a chain-like material field correlation matrix ,in The correlation length is used to control structural complexity and minimum length scale. Subsequently, the correlation matrix is ​​expanded using a Karhunen-Loève series, truncating the expansion terms corresponding to small eigenvalues ​​to reduce the number of design variables. The field function characterizing a periodically continuous chain material is defined in the following form: (10) in, These are the parameters that control the chain-like material field function, and also the design variables for the optimization problem; and These are the correlation matrices. Arranged in descending order m eigenvalues ​​of order and the first m eigenvectors of order 1; Its function is similar to that of the basis functions in the Fourier transform; M represents the order of the chain material field retained after truncation; This represents a diagonal matrix composed of eigenvalues ​​in descending order; This represents a matrix composed of eigenvectors; This represents the correlation matrix. Finally, the chain-like material field function, maintaining periodic continuity, is obtained. .

[0023] Step 4.3, using a chain-like material field function with a preset spatial correlation. Characterizing the topological distribution of the supercellular solid scatterer in the air medium, where This is the material field expansion coefficient. For considering only the initial state... At that time, calculate the initial state nonlocal two-wave propagation acoustic model. Corresponding solid scattering region Corresponding air zone. When considering dynamic control scenarios, i.e. At that time, calculate the nonlocal two-wave propagation acoustic model of the stretched state. Corresponding solid scattering region Corresponding to the air region; when calculating the large deformation analysis model of the flexible substrate in step 2.6, Corresponding solid scattering region Corresponding to the flexible substrate region.

[0024] Step 4.4: Based on the chain material field function obtained in Step 4.2, initial samples are generated using Latin hypercube sampling. Finite element analysis is called for each sample to calculate the reflection and transmission local acoustic power intensity vector direction, energy balance penalty, and total objective function value in the initial state and the optional stretched state.

[0025] Step 4.5: Construct design variables based on sample data With the overall objective function The Kriging surrogate model searches for candidate optimal solutions within the current sub-design domain. Then, it narrows down and moves to the next sub-design domain centered on the current optimal solution, repeating sampling, finite element evaluation, surrogate modeling, and optimization search until a preset convergence condition is reached. The preset convergence condition refers to two finite element evaluations where the change in the objective function is less than a preset value, or the maximum number of sub-optimization iterations is reached.

[0026] The fifth step involves conducting dual-wave performance verification and outputting final design parameters, and forming a closed-loop correction based on the verification results, as detailed below: Step 5.1: Perform full-wave simulation on multiple supercell arrays of the dual-wave coordinated control multiplexed nonlocal acoustic metasurface structure obtained in step 4. Apply plane wave and Gaussian wave incident, calculate the sound pressure field and local sound power intensity vector direction on the reflection side and transmission side, and calculate the deviation of the reflected sound wave / transmitted sound wave from the target direction. Determine whether the reflected sound wave and transmitted sound wave are deflected to the preset target direction.

[0027] Step 5.2, when the first step considers the dynamic control scenario, i.e. Step 5.1 is repeated for structures under different tensile strains to obtain the relationship between the reflection deflection and transmission deflection directions and the tensile strain. The deviations of the reflected / transmitted sound waves from the target direction are calculated. It is then determined whether the reflected and transmitted sound waves in the initial and stretched states are deflected to the preset target directions.

[0028] Step 5.3: For validated dual-wave synergistic control multiplexed nonlocal acoustic metasurface structures, output the supercell topology, material parameters, operating frequency, initial / stretched target deflection angle, and stretching control parameters. For unvalidated dual-wave synergistic control multiplexed nonlocal acoustic metasurface structures, feed back the deviation of the reflected / transmitted acoustic waves from the target direction to step 3 to adjust the weights or constraints, and re-execute steps 4 and 5.

[0029] A multi-channel nonlocal acoustic metasurface design system considering dual-wavelength coordinated modulation includes: Parameter and target setting module: used to perform the first step, receive and uniformly store the operating frequency, incident conditions, material parameters, manufacturing constraints and static or dynamic dual-wave target requirements; Nonlocal dual-wave propagation and deformation modeling module: connected to the parameter and target setting module, used to perform the second step, construct the initial state nonlocal dual-wave propagation acoustic model, solve the geometric configuration of the flexible substrate after stretching in dynamic control mode, and construct the stretching state nonlocal dual-wave propagation acoustic model. Dual-wave collaborative regulation optimization model construction module: connected to the nonlocal dual-wave propagation and deformation modeling module, used to perform the third step, constructing the objective function based on the deviation of the local acoustic power intensity vector direction in the reflection target domain and the transmission target domain, and applying energy balance, connectivity and periodic constraints; Chain-type material field series expansion and gradient-free solution module: connected to the dual-wave collaborative control optimization model construction module, used to execute the fourth step, outputting a dual-wave collaborative control multiplexed nonlocal acoustic metasurface structure through chain-type material field sequence expansion, Latin hypercube sampling, finite element evaluation, Kriging proxy modeling and sub-design domain adaptive adjustment; Performance verification and design output module: Connected to the chain material field sequence expansion and gradient-free solution module, it is used to perform the fifth step, perform full-wave simulation of the dual-wave performance in static and optional stretched states, output the verified structure and control parameters, and feed back the results that do not meet the requirements to the dual-wave collaborative regulation and optimization model construction module.

[0030] The beneficial effects of this invention are as follows: (1) This invention establishes a novel topology optimization framework for designing multiplexed nonlocal acoustic metasurfaces capable of coordinating the transmission and reflection wave fields, aiming to achieve precise acoustic wave manipulation that integrates dynamic tuning and multifunctional characteristics. This invention takes the entire supercell as the optimization design object and utilizes the nonlocal coupling and lateral energy exchange between adjacent unit cells to overcome the limitations of traditional independent unit cell phase splicing.

[0031] (2) At the same time, the direction of the local sound power intensity vector in the reflection target domain and the transmission target domain is used as the collaborative optimization index. Energy balance penalty and adaptive weight are introduced to achieve unified control of the direction of the transmission / reflection sound field and the energy distribution.

[0032] (3) In addition, a flexible substrate stretching control method is introduced, and the initial state and the stretching state target are incorporated into the same optimization model. The optimized multiplexed nonlocal acoustic metasurface can be continuously adjusted by stretching the flexible substrate. Combined with the chain material field sequence expansion and the adaptive sequence Kriging gradient-free optimization algorithm, the solution efficiency of complex dual-wave coupling problems is improved. Attached Figure Description

[0033] Figure 1 The flowchart illustrates the implementation of the design of a multiplexed nonlocal acoustic metasurface that considers dual-wavelength coordinated modulation, as provided in this invention.

[0034] Figure 2 This is a schematic diagram illustrating the working mechanism of the present invention for achieving coordinated control of transmitted / reflected waves based on the stretching of a flexible substrate.

[0035] Figure 3 This is a schematic diagram of the chain material field correlation calculation provided by the present invention.

[0036] Figure 4 The schematic diagram of the multiplexed nonlocal acoustic metasurface structure considering dual-wavelength coordinated control provided by the present invention includes the acoustic metasurface structure in its initial state and the acoustic metasurface structure after stretching.

[0037] Figure 5 The initial sound wave transmission cloud diagram; Figure 6 This is a cloud map showing the transmission of sound waves after stretching.

[0038] Figure 7 The image shows the far-field sound pressure intensity radiation pattern in the initial state. Figure 8 This is the far-field sound pressure intensity radiation diagram after stretching. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. In a specific embodiment, a design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated control includes five steps, which correspond to the technical solutions described above. In the embodiments, specific parameters are assigned according to static or dynamic control requirements.

[0040] Implementation Case: Design of Multiplexed Nonlocal Acoustic Metasurface with Dual-Wave Coordinated Control Considering Dynamic Regulation This implementation case illustrates the scenario where, when considering the stretching of a flexible substrate, both the initial and post-stretched states of the reflected and transmitted wave targets are simultaneously incorporated into the optimization model. The specific steps include: The first step is to collect the acoustic functional target parameters, material parameters, and geometric constraint parameters of the metasurface, as follows: Step 1.1, set the target acoustic parameters. The operating frequency is... f =3000 Hz, background medium is air, air density is The speed of sound is Angle of incidence Incident sound pressure amplitude Metasurface thickness h =0.12m, periodic boundary conditions are applied to both sides of the supercell. A dual-wave coordinated control target is set as needed, with the initial target reflection angle being... The target's transmission angle is Further define the target reflection angle after stretching. Target transmission angle .

[0041] Step 1.2, assuming the solid scatterer material is ABS, its density is... The speed of sound is Due to the significant difference in acoustic impedance between ABS and air, ABS is approximated as a rigid scattering material in acoustic analysis. Ecoflex 0030 is selected as the flexible substrate material, and its large deformation behavior is described using the Neo-Hookean hyperelastic model. Material parameters are taken as... , The density is .

[0042] Step 1.3 sets manufacturing constraints and evaluation requirements, including a minimum structural feature size of 0.1 mm, an upper limit of solid material volume fraction of 0.5, and an energy balance range for reflected and transmitted waves. The plane wave or Gaussian wave used for verification is always incident normally, i.e. .

[0043] The second step involves constructing a nonlocal dual-wave propagation and deformation analysis model based on the acoustic functional objectives, and evaluating the energy flow direction based on the acoustic power intensity vector, as detailed below: Step 2.1, based on the operating frequency and initial target transmission angle set in Step 1.1 Supercell periodicity of initial state Based on the target transmission angle of the stretched structure Determine the supercell period after stretching The target tensile strain is calculated from the supercell periodic dimensions of the initial and stretched states. It is approximately 14.3%.

[0044] Step 2.2, using metasurface supercell periodicity An initial nonlocal dual-wave propagation acoustic model was constructed. A nonlocal supercell finite element model was established in the COMSOL pressure acoustics module. Air domains were set on the upper and lower sides of the supercell, and plane wave radiation boundary conditions were applied to the boundaries of these air domains. Periodic boundary conditions were applied to the left and right boundaries of the supercell. To avoid near-field scattering, a rectangular domain was selected as the reflection target domain 280 mm above the supercell. Similarly, a rectangular region is selected at -280mm below the supercell as the transmission target region. The acoustic pressure fields of the incident wave, reflected wave, and transmitted wave in the initial state are calculated according to formula (1). , and .

[0045] Step 2.3: Based on the sound pressure field calculated in Step 2.2, further calculate the velocity vector. Harmony power intensity vector Using the COMSOL pressure acoustic module, the sound power intensity vector is calculated according to formula (2). The local acoustic power intensity vector direction of each node in the initial reflection target domain and transmission target domain is obtained by formula (3).

[0046] Step 2.4: Establish a large deformation analysis model for the flexible substrate, setting the tensile strain to 14.3%, and solve the nonlinear equilibrium equations under periodic boundary conditions. The spatial position of the stretched solid scatterer is obtained.

[0047] Step 2.5, using the supercell period of the stretched metasurface. A nonlocal dual-wave propagation acoustic model of the stretched state is constructed. A nonlocal supercell finite element model of the stretched state is established in the COMSOL pressure acoustics module. Similar to step 2.2, air domains are set on the upper and lower sides of the supercell, and plane wave radiation boundary conditions are set at the boundaries of the air domains on both sides. Periodic boundary conditions are applied at the left and right boundaries of the supercell. A rectangular domain is selected at the same location and designated as the reflection target domain. and transmission target domain The acoustic pressure fields of the incident wave, reflected wave, and transmitted wave under the stretched state are calculated according to formula (1). , and .

[0048] Step 2.6: Based on the sound pressure field calculated in Step 2.5, further calculate the velocity vector. Harmony power intensity vector Using the COMSOL pressure acoustics module, the sound power intensity vector after stretching is calculated. The local acoustic power intensity vector direction of each node in the reflection target domain and the transmission target domain of the stretched structure is obtained by formula (3).

[0049] The third step involves constructing a topology optimization model for a multiplexed nonlocal acoustic metasurface that considers dual-wavelength co-modulation. Here, "nonlocal" means that there are interactions between adjacent and next-nearest unit cells, and the acoustic response of the metasurface is determined by the overall metacell mode, rather than by the simple superposition of scattering from individual unit cells. The constructed topology optimization model for a multiplexed nonlocal acoustic metasurface considering dual-wavelength co-modulation uses the deviation of the local acoustic power intensity vector direction within the target domain from the target direction as the objective function. Specifically: Step 3.1: First, calculate the direction of the nodal acoustic power intensity vector within the initial reflection target domain. With the target reflection angle The deviation, and the direction of the acoustic power intensity vector of the nodes within the transmission target domain. With the target transmission angle The deviation is solved by determining the cooperative deviation function of the two waves. . It is 15. It is 10.

[0050] Step 3.2, then calculate the direction of the nodal acoustic power intensity vector within the target domain after stretching. With the target reflection angle The deviation, and the direction of the acoustic power intensity vector of the nodes within the transmission target domain. With the target transmission angle The deviation is solved by determining the cooperative deviation function of the two waves. .

[0051] Step 3.3, define the transmitted / reflected sound pressure amplitude ratio Construct an energy balance penalty function ,make Located in the preset range It takes a smaller value when the value is within the specified range, and increases rapidly when the value exceeds this range. It can be represented as: (11) Step 3.4, based on steps 3.1 to 3.3, construct a multiplexed nonlocal acoustic metasurface topology optimization model considering dual-wavelength coordinated modulation: (12) in, Represents the chain material field function, used to describe the nonlocal acoustic metasurface topology with predetermined spatial correlation; The unknown coefficients represent the field function of the chain material, and are also the design variables for optimization; This represents the objective function of the optimization model; This represents the energy balance penalty function between the reflecting and transmitting sides in the initial state; This represents the energy balance penalty function between the reflecting and transmitting sides under stretched conditions. It includes the pressure acoustic governing equations. Optional flexible substrate nonlinear equilibrium equation Chain material field confinement Solid material volume fraction constraint And the periodic continuity constraints of the left and right boundaries of the supercell.

[0052] The fourth step involves using a chain-like material field series expansion that maintains periodic continuity and an adaptive sequence Kriging gradient-free optimization algorithm to solve the topology optimization model of a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation, as detailed below: Step 4.1: Discretize the design domain into 280×240 rectangular units. Consider the correlation between the design domain and the left and right adjacent domains, and solve the correlation distance between any two points according to formula (9).

[0053] Step 4.2, take the relevant length of the material field. The Karhunen-Loève series was expanded according to formula (10) and truncated to reduce the dimensionality of the design variables. After truncation, 72 independent MFSE coefficients were selected as design variables.

[0054] Step 4.3: Initial samples are generated using Latin hypercube sampling, and finite element analysis is performed on each candidate topology. First, the direction of the local acoustic power intensity vector for reflection and transmission in the initial state, as well as the energy balance penalty, are calculated. Then, a large deformation tensile finite element analysis of the flexible substrate is conducted to obtain the spatial distribution of the scattering structure after stretching. Further, the direction of the local acoustic power intensity vector for reflection and transmission on the metasurface after stretching, as well as the energy balance penalty, are calculated. Finally, the overall objective function value is obtained.

[0055] Step 4.4: Based on the sample results, a Kriging surrogate model is established, and gradient-free optimization is performed using a strategy of gradually moving and shrinking the sub-design domain. The preset convergence condition is that after two finite element evaluations, the change in the objective function is less than 0.005, or the maximum number of sub-optimization iterations (15) is reached. In this embodiment, the optimization process converges after 15 sub-optimization iterations, completing a total of 2035 finite element calculations, including 1620 sampling points and 415 surrogate model optimization iterations.

[0056] The fifth step involves conducting dual-wave performance verification and outputting final design parameters, and forming a closed-loop correction based on the verification results, as detailed below: Step 5.1, with the initial state having Reflection angle and Transmission angle and stretched state have Reflection angle and The design of a multiplexed nonlocal acoustic metasurface with dual-wavelength coordinated control, optimized for the transmission angle as the target, considering dynamic regulation. Figure 4 As shown. Figure 4 The image shows the acoustic metasurface structure in its initial state and after stretching.

[0057] Step 5.2 involves performing full-wave simulations of the obtained dual-wave collaboratively modulated multiplexed nonlocal acoustic metasurface structure across multiple supercell arrays. Gaussian waves are applied as incident radiation, and the sound pressure fields on the reflection and transmission sides are calculated. The sound wave propagation contour map is shown below. Figure 5 , Figure 6 As shown, Figure 5 , Figure 6 The present invention provides an acoustic wave propagation contour map of a multiplexed nonlocal acoustic metasurface subjected to a 3000Hz Gaussian wave under dynamic control with dual-wave synergistic modulation. The results show that, in the initial state, the incident wave is mainly deflected on both the reflection and transmission sides. When the flexible substrate is stretched to approximately 14.3%, the relative positions of the scatterers change, and the nonlocal coupling relationship within the structure changes accordingly, causing both reflected and transmitted waves to deflect. direction.

[0058] Step 5.3: Calculate the far-field sound pressure intensity radiation of the multiplexed nonlocal acoustic metasurface considering dynamic control with dual-wave coordinated modulation. Results: The far-field sound pressure intensity radiation diagram of the multiplexed nonlocal acoustic metasurface considering dynamic control with dual-wave coordinated modulation is shown below. Figure 7 , Figure 8 As shown, Figure 7 The image shows the far-field sound pressure intensity radiation pattern in the initial state. Figure 8 This is the far-field sound pressure intensity radiation pattern after stretching. The results show that the directivity peak is consistent with the target direction, and the sound wave can be well deflected to the preset target angle direction.

[0059] Step 5.4: Output supercell topology, material parameters, operating frequency, target deflection angle in the initial state / post-stretching state, and stretching control parameters.

[0060] The key to this embodiment lies not in simply changing the supercell spacing, but in simultaneously introducing a dual-wave cooperative objective of the initial state and the stretched state during the topology optimization stage. This allows the chain-like material field topology, nonlocal coupling relationships, and flexible large deformation response to participate in the design. Furthermore, this invention does not limit the reflected wave and transmitted wave to having the same deflection direction; it is sufficient to include the corresponding target direction in the dual-wave cooperative deviation function of step three. The above-described embodiments are merely preferred implementations of this invention and are not intended to limit the invention. For those skilled in the art, various modifications and improvements can be made without departing from the principles of this invention, and all such modifications and improvements fall within the scope of protection of this invention.

Claims

1. A design method for multiplexed nonlocal acoustic metasurfaces considering dual-wavelength coordinated modulation, characterized in that, The multiplexed nonlocal acoustic metasurface design method includes the following steps: The first step is to collect the acoustic functional target parameters, material parameters, and geometric constraint parameters of the metasurface; Determine whether dynamic adjustment is needed; if dynamic adjustment is needed, set the target reflection angle and target transmission angle after stretching. The second step is to construct a nonlocal dual-wave propagation and deformation analysis model based on the acoustic functional objectives, and to evaluate the energy flow direction based on the acoustic power intensity vector. Based on metasurface supercell period An initial-state nonlocal dual-wave propagation acoustic model is constructed, and the velocity vector and acoustic power intensity vector are calculated to obtain the direction of the acoustic power intensity vector at each node in the reflection and transmission target domains. When dynamic control is required, the hypercell period of the stretched metasurface is determined, thereby determining the target tensile strain. Based on the large deformation analysis model of the flexible substrate, a stretched nonlocal dual-wave propagation acoustic model is constructed, and nonlocal dual-wave propagation acoustic models are constructed for both the initial and stretched states. Under static design, the initial-state nonlocal dual-wave propagation model is directly used as the physical basis for the next optimization model. The third step is to construct a multi-channel multiplexed nonlocal acoustic metasurface topology optimization model that considers dual-wave coordinated control, and use the deviation between the local acoustic power intensity vector direction and the target direction in the target domain as the objective function. The multiplexed nonlocal acoustic metasurface topology optimization model considering dual-wave cooperative modulation is as follows: (8) in, Represents the field function of a chain-like material; The unknown coefficients represent the field function of the chain material, and are also the design variables for optimization; This represents the objective function of the optimization model; The initial state is the two-wave cooperative deviation function; This represents the energy balance penalty function between the reflecting and transmitting sides in the initial state; The two-wave cooperative deviation function for the stretched state: This represents the energy balance penalty function between the reflection and transmission sides under stretched conditions. Representation of tensile strain A related step coefficient; Represents the sound pressure field; Indicates the density of the material; Indicates angular frequency; Indicates the speed of sound; The equations are nonlinear equilibrium equations. and These are the sound pressure fields of the reflected wave and the transmitted wave, respectively; The ratio of transmitted to reflected sound pressure amplitude; This is the volume constraint value; Design domain for acoustic metasurfaces; The fourth step involves using the chain-like material field series expansion that maintains periodic continuity and the adaptive sequence Kriging gradient-free optimization algorithm to solve the topology optimization model of the multiplexed nonlocal acoustic metasurface that considers dual-wave coordinated control. The fifth step is to conduct dual-wave performance verification and output the final design parameters, and form a closed-loop correction based on the verification results.

2. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 1, characterized in that, The first step is as follows: Step 1.1, Set the target acoustic parameters: including operating frequency f Background medium density Background medium sound velocity Angle of incidence Incident sound pressure amplitude Metasurface thickness h , supercellular periodic boundary conditions for metasurfaces; The dual-wave coordinated control target can be set as needed, including the target reflection angle in the initial state. and target transmission angle ; Determine whether dynamic adjustment is needed. If dynamic adjustment is needed, further set the target reflection angle after stretching. and target transmission angle ; Step 1.2, Set material parameters: Set the acoustic and mechanical parameters of the metasurface candidate solid scatterer material, air medium, and optional flexible substrate material; wherein, the parameters of the flexible substrate material include at least the hyperelastic constitutive parameters, density, and allowable deformation range, and the acoustic impedance of the candidate solid scatterer material is approximately acoustically rigid when it is significantly greater than that of the background medium; Step 1.3, Set geometric constraint parameters: Set manufacturing constraints and evaluation requirements, including minimum structural feature size, air channel connectivity, supercell periodic continuity, upper limit of solid material volume fraction, energy balance range of reflected and transmitted waves, and plane wave or Gaussian wave incident conditions for verification.

3. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 2, characterized in that, The second step is as follows: Step 2.1, based on the operating frequency and initial target transmission angle set in Step 1.

1. Determining the supercell period of a metasurface ; Let the background medium wavelength be... sound wave number Under normal incidence conditions, the metasurface supercell periodicity Determined based on the initial target transmission angle ; Step 2.2, using metasurface supercell periodicity An initial-state nonlocal dual-wave propagation acoustic model is constructed, utilizing nonlocal coupling and lateral energy exchange between adjacent unit cells; Set the reflective target domain above the supercell A transmission target domain is set below the supercell. A pressure acoustic model with periodic boundaries is established as the initial state nonlocal two-wave propagation acoustic model; the sound pressure fields of the incident wave, reflected wave, and transmitted wave are denoted as follows: , and , represented as: (1) in, The incident wave acoustic pressure field; The sound pressure field of the reflected wave; This represents the acoustic pressure field of the transmitted wave. , and These represent the amplitudes of the incident wave, reflected wave, and transmitted wave, respectively. x Let be the lateral coordinate of any point in the sound pressure field; y Let be the longitudinal coordinate of any point in the sound pressure field; j This refers to the imaginary part in numerical computation. k It is the wavenumber in the background medium at the operating frequency; , and These are the angle of incidence, the angle of reflection, and the angle of transmission, respectively. Step 2.3: Calculate the velocity vector based on the incident wave acoustic pressure field in formula (1). Harmony power intensity vector ; velocity vector satisfies The sound power intensity vector is defined as follows: (2) in, To calculate the real part of "[]"; For the incident wave acoustic pressure field, select , , ; This is the velocity vector; superscript " "Represents complex conjugation; The sound power intensity vector along x Component of direction; The sound power intensity vector along y Component of direction; It is a defined metasurface structure x The normal vector of the direction; It is a defined metasurface structure y The normal vector of the direction; Step 2.4: Calculate the sound power intensity vector using formula (2). The sound power intensity vector direction of each node in the reflection target domain and the transmission target domain is obtained by formula (3), and the actual deflection direction of the sound wave is characterized by the local sound power intensity vector direction. (3) in, and These represent the directions of the acoustic power intensity vectors at each node within the reflection and transmission target domains, respectively. i Represents the first target within the reflection target domain and the transmission target domain. i One node; and For the first in the reflection target domain i The sound power intensity vector of each node along x and y Component of direction; and For the first in the transmission target domain i The sound power intensity vector of each node along x and y Component of direction; Step 2.5, when the dynamic adjustment function is required as set in step 1.1, i.e. Based on the target transmission angle of the stretched metasurface structure Determine the supercell period of the metasurface after stretching Then the target tensile strain Should meet: (4) Step 2.6: Based on the initial nonlocal dual-wave propagation acoustic model constructed in Step 2.2, establish a large deformation analysis model for the flexible substrate; describe the flexible substrate using reference configuration coordinates D and current configuration coordinates d, and calculate the deformation gradient F and Cauchy-Green tensor. , represented as Cauchy-Green tensor The flexible substrate is described using a hyperelastic strain energy function, and the nonlinear equilibrium equations are solved under given boundary displacement and periodic boundary conditions. The spatial position of the stretched solid scatterer is obtained; where R represents the residual stress; u is the displacement vector in the finite element analysis considering large deformation; Step 2.7: After obtaining the acoustic metasurface structure after large deformation stretching in step 2.6, construct the nonlocal dual-wave propagation acoustic model in the stretched state, and calculate the acoustic power intensity vector of the acoustic metasurface structure in the stretched state and the local acoustic power intensity vector direction of each node in the reflection target domain and the transmission target domain, respectively. Step 2.8: In cases requiring dynamic control, construct nonlocal dual-wave propagation acoustic models for the initial state and the stretched state respectively; in static design, omit steps 2.5-2.7, and directly use the initial state nonlocal dual-wave propagation model as the physical basis for the next optimization model.

4. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 3, characterized in that, In the third step, nonlocality refers to the interaction between adjacent and next-nearest unit cells, and the acoustic response of the metasurface is determined by the overall supercell mode; the specific steps are as follows: Step 3.1: When considering only the initial state and not the dynamic control situation, calculate the direction of the acoustic power intensity vector of each node in the reflection target domain. With the target reflection angle The deviation, and the direction of the acoustic power intensity vector of the nodes within the transmission target domain. With the target transmission angle The deviation is defined by the initial state dual-wave cooperative deviation function. for: (5) in, The first adaptive weighting factor, This is the second adaptive weighting factor; n This represents the number of nodes within the reflection target domain and the transmission target domain; Step 3.2: When considering the dynamic control scenario, i.e., including the stretched state model, calculate the direction deviation of the acoustic power intensity vector between the reflected and transmitted target domains in the stretched state as in Step 3.1, and define the dual-wave cooperative deviation function in the stretched state. : (6) Step 3.3, Define the transmission / reflection sound pressure amplitude ratio And construct an energy balance penalty function. ,make Located in the preset range When the value is small, it is increased when it exceeds the preset range. Specifically, it is expressed as follows: (7) Step 3.4: Based on steps 3.1 to 3.3, construct a multi-channel multiplexed nonlocal acoustic metasurface topology optimization model that considers dual-wave cooperative control, as shown in formula (8); When tensile deformation is not considered, i.e. At that time, with the initial state objective function To optimize the objective, and at this time When considering tensile deformation, i.e. At that time, the joint objective function of the initial state and the stretched state. To optimize the objective, and at this time The adaptive weighting factor in the objective function and Used to balance the competition between reflected and transmitted wave targets; Step 3.5: Apply constraints to the topology optimization model constructed in step 3.

4.

5. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 4, characterized in that, In step 3.5, the constraints include the pressure acoustic control equation. Optional flexible substrate nonlinear equilibrium equation Material field constraints Solid material volume fraction constraint And the periodic continuity constraints of the left and right boundaries of the supercell.

6. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 5, characterized in that, The fourth step specifically involves: Step 4.1: For the supercell periodic continuity constraint, arrange material field observation points within the design domain, and align the material field observation points within the left and right adjacent periodic domains; calculate the observation points for any two points within the design domain. and Relevant distance ; Step 4.2, using the exponential correlation function Constructing a chain-like material field correlation matrix ,in The correlation length is given; the correlation matrix is ​​expanded using the Karhunen-Loève series, defined as follows: (10) in, These are the parameters that control the chain-like material field function, and also the design variables for the optimization problem; and These are the correlation matrices. Arranged in descending order m eigenvalues ​​of order and the first m eigenvectors of order 1; Its function is similar to that of the basis functions in the Fourier transform; M represents the order of the chain material field retained after truncation; This represents a diagonal matrix composed of eigenvalues ​​in descending order; This represents a matrix composed of eigenvectors; Represents the correlation matrix; Finally, a chain-like material field function that maintains periodic continuity is obtained. ; Step 4.3, using a chain-like material field function with a preset spatial correlation. Characterizing the topological distribution of the supercellular solid scatterer in the air medium, where This is the material field expansion coefficient; Step 4.4: Based on the chain material field function, generate initial samples, call finite element analysis for each sample, and calculate the reflection and transmission local sound power intensity vector direction, energy balance penalty and total objective function value in the initial state and optional stretched state respectively. Step 4.5: Construct design variables based on sample data With the overall objective function The Kriging surrogate model searches for candidate optimal solutions within the current sub-design domain; it then narrows and moves to the next sub-design domain centered on the current optimal solution, repeating sampling, finite element evaluation, surrogate modeling, and optimization search until the preset convergence condition is met.

7. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 6, characterized in that, In the fourth step: In step 4.1: relevant distance The calculation formula is: (9) in, Represents any two observation points and The relevant distance; This represents the set of distances between periodic pairs of points in the adjacent design domain. For any observation point in the design domain; For the design domain The corresponding sites are the same; In the left adjacent domain The corresponding site; In the right adjacent domain The corresponding site; In step 4.3: for considering only the initial state, i.e. At that time, calculate the initial state nonlocal two-wave propagation acoustic model. Corresponding solid scattering region Corresponding air zone; when considering dynamic control scenarios, i.e. At that time, calculate the nonlocal two-wave propagation acoustic model of the stretched state. Corresponding solid scattering region Corresponding to the air region; when calculating the large deformation analysis model of the flexible substrate in step 2.6, Corresponding solid scattering region Corresponding flexible substrate region; In step 4.4: Latin hypercube sampling is used to generate initial samples; In step 4.5: the preset convergence condition refers to the objective function changing less than a preset value after two finite element evaluations, or reaching the maximum number of sub-optimization iterations.

8. The design method for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation according to claim 7, characterized in that, The fifth step is specifically as follows: Step 5.1: Perform full-wave simulation on the dual-wave collaborative control multiplexed nonlocal acoustic metasurface structure obtained in step 4 in multiple supercell arrays. Apply plane wave and Gaussian wave incident, calculate the sound pressure field and local sound power intensity vector direction on the reflection side and transmission side, and calculate the deviation of the reflected sound wave / transmitted sound wave from the target direction. Determine whether the reflected sound wave and transmitted sound wave are deflected to the preset target direction respectively. Step 5.2, when the first step considers the dynamic control scenario, i.e. At that time, step 5.1 is repeated for structures under different tensile strains to obtain the relationship between the reflection deflection and transmission deflection directions and the tensile strain; and the deviation of the reflected sound wave / transmission sound wave from the target direction is calculated; and it is determined whether the reflected sound wave and transmission sound wave in the initial state and the tensile state are deflected to the preset target direction respectively. Step 5.3: For the verified dual-wave synergistic control multiplexed nonlocal acoustic metasurface structure, output the supercell topology, material parameters, operating frequency, initial state / stretched state target deflection angle, and stretching control parameters; for the unverified dual-wave synergistic control multiplexed nonlocal acoustic metasurface structure, feed back the deviation of the reflected / transmitted sound wave from the target direction to the third step to adjust the weights or constraints, and re-execute the fourth and fifth steps.

9. A design system for a multiplexed nonlocal acoustic metasurface considering dual-wavelength coordinated modulation, characterized in that, The design method of multiplexed nonlocal acoustic metasurface as described in any one of claims 1-8 is implemented using a multiplexed nonlocal acoustic metasurface design system, including a parameter and target setting module, a nonlocal dual-wave propagation and deformation modeling module, a dual-wave collaborative control optimization model construction module, a chain-like material field series expansion and gradient-free solution module, and a performance verification and design output module.

10. A multiplexed nonlocal acoustic metasurface design system considering dual-wavelength coordinated modulation according to claim 9, characterized in that, The multiplexed nonlocal acoustic metasurface design system is specifically as follows: Parameter and target setting module: used to perform the first step, receive and uniformly store the operating frequency, incident conditions, material parameters, manufacturing constraints and static or dynamic dual-wave target requirements; Nonlocal dual-wave propagation and deformation modeling module: connected to the parameter and target setting module, used to perform the second step, construct the initial state nonlocal dual-wave propagation acoustic model, solve the geometric configuration of the flexible substrate after stretching in dynamic control mode, and construct the stretching state nonlocal dual-wave propagation acoustic model. Dual-wave collaborative regulation optimization model construction module: connected to the nonlocal dual-wave propagation and deformation modeling module, used to perform the third step, constructing the objective function based on the deviation of the local acoustic power intensity vector direction in the reflection target domain and the transmission target domain, and applying energy balance, connectivity and periodic constraints; Chain-type material field series expansion and gradient-free solution module: connected to the dual-wave collaborative control optimization model construction module, used to execute the fourth step, outputting a dual-wave collaborative control multiplexed nonlocal acoustic metasurface structure through chain-type material field sequence expansion, Latin hypercube sampling, finite element evaluation, Kriging proxy modeling and sub-design domain adaptive adjustment; Performance verification and design output module: Connected to the chain material field sequence expansion and gradient-free solution module, it is used to perform the fifth step, perform full-wave simulation of the dual-wave performance in static and optional stretched states, output the verified structure and control parameters, and feed back the results that do not meet the requirements to the dual-wave collaborative regulation and optimization model construction module.

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