Acoustic superstructure forward calculation and performance prediction method, system, device and medium

Abstract

This invention discloses a method, system, device, and medium for forward calculation and performance prediction of acoustic superstructures, relating to the field of vibration reduction and noise reduction technology. The method includes: constructing a finite element model of periodic elements to obtain the stiffness and mass matrices; introducing periodic boundary conditions to transform the wave control equations into a nonlinear eigenvalue problem of complex wavenumbers; employing a contour integral algorithm to solve all characteristic wavenumbers and corresponding generalized eigenvectors in one step within a pre-set closed contour in the complex wavenumber plane; automatically matching and tracking characteristic wavenumbers of the same physical wave branch based on eigenvector similarity in the target frequency domain, and plotting a continuous dispersion curve; identifying vibration bandgap based on the dispersion curve, recovering the generalized eigenvectors to physical space for wave mode analysis, and completing performance prediction. This invention overcomes the computational efficiency bottleneck of traditional methods in complex element and mid-to-high frequency analysis, reveals the wave coupling mechanism of bandgap generation, and provides core support for topology optimization of acoustic superstructures.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction and noise reduction technology, and more specifically to methods, systems, devices and media for forward calculation and performance prediction of acoustic superstructures. Background Technology

[0002] Acoustic metastructures, through the artificial design of periodic units, can generate elastic wave band gaps not found in traditional materials. This allows for the efficient suppression of vibration and noise propagation within a specific frequency range, making them a revolutionary approach for low-frequency broadband vibration and noise reduction in fields such as aerospace vehicles, high-speed rail vehicles, and precision instruments. Their performance hinges on their wave characteristics, specifically dispersion relations and wave modes. The core physical mechanism involves the scattering and interference of elastic waves by periodic units, creating a frequency bandgap. Predictions of their bandgap characteristics and vibratory acoustic response primarily rely on numerical methods.

[0003] In numerical methods, the finite element method (FEM) has become the mainstream tool for studying superstructures due to its high adaptability to complex geometries and materials. The frequency domain finite element method combined with Bloch's theorem can directly calculate the dispersion curves of periodic elements. To analyze the dynamic response of finite-size superstructures under mechanical or acoustic excitation, it is necessary to build a finite-size model containing a large number of periodic elements for harmonic response analysis or transient analysis. While this method is highly versatile, its computational cost is extremely high. A large model containing tens of thousands of elements can have millions of degrees of freedom, and a single simulation often takes several days or even longer, completely failing to meet the frequent iterative computational requirements of optimization design.

[0004] To improve computational efficiency, the Wave-based Finite Element Method (WFEM) was developed based on the Finite Element Method (FEM). WFEM offers a significant efficiency improvement over the full-size Finite Element Method. However, the periodic elements of acoustic superstructures often have complex geometries, such as honeycomb sandwich structures, stiffened plates, multi-layered composite structures, or use novel materials like shape memory polymers. The meshes required for accurate modeling remain very dense, resulting in large element stiffness-mass matrices and excessively long computation times for subsequent wave eigenvalue calculations. This is especially true when the research frequency range extends to the mid-to-high frequencies, requiring the retention of more higher-order modes to accurately characterize the wave behavior within the superstructure elements, further increasing the computational burden and severely limiting its application in engineering optimization design.

[0005] Therefore, how to provide a method for analyzing the wave characteristics of acoustic superstructures that combines computational accuracy and efficiency and can effectively handle complex periodic units and mid-to-high frequency analysis is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for forward calculation and performance prediction of acoustic superstructures based on the wave finite element method, so as to solve the problem of computational efficiency bottleneck faced by the traditional wave finite element method when dealing with complex elements or mid-to-high frequency analysis.

[0007] In a first aspect, embodiments of the present invention provide a method for forward calculation and performance prediction of acoustic superstructures, comprising the following steps:

[0008] S1. Construct a finite element model of the acoustic superstructure with the minimum repeating periodic element, and obtain its dynamic stiffness matrix. ; S2. Introducing periodic boundary conditions, based on the wave finite element theory, the wave control equation of the periodic element is transformed into a nonlinear eigenvalue problem with respect to the complex wave number k. S3. Solve the nonlinear eigenvalue problem using the contour integral algorithm, specifically including: pre-setting a closed contour on the complex wavenumber plane, configuring Gauss-Legend integration points and corresponding weights on the contour, and calculating the moment matrix sequence; constructing block Hankel matrices H0 and H1 from the moment matrix, performing singular value decomposition and low-rank approximation on H0, solving the generalized eigenvalue problem of reduced scale, and obtaining all eigenwavenumbers and their corresponding generalized eigenvectors within the contour Γ in one go; S4. In the target frequency domain, based on the similarity between the generalized eigenvectors obtained at different frequencies, the characteristic wavenumbers belonging to the same physical wave branch are automatically matched and tracked, thereby drawing a continuous dispersion curve. S5. Based on the dispersion curve, identify the vibration band gap, and perform modal analysis by restoring the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0009] Furthermore, in step S1, the acoustic superstructure includes a one-dimensional phononic crystal, a two-dimensional phononic crystal, a three-dimensional phononic crystal, a honeycomb sandwich panel, a stiffening plate, laminated glass, a sandwich structure containing a shape memory polymer core layer, a cross-laminated wood panel, or a curved periodic shell.

[0010] Furthermore, in step S1, the dynamic stiffness matrix Assembled based on the equilibrium equations of simple harmonic motion:

[0011] Among them, the stiffness matrix Describes the resistance of the element to elastic deformation and its mass matrix. This describes the inertial characteristics of the element during elastic deformation, and the nodal displacement vector. The complex amplitude response of the periodic element is given by ω, which is the oscillation frequency.

[0012] Furthermore, the periodic boundary condition in step S2 is a Bloch periodic boundary condition: , , , ,

[0013] in, , These are the nodal displacement vectors of the left and right boundaries of the periodic element, respectively. , These are the nodal displacement vectors at the lower and upper boundaries of the periodic element, respectively. , , , These are the displacement vectors of the lower left, lower right, upper left, and upper right nodes of the periodic element, respectively. , These are the Bloch phase factors in the x and y directions, respectively. , k x k y Let L be the complex wave number in the x and y directions. x L y The geometric dimensions of the periodic unit in the x and y directions; At the same time, the nodal forces on the periodic boundary satisfy the action-reaction relationship; Construct the displacement transformation matrix Force balance transformation matrix By embedding the periodic boundary conditions into the dynamic stiffness matrix, the reduced system matrix is ​​obtained. :

[0014] This transforms the wave control equation of the periodic unit into a nonlinear eigenvalue problem with respect to the complex wave number k:

[0015] in, For the wave propagation angle, It is the generalized eigenvector after periodic transformation compression.

[0016] Furthermore, in step S3, a closed contour Γ is preset on the complex wavenumber plane, and Gauss-Legend integration points k are arranged on the contour Γ. g and corresponding weight w g In this context, the sequence of moments is calculated as follows:

[0017] Among them, S p Let N be the p-th order moment matrix.G w represents the number of integration points on the boundary line. g Let g be the weight of the g-th integration point. Let p be the complex wave value at the g-th integration point, where the superscript p indicates the order of the moment. V is the inverse of the dynamic stiffness matrix, V is the random probe matrix, and M is the preset number of moments. The closed boundary Γ can be rectangular, circular, or elliptical, and its range is adaptively adjusted according to the distribution of eigenvalues.

[0018] Furthermore, in step S4, automatically matching and tracking characteristic wavenumbers belonging to the same physical wave branch specifically includes: For adjacent frequency points ω n and ω n+1 Generalized eigenvectors and The weighted modal confidence factor is calculated using the weighted modal confidence criterion:

[0019] in, The weighted matrix is ​​selected from the mass matrix. H is the conjugate transpose. A matching threshold is set, and generalized feature vectors with weighted mode confidence factors greater than or equal to the threshold are determined to be the same physical wave branch. The feature values ​​of each frequency point are automatically matched through an optimization algorithm to form a continuous dispersion curve.

[0020] Furthermore, in step S5, identifying the vibration bandgap and performing wave mode analysis specifically includes: Scanning the complex wavenumbers corresponding to all frequency points, if within a certain continuous frequency interval Δω, the imaginary part Im(k) of the complex wavenumbers of all propagation modes is... i All of them satisfy:

[0021] Among them, Im(k i ) represents the imaginary part of the i-th characteristic wavenumber, indicating the degree of wave attenuation, and L is the geometric dimension of the periodic unit in the direction of wave propagation; Then, the interval Δω is determined to be a complete bandgap, and the vibration bandgap or acoustic attenuation bandgap of the acoustic superstructure is identified; The generalized eigenvectors obtained by solving By reconstructing the physical space using the periodic transformation matrix, the physical displacement field of the periodic unit at the corresponding wavenumber can be obtained:

[0022] in, Let k be the generalized eigenvector corresponding to the i-th characteristic wavenumber. iLet θ be the i-th characteristic wavenumber, and θ be the wave propagation angle. Let q be the displacement transformation matrix. i This is the physical displacement field vector of the periodic unit at the corresponding wavenumber; For the physical displacement field vector q i Visualization is performed to obtain wave modes. Based on the spatial distribution characteristics of the displacement field, bending waves, shear waves, stretching waves and their coupling modes are distinguished, and the physical mechanism of bandgap generation is explained.

[0023] Secondly, embodiments of the present invention provide an acoustic superstructure forward computation and performance prediction system, the system comprising: The modeling and matrix construction module is used to construct the finite element model of the minimum repeating periodic element of the acoustic superstructure and obtain its dynamic stiffness matrix. ; The eigenvalue problem transformation module is used to introduce periodic boundary conditions and transform the wave control equation of the periodic element into a nonlinear eigenvalue problem with respect to the complex wave number k based on the wave finite element theory. The contour integral solving module is used to solve the nonlinear eigenvalue problem using the contour integral algorithm, based on a pre-defined closed contour in the complex wavenumber plane. Within this process, all characteristic wavenumbers k and their corresponding generalized eigenvectors are obtained in a single solution. ; The dispersion curve tracking module is used to automatically match and track the characteristic wavenumbers belonging to the same physical wave branch in the target frequency domain based on the similarity between the generalized eigenvectors obtained at different frequencies, thereby drawing a continuous dispersion curve. The performance prediction module is used to identify the vibration band gap based on the dispersion curve, and perform modal analysis by recovering the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0024] Thirdly, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the acoustic superstructure forward calculation and performance prediction method of the first aspect embodiment described above.

[0025] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the acoustic superstructure forward calculation and performance prediction method of the first aspect embodiment described above.

[0026] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following: 1. Breaking through the bottleneck of mid-to-high frequency analysis of complex acoustic superstructures. The contour integral method provided by this invention can systematically solve nonlinear eigenvalue problems, obtaining all characteristic solutions within a specific region of the complex wavenumber plane in one go. It avoids the dependence on initial values ​​and root omission problems of traditional iterative methods, and is particularly suitable for analyzing complex acoustic superstructures with dense spectra and strong attenuation characteristics, such as multilayer composite plates and honeycomb sandwich structures. It can still maintain efficient and stable solution capabilities in the mid-to-high frequency range.

[0027] 2. Providing efficient design tools for large-scale periodic structure engineering applications. This invention targets large acoustic superstructures composed of numerous periodic cells, such as aircraft fuselages and high-speed train bodies, providing scalable and programmable efficient design tools. This significantly shortens the cycle of full-scale structural simulation and optimization iteration, and possesses greater engineering applicability and promotional value.

[0028] 3. Achieving positive prediction of sound insulation performance under service conditions. This invention achieves positive prediction of the sound insulation performance of acoustic superstructures under service conditions by solving the contour integral of nonlinear eigenvalues, directly linking the analysis of wave characteristics with macroscopic acoustic indicators, filling the gap of traditional methods that can only analyze dispersion characteristics and cannot directly evaluate acoustic indicators.

[0029] 4. Supporting physically interpretable optimization design of superstructures. The wave mode visualization analysis method provided by this invention can intuitively reveal the wave coupling mechanism generated by the bandgap, providing core support for the physically interpretable optimization design of acoustic superstructure topology, thereby enabling more targeted vibration reduction and noise reduction design. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0031] Figure 1 This is a flowchart of the acoustic superstructure forward calculation and performance prediction method provided in the embodiments of the present invention.

[0032] Figure 2 This is a dispersion curve obtained by tracking using the constant frequency gradient method in an embodiment of the present invention.

[0033] Figure 3 This is a dispersion curve obtained by tracking using the weighted modal confidence criterion of the present invention, as provided in an embodiment of the present invention.

[0034] Figure 4 This is a schematic diagram of the structure of a six-layer cross-laminated wood panel provided in an embodiment of the present invention.

[0035] Figure 5 This is a schematic diagram of the wave mode analysis results of a six-layer cross-laminated wood panel provided in an embodiment of the present invention.

[0036] Figure 6 This is a structural diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0037] 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.

[0038] Example 1: like Figure 1 As shown, this invention discloses a method for forward calculation and performance prediction of acoustic superstructures, including the following steps: S1. Construct a finite element model of the acoustic superstructure with the minimum repeating periodic element, and obtain its dynamic stiffness matrix. ; Within the finite element framework, a discretized model of a representative periodic element of the target periodic structure is established, and its performance at angular frequencies is derived. Stiffness matrix under With the mass matrix The dynamic stiffness matrix in the form of the degrees of freedom of the assembled periodic element. In the periodic elements of the acoustic superstructure, the stiffness matrix... and mass matrix The resistance to elastic deformation and inertial characteristics of the element are described respectively. Among them, the stiffness matrix... This reflects the elastic restoring force distribution of the periodic elements of the superstructure along the wave propagation direction, and the mass matrix. This characterizes the spatial distribution of mass within the element and its contribution to inertial forces. Nodal displacement vector. This represents the complex amplitude response of a periodic element in each degree of freedom, with angular frequency ω being the wave frequency.

[0039] S2. Introducing periodic boundary conditions, based on the wave finite element theory, the wave control equation of the periodic element is transformed into a nonlinear eigenvalue problem with respect to the complex wave number k. This matrix satisfies the harmonic equilibrium equation. ,in This represents the nodal displacement. Let be the nodal force vector. Divided into internal degrees of freedom and boundary degrees of freedom And based on the periodicity of the superstructure and the wave propagation direction angle The phase relationship between the boundary degrees of freedom is established using the Bloch-Floquet theorem. Based on this phase relationship, an explicit periodic transformation matrix is ​​constructed. This matrix represents a set of independent boundary master degrees of freedom. Mapped to the complete set of boundary degrees of freedom: .

[0040] Simultaneously, based on the equilibrium condition of the force on the periodic boundary, the corresponding left transformation matrix is ​​constructed. By embedding the periodic condition into the dynamic stiffness matrix through a transformation matrix, information about the wavenumber is obtained. The nonlinear matrix. At this point, the free wave propagation problem is transformed into solving for a nonlinear matrix that satisfies... eigenvalues and their corresponding eigenvectors The problem.

[0041] S3. Solve the nonlinear eigenvalue problem using the contour integral algorithm, specifically including: pre-setting a closed contour on the complex wavenumber plane, configuring Gauss-Legend integration points and corresponding weights on the contour, and calculating the moment matrix sequence; constructing block Hankel matrices H0 and H1 from the moment matrix, performing singular value decomposition and low-rank approximation on H0, solving the generalized eigenvalue problem of reduced scale, and obtaining all eigenwavenumbers and their corresponding generalized eigenvectors within the contour Γ in one go; For a given frequency and direction In the complex wavenumber plane (the horizontal axis is...) The vertical axis is Define a closed integration path on ). The shape of the region enclosed by this path, which is expected to contain physically meaningful eigenvalues, including both propagating and attenuating waves, can be rectangular, circular, or elliptical.

[0042] This invention employs the spectral projection method, through calculation reverse edge contour To extract feature information using moments, define the first... The order moment is: ,

[0043] in, This represents the preset number of moments. In actual numerical calculations, this contour integral is calculated at discrete contour points using numerical integration methods such as Gaussian integration. The calculated moments are then used... Construct two block Hankel matrices , ,right Singular value decomposition is performed, and a low-rank approximation is applied based on a preset tolerance threshold to eliminate numerical errors and reduce dimensionality. Using the approximated matrix, a generalized eigenvalue problem of reduced size is solved.

[0044] Solution to the generalized eigenvalue problem That is, located within the enclosure line The original nonlinear eigenvalue problem Approximate eigenvalues The eigenvectors of the original problem in modal coordinates can be recovered through linear transformation. .

[0045] S4. In the target frequency domain, based on the similarity between the generalized eigenvectors obtained at different frequencies, the characteristic wavenumbers belonging to the same physical wave branch are automatically matched and tracked, thereby drawing a continuous dispersion curve. Within the frequency range of 500-5000Hz, a series of discrete frequency points are selected with a certain step size or logarithmic interval. }, for each frequency point By performing the above steps, the set of all eigenvalues ​​located within the preset boundaries at that frequency is obtained. } and its eigenvectors { }

[0046] To correctly connect eigenvalues ​​at different frequencies into continuous dispersion branches, a modal confidence criterion is used for automated association.

[0047] For adjacent frequencies and The two eigenvectors below and Calculate its weighted volatility confidence parameter:

[0048] in, The weighted matrix is ​​selected from the mass matrix. H is the conjugate transpose. A matching threshold is set, and generalized feature vectors with weighted mode confidence factors greater than or equal to the threshold are determined to be the same physical wave branch. The feature values ​​of each frequency point are automatically matched through an optimization algorithm to form a continuous dispersion curve.

[0049] S5. Based on the dispersion curve, identify the vibration band gap, and perform modal analysis by restoring the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0050] Analyzing the final constructed dispersion curve, if within a certain frequency range... Inside, there is no Propagation patterns that approximate real numbers, i.e., all patterns If all values ​​are significantly greater than 0, then the interval is considered to be... It is a complete bandgap. Simultaneously, the attenuation constant... Contour plots that vary with frequency can visually demonstrate the distribution of attenuation intensity.

[0051] For any specific point on the dispersion curve ( , ), and its corresponding feature vector Restore the total nodal displacement vector to physical space: Each element corresponds to a complex amplitude of a physical degree of freedom. The amplitude and phase information are mapped back onto the periodic element finite element mesh for visualization. By observing the spatial distribution pattern of the displacement field, different wave types can be clearly distinguished and identified, thereby completing the prediction of vibration reduction and noise reduction performance.

[0052] This invention proposes a method for forward computation and performance prediction of acoustic superstructures based on wave finite element method and contour integral algorithm. By constructing a finite element model of periodic elements and introducing periodic boundary conditions, the wave control equations are transformed into a nonlinear eigenvalue problem with respect to complex wavenumbers. The contour integral algorithm is then used to solve for all characteristic wavenumbers and their eigenvectors within a preset region in one step. Based on this, a weighted modal confidence criterion is used to automatically match eigenvalues ​​at different frequencies and track dispersion curves, thereby identifying vibration band gaps. Through the reconstruction and visualization of eigenvectors in physical space, wave mode analysis and vibration reduction / noise reduction performance prediction are completed. This method overcomes the limitations of traditional iterative methods, such as strong dependence on initial values ​​and susceptibility to root omissions. It is applicable to complex periodic structures with dense spectra and strong attenuation characteristics, providing an efficient and scalable computational tool for the acoustic performance design and optimization of large periodic structures.

[0053] The above-mentioned method for forward calculation and performance prediction of acoustic superstructures of the present invention will be described in detail below: To overcome the computational efficiency bottleneck encountered when processing complex units or performing mid-to-high frequency analysis, the present invention aims to provide a method for forward computation and performance prediction of acoustic superstructures, comprising the following steps: Step S1: Construct the finite element model of the acoustic superstructure's minimum repeating periodic element and obtain its dynamic stiffness matrix. In the specific implementation process, it is first necessary to perform fine modeling of the smallest representative periodic unit of the acoustic superstructure.

[0054] Extract the smallest representative periodic unit of the acoustic superstructure and select the unit type based on its geometric and topological characteristics: for thin-walled periodic structures, layered solid shell units or continuous shell units are preferred; for three-dimensional periodic cells, hexahedral fully integral units are used to avoid hourglass mode.

[0055] The mesh density must satisfy the spatial sampling theorem of the wave finite element method: at the highest analysis frequency set by the user. Below, the shortest elastic wavelength The internal structure should contain no fewer than 6 linear elements or 5 quadratic elements. The element stiffness matrix is ​​derived after discretization. Element mass matrix A mapping table of node coordinates and degrees of freedom numbers. Modulo operations are performed on all node coordinates, based on the period length. , Establish node pairs within the tolerance range. Classify nodes into internal nodes, corner nodes, edge nodes, and face nodes, and generate a global degree-of-freedom index vector.

[0056] Assemble the overall stiffness matrix using a sparse storage format. With the mass matrix If the material properties exhibit frequency-dependent characteristics, the relaxation spectrum parameters must be entered in tabular form and updated via interpolation at each discrete frequency point. This leads to the formation of the dynamic stiffness matrix. .

[0057] The goal is to provide standardized matrix data for subsequent eigenvalue solving.

[0058] Step S2: Introduce periodic boundary conditions. Based on the wave finite element theory, the wave control equation of the periodic element is transformed into a nonlinear eigenvalue problem with respect to the complex wave number k. After obtaining the dynamic stiffness matrix of the periodic element, periodic boundary conditions need to be introduced to establish the wave propagation relationship between elements.

[0059] To complete the algebraic embedding of the Bloch periodic boundary conditions, the wave propagation direction angle needs to be defined. Let the complex wave number be... Components in the periodic plane , Establish phase relationship: , , , , , in, , These are the nodal displacement vectors of the left and right boundaries of the periodic element, respectively. , These are the nodal displacement vectors at the lower and upper boundaries of the periodic element, respectively. , , , These are the displacement vectors of the lower left, lower right, upper left, and upper right nodes of the periodic element, respectively. , These are the Bloch phase factors in the x and y directions, respectively. , k x k y Let L be the complex wave number in the x and y directions. x L y The geometric dimensions of the periodic unit in the x and y directions.

[0060] First, construct the displacement transformation matrix based on the displacement-phase relationship determined by Bloch's theorem. Express all boundary degrees of freedom linearly using independent boundary master degrees of freedom: Simultaneously, based on the force balance condition on the periodic boundary, i.e., the nodal forces of adjacent elements on the common boundary satisfy the action-reaction relationship, a left transformation matrix is ​​constructed. , making In actual construction, Take as the displacement transformation matrix conjugate transpose Applying the transformation matrix directly to the dynamic stiffness matrix yields the final ensemble matrix used for solving nonlinear eigenvalues:

[0061] At this point, the free wave propagation problem is transformed into a problem of solving nonlinear eigenvalues:

[0062] in, For the wave propagation angle, This represents the generalized coordinate vector after periodic transformation compression. After periodic transformation, the main degrees of freedom of the independent boundaries are... The dimension of the problem is much smaller than the total number of degrees of freedom of the original nodes, which significantly reduces the computational scale of subsequent eigenvalue solving. The problem size is much smaller than the full-order model of the traditional wave finite element method, laying the foundation for the rapid solution of the contour integral.

[0063] Step S3: Solve the nonlinear eigenvalue problem using the contour integration algorithm, based on a pre-defined closed contour on the complex wavenumber plane. Within this process, all characteristic wavenumbers k and their corresponding generalized eigenvectors are obtained in a single solution. After transforming the wave control equation into a nonlinear eigenvalue problem, an efficient numerical method is needed to solve it. The contour integral algorithm is introduced to achieve systematic capture of eigenvalues.

[0064] For a given frequency and direction of dissemination In the recovery Define a closed boundary on a plane The initial analysis uses a wide-range rectangular bounding box: real axis range. imaginary axis range ,in, , These represent the minimum and maximum geometric dimensions of the periodic unit in the wave propagation direction and its perpendicular direction, respectively. Based on the characteristic value distribution density obtained from the coarse screening, the boundary line is automatically tightened for subsequent frequency points.

[0065] For example, the real axis boundary can be set at ±30% of the extreme real part of the propagation wavenumber identified at the current frequency, and the imaginary axis boundary can be set at +50% of the maximum imaginary imaginary part of the attenuation wavenumber. The contour shape can also be selected as an ellipse or a polygon composed of multiple line segments to accommodate asymmetric eigenvalue distributions. In the contour... configuration Gauss-Legendal integral points and corresponding weights . The selection of the integral points is related to the perimeter of the contour line and the number of estimated eigenvalues: 16 basic points are used, and 2 integration points are added for every 5 additional estimated eigenvalues. For each integration point, the integral is calculated. Perform LU decomposition and store its inverse matrix. Generate a random probe matrix. Its elements follow a standard normal distribution, and the number of columns is an integer not less than the estimated number of eigenvalues. Calculate the sequence of moments:

[0066] Among them, S p Let N be the p-th order moment matrix. G w represents the number of integration points on the boundary line. g Let g be the weight of the g-th integration point. Let p be the complex wave value at the g-th integration point, where the superscript p indicates the order of the moment. Let V be the inverse of the dynamic stiffness matrix, V be the random probe matrix, and M be the preset number of moments; the order of moments... A value of 4-6 is recommended. (Moment matrix) It encapsulates information about all feature solutions within the enclosure.

[0067] Constructing block Hankel matrices from moment matrices:

[0068] right Perform singular value decomposition Based on singular value sequences Determine the cutoff tolerance :Pick ,in for The smallest integer. (Keep the first...) Construct low-rank near-ones with principal singular values. Then calculate the projection matrix. Solving the standard eigenvalue problem .feature This is the approximate characteristic wave of the original nonlinear eigenvalue problem within the contour lines. The corresponding feature vector recover.

[0069] This method has quadratic convergence accuracy and can capture all propagating and attenuating waves within the enclosure in a single solution, making it particularly suitable for acoustic superstructures with dense modes or strong attenuation.

[0070] Step S4: In the target frequency domain, based on the similarity between the generalized eigenvectors obtained at different frequencies, the characteristic wavenumbers belonging to the same physical wave branch are automatically matched and tracked, thereby drawing a continuous dispersion curve. After obtaining the characteristic solutions at each frequency point, it is also necessary to associate these discrete characteristic values ​​according to the physical wave branch to form a continuous dispersion curve.

[0071] Through feature vectors The norm and phase distribution preliminarily classify wave types: out-of-plane displacement dominant waves are labeled as bending waves, in-plane slip dominant waves as shear waves, in-plane tension dominant waves as stretching waves, and waves exhibiting a standing wave morphology in the thickness direction are labeled as higher-order thickness shear waves. To address the issues of eigenvalue sequence jumps and branching intersections in frequency steps, the weighted modal confidence criterion (WwAC) is used to achieve accurate matching of cross-frequency eigenvectors. For adjacent frequencies... and Calculate the eigenvector pairs Weighted modal confidence factors:

[0072] in, The weighted matrix is ​​selected from the mass matrix. H is the conjugate transpose, setting the matching threshold. ,like If the two eigenvectors correspond to the same physical wave branch, then the two eigenvectors are determined to be of the same physical wave branch. For potential one-to-many matching, the Hungarian algorithm is used for globally optimal allocation to ensure global uniqueness of the matching. For strongly coupled wave turning regions, a group velocity sign consistency criterion is introduced: if the group velocities of adjacent frequency points in the same branch are consistent... If the signs are opposite, the local frequency step size is automatically encrypted and the eigenvalue solution is recalculated. After completing the cross-frequency matching of eigenvalues, the eigenvalue sequence corresponding to each wave branch is obtained. For each frequency point Extracting complex wavenumbers and its eigenvectors .

[0073] Waveform properties are determined by the product of the imaginary part of the wavenumber and the period length: If and If the frequency is positive, it is determined to be a propagating wave; otherwise, it is a decaying or evanescent wave. Only propagating waves are retained for dispersion curve plotting to avoid image clutter. The x-axis represents the complex wave number. real part Using the vertical axis as the ordinate, connecting the eigenvalue points of the same branch at different frequencies sequentially yields the dispersion curve.

[0074] For attenuated waves, the imaginary part can be plotted simultaneously. The attenuation intensity distribution can be displayed as a curve varying with frequency, or as a color gradient. Different wave branches can be distinguished by different colors or line types, and the corresponding wave types, such as bending waves and shear waves, can be labeled in the legend to facilitate intuitive analysis of the wave characteristics of the structure.

[0075] Step S5: Identify the vibration band gap based on the dispersion curve, and perform modal analysis by restoring the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0076] After obtaining the dispersion curve, the bandgap characteristics of the acoustic superstructure can be identified based on it, and the intrinsic relationship between wave modes and vibration reduction and noise reduction performance can be further revealed by reconstructing the physical space of the eigenvectors.

[0077] Bandgap identification and analysis are performed based on the constructed dispersion curves. For each propagation direction... Scan all frequency points Corresponding complex wave number If within a certain continuous frequency range There is no real part inside. Propagation modes with real parts close to zero or non-zero, i.e., the imaginary part of all modes. All are significantly greater than zero (satisfying) If ), then determine the interval. It is a full bandgap. Within the full bandgap range, elastic waves cannot propagate in the structure, and vibration and noise are effectively suppressed.

[0078] Further distinguish between vibration bandgap and acoustic attenuation bandgap: If the bandgap is mainly caused by the attenuation of structural vibration modes, i.e. If the larger wave mode is dominated by bending or shearing waves, it is identified as a vibration bandgap; if the bandgap is related to acoustic radiation or fluid-structure interaction, it needs to be comprehensively determined in conjunction with subsequent acoustic propagation loss analysis.

[0079] The bandgap boundary frequency is determined by the appearance and disappearance points of the propagation modes in the dispersion curve, corresponding to the characteristic wavenumber. and its eigenvectors It can be used for subsequent wave mode analysis to explain the physical mechanism of bandgap generation.

[0080] The feature vector obtained by tracking The physical space is restored sequentially through periodic transformations:

[0081] Reset shift vector This reflects the complete vibrational morphology of periodic elements at specific frequencies and wave numbers. The vector is imported into the finite element post-processing module, and the wave modes are displayed through contour plots or vector diagrams. To clearly present the wave characteristics, the displacement field can be normalized, and the continuous field distribution can be obtained by interpolation based on the element shape function. The visualization criteria for typical wave modes are as follows: bending waves exhibit dominant out-of-plane displacement with an approximately linear phase change along the thickness; shear waves show relative cross-sectional displacement with small out-of-plane displacement; stretching waves are dominated by in-plane stretching / compression, with negligible out-of-plane displacement; higher-order waves are often accompanied by standing wave nodules in the thickness direction. This visualization analysis provides an intuitive physical picture for explaining the bandgap mechanism and designing superstructure dynamics, thereby enabling the prediction of vibration reduction and noise reduction performance.

[0082] The following specific embodiment verifies the accuracy and robustness of the weighted modal confidence criterion proposed in this invention in tracking dispersion curves of orthogonal anisotropic periodic structures.

[0083] This embodiment uses a 20cm thick six-layer cross-laminated laminate (CLT) board as the object to verify the accuracy and robustness of the weighted wave guarantee criterion proposed in this invention in tracking the dispersion curve of orthotropic periodic structures. The CLT board is composed of six layers of wood panels orthogonally laid in the thickness direction, with the layup sequence being 0°, 90°, 0°, 0°, 90°, 0°. The wood panels are anisotropic materials, and the layup design in different directions can maximize the interlaminar shear effect through the differences in interlayer material parameters, thereby enhancing vibration reduction and noise reduction performance.

[0084] Using the method of this invention, a representative periodic element of the CLT plate is first established, with an element size of 2mm × 2mm. Each layer in the thickness direction is divided into 4 solid elements, and each layer in the in-plane direction is divided into 2 elements, for a total of 48 elements. Following the steps described in claim 1, the dynamic stiffness matrix is ​​assembled and Bloch periodic boundary conditions are embedded. Frequency points are discretized in a frequency range of 0–5000Hz with a step size of 5Hz. The complex wavenumber and its eigenvector at each frequency point and in each propagation direction are solved using a contour integral algorithm. To verify the accuracy of dispersion curve tracking, the constant frequency gradient method and the weighted wave guarantee criterion proposed in this invention are used respectively. The dispersion curve of the direction is tracked.

[0085] Please refer to Figures 2-3 The embodiments of this invention employ different methods to process six-layer cross-laminated wood panels (CLT). A schematic diagram illustrating the comparison results of wavenumber tracking in different directions. The horizontal axis represents frequency, ranging from 0 to 5000. The vertical axis represents the real part of the complex wavenumber. ), range 0-200 . Figure 2 The dispersion curve was obtained by tracing using the constant frequency gradient method. At 4000... Nearby, due to the strong coupling between the curved wave branch and the higher-order shear wave branch, the dispersion curves tend to overlap. The constant frequency gradient method, based on the criterion of "no abrupt change in slope between eigenvalues," leads to tracking errors: the shear wave branch at approximately 4000... The real part of the wavenumber at a certain point begins to surge, exhibiting an abnormal "peak" shape, which is significantly inconsistent with the trend of change at adjacent frequency points, indicating that the tracking results are distorted. Figure 3 The dispersion curve is obtained by tracing using the weighted modal confidence criterion (WwAC) of this invention. Similarly, the three dispersion branches are at 2300... The nearby bending wave branch and shear wave branch are clearly separated and continuous and smooth, with the shear wave branch at 4000-5000. The real part of the wavenumber within the interval is 120 Smooth transition to 150 No abnormal spikes were observed. Comparative results show that the tracking method based on energy continuity in the frequency domain of this invention can accurately distinguish strongly coupled physical branches and avoid tracking errors.

[0086] Please refer to Figures 4-5 The diagram shows the structure of the six-layer cross-laminated wood board in this embodiment of the invention and the wave mode analysis results. The wave mode displacement field distribution is obtained by restoring the characteristic wavenumber and its corresponding generalized eigenvector to the physical space after periodic transformation matrix based on WwAC tracking. Figure 5 The horizontal axis represents the wave number, ranging from 0 to 40. The vertical axis represents frequency, ranging from 0 to 5000. By visualizing wave modes, the physical wave types corresponding to different dispersion branches can be clearly distinguished, providing an intuitive basis for explaining the physical mechanism of bandgap generation. For example, the wave modes corresponding to curves 3 and 5 are dominated by out-of-plane displacement, intuitively reflecting that curves 3 and 5 are bending waves.

[0087] Example 2: Based on the same inventive concept, embodiments of the present invention also provide an acoustic superstructure forward calculation and performance prediction system, the system comprising: The modeling and matrix construction module is used to construct the finite element model of the minimum repeating periodic element of the acoustic superstructure and obtain its dynamic stiffness matrix. ; The eigenvalue problem transformation module is used to introduce periodic boundary conditions and transform the wave control equation of the periodic element into a nonlinear eigenvalue problem with respect to the complex wave number k based on the wave finite element theory. The contour integral solving module is used to solve the nonlinear eigenvalue problem using the contour integral algorithm, based on a pre-defined closed contour in the complex wavenumber plane. Within this process, all characteristic wavenumbers k and their corresponding generalized eigenvectors are obtained in a single solution. ; The dispersion curve tracking module is used to automatically match and track the characteristic wavenumbers belonging to the same physical wave branch in the target frequency domain based on the similarity between the generalized eigenvectors obtained at different frequencies, thereby drawing a continuous dispersion curve. The performance prediction module is used to identify the vibration band gap based on the dispersion curve, and perform modal analysis by recovering the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0088] Since these systems and the principles underlying the problems they address are similar to the aforementioned methods for forward computation and performance prediction of acoustic superstructures, the implementation of these systems can be found in the implementation of the aforementioned methods, and the repetitions will not be repeated.

[0089] Example 3: Based on the same inventive concept, the present invention also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; When the processor executes the program stored in the memory, it is able to implement the acoustic superstructure forward calculation and performance prediction method as described in any one of Embodiment 1.

[0090] like Figure 6 As shown, the electronic device may include: a processor 10, a communication interface 20, a memory 30, and a communication bus 40, wherein the processor 10, the communication interface 20, and the memory 30 communicate with each other via the communication bus 40. The processor 10 can call logical instructions in the memory 30 to execute an acoustic superstructure forward calculation and performance prediction method, which includes the following steps: S1. Construct a finite element model of the acoustic superstructure with the minimum repeating periodic element, and obtain its dynamic stiffness matrix. ; S2. Introducing periodic boundary conditions, based on the wave finite element theory, the wave control equation of the periodic element is transformed into a nonlinear eigenvalue problem with respect to the complex wave number k. S3. Solve the nonlinear eigenvalue problem using the contour integral algorithm, based on a pre-defined closed contour on the complex wavenumber plane. Within this process, all characteristic wavenumbers k and their corresponding generalized eigenvectors are obtained in a single solution. ; S4. In the target frequency domain, based on the similarity between the generalized eigenvectors obtained at different frequencies, the characteristic wavenumbers belonging to the same physical wave branch are automatically matched and tracked, thereby drawing a continuous dispersion curve. S5. Based on the dispersion curve, identify the vibration band gap, and perform modal analysis by restoring the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

[0091] Example 4: This invention also provides a computer-readable storage medium containing a program for executing the acoustic superstructure forward calculation and performance prediction method of Embodiment 1 described above. This program can be executed on a processor.

[0092] Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0093] The program stored on this medium is loaded into the processor's memory and executed to perform various functions. This storage medium, connected to hardware devices, enables the computer to perform the steps of Embodiment 1 described above.

[0094] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0095] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for forward calculation and performance prediction of acoustic superstructures, characterized in that, Includes the following steps: S1. Construct a finite element model of the acoustic superstructure with the minimum repeating periodic element and obtain its dynamic stiffness matrix; S2. Introducing periodic boundary conditions, the wave control equation of the periodic element is transformed into a nonlinear eigenvalue problem with respect to the complex wave number based on the wave finite element theory. S3. Solve the nonlinear eigenvalue problem using the contour integral algorithm, specifically including: pre-setting a closed contour on the complex wavenumber plane, configuring Gauss-Legend integration points and corresponding weights on the contour, and calculating the moment matrix sequence; constructing block Hankel matrices H0 and H1 from the moment matrix, performing singular value decomposition and low-rank approximation on H0, solving the generalized eigenvalue problem of reduced scale, and obtaining all eigenwavenumbers and their corresponding generalized eigenvectors within the contour Γ in one go; S4. In the target frequency domain, based on the similarity between the generalized eigenvectors obtained at different frequencies, the characteristic wavenumbers belonging to the same physical wave branch are automatically matched and tracked, thereby drawing a continuous dispersion curve. S5. Based on the dispersion curve, identify the vibration band gap, and perform modal analysis by restoring the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

2. The method as described in claim 1, characterized in that, In step S1, the acoustic superstructure includes one-dimensional phononic crystals, two-dimensional phononic crystals, three-dimensional phononic crystals, honeycomb sandwich panels, stiffened panels, laminated glass, sandwich structures with shape memory polymer core layers, cross-laminated wood panels, or curved periodic shells.

3. The method as described in claim 1, characterized in that, In step S1, the dynamic stiffness matrix Assembled based on the equilibrium equations of simple harmonic motion: Among them, the stiffness matrix Describes the resistance of the element to elastic deformation and its mass matrix. This describes the inertial characteristics of the element during elastic deformation, and the nodal displacement vector. The complex amplitude response of the periodic element is given by ω, which is the oscillation frequency.

4. The method as described in claim 1, characterized in that, The periodic boundary condition in step S2 is the Bloch periodic boundary condition: ， ， ， ， in, , These are the nodal displacement vectors of the left and right boundaries of the periodic element, respectively. , These are the nodal displacement vectors at the lower and upper boundaries of the periodic element, respectively. , , , These are the displacement vectors of the lower left, lower right, upper left, and upper right nodes of the periodic element, respectively. , These are the Bloch phase factors in the x and y directions, respectively. , k x k y Let L be the complex wave number in the x and y directions. x L y The geometric dimensions of the periodic unit in the x and y directions; At the same time, the nodal forces on the periodic boundary satisfy the action-reaction relationship; Construct the displacement transformation matrix Force balance transformation matrix By embedding the periodic boundary conditions into the dynamic stiffness matrix, the reduced system matrix is ​​obtained. : This transforms the wave control equation of the periodic unit into a nonlinear eigenvalue problem with respect to the complex wave number k: in, For the wave propagation angle, It is the generalized eigenvector after periodic transformation compression.

5. The method as described in claim 1, characterized in that, In step S3, a closed contour Γ is preset on the complex wavenumber plane, and Gauss-Legend integration points k are arranged on the contour Γ. g and corresponding weight w g In this context, the sequence of moments is calculated as follows: Among them, S p Let N be the p-th order moment matrix. G w represents the number of integration points on the boundary line. g Let g be the weight of the g-th integration point. Let p be the complex wave value at the g-th integration point, where the superscript p indicates the order of the moment. V is the inverse of the dynamic stiffness matrix, V is the random probe matrix, and M is the preset number of moments. The closed boundary Γ can be rectangular, circular, or elliptical, and its range is adaptively adjusted according to the distribution of eigenvalues.

6. The method as described in claim 1, characterized in that, In step S4, automatically matching and tracking characteristic wavenumbers belonging to the same physical wave branch specifically includes: For adjacent frequency points ω n and ω n+1 Generalized eigenvectors and The weighted modal confidence factor is calculated using the weighted modal confidence criterion: in, The weighted matrix is ​​selected from the mass matrix. H is the conjugate transpose. A matching threshold is set, and generalized feature vectors with weighted mode confidence factors greater than or equal to the threshold are determined to be the same physical wave branch. The feature values ​​of each frequency point are automatically matched through an optimization algorithm to form a continuous dispersion curve.

7. The method as described in claim 1, characterized in that, In step S5, identifying the vibration bandgap and performing wave mode analysis specifically includes: Scanning the complex wavenumbers corresponding to all frequency points, if within a certain continuous frequency interval Δω, the imaginary part Im(k) of the complex wavenumbers of all propagation modes is... i All of them satisfy: Among them, Im(k i ) represents the imaginary part of the i-th characteristic wavenumber, indicating the degree of wave attenuation, and L is the geometric dimension of the periodic unit in the direction of wave propagation; Then, the interval Δω is determined to be a complete bandgap, and the vibration bandgap or acoustic attenuation bandgap of the acoustic superstructure is identified; The generalized eigenvectors obtained by solving By reconstructing the physical space using the periodic transformation matrix, the physical displacement field of the periodic unit at the corresponding wavenumber can be obtained: in, Let k be the generalized eigenvector corresponding to the i-th characteristic wavenumber. i Let θ be the i-th characteristic wavenumber, and θ be the wave propagation angle. Let q be the displacement transformation matrix. i This is the physical displacement field vector of the periodic unit at the corresponding wavenumber; For the physical displacement field vector q i Visualization is performed to obtain wave modes. Based on the spatial distribution characteristics of the displacement field, bending waves, shear waves, stretching waves and their coupling modes are distinguished, and the physical mechanism of bandgap generation is explained.

8. A system for forward computation and performance prediction of acoustic superstructures, characterized in that, The system comprises: The modeling and matrix construction module is used to construct the finite element model of the minimum repeating periodic element of the acoustic superstructure and obtain its dynamic stiffness matrix. ; The eigenvalue problem transformation module is used to introduce periodic boundary conditions and transform the wave control equation of the periodic element into a nonlinear eigenvalue problem with respect to the complex wave number k based on the wave finite element theory. The contour integral solving module is used to solve the nonlinear eigenvalue problem using the contour integral algorithm, based on a pre-defined closed contour in the complex wavenumber plane. Within this process, all characteristic wavenumbers k and their corresponding generalized eigenvectors are obtained in a single solution. ; The dispersion curve tracking module is used to automatically match and track the characteristic wavenumbers belonging to the same physical wave branch in the target frequency domain based on the similarity between the generalized eigenvectors obtained at different frequencies, thereby drawing a continuous dispersion curve. The performance prediction module is used to identify the vibration band gap based on the dispersion curve, and perform modal analysis by recovering the generalized feature vector to the physical space to complete the prediction of vibration reduction and noise reduction performance.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the acoustic superstructure forward calculation and performance prediction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the method for forward calculation and performance prediction of acoustic superstructures as described in any one of claims 1 to 7.

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