Method and device for determining frequency dispersion characteristic of waveguide structure and electronic equipment

Abstract

The invention belongs to the technical field of calculation of frequency dispersion characteristics of waveguide structures, and provides a method and a device for determining the frequency dispersion characteristics of a waveguide structure, and electronic equipment, and the method comprises the steps: distributing the rigidity to waveguide nodes based on the longitudinal rigidity, the transverse rigidity and the vertical rigidity, and determining the node rigidity, the node rigidity comprises longitudinal node rigidity, transverse node rigidity and vertical node rigidity; generating a support stiffness matrix based on the node stiffness; generating a fluctuation control equation based on the support stiffness matrix; and solving the fluctuation control equation, generating a frequency dispersion curve of the waveguide structure, and determining the frequency dispersion characteristics of the waveguide structure under different support stiffness conditions through the frequency dispersion curve. According to the method for determining the frequency dispersion characteristics of the waveguide structure, due to the fact that the supporting stiffness matrix is introduced, the frequency dispersion characteristics of the waveguide structure under different supporting stiffness conditions can be accurately determined through the frequency dispersion curve.

Description

Technical Field

[0001] The present disclosure belongs to the technical field of calculating the dispersion characteristics of waveguide structures, and particularly relates to a method, apparatus, and electronic device for determining the dispersion characteristics of a waveguide structure. Background Art

[0002] Existing calculation methods for the dispersion characteristics of waveguide structures often ignore the boundary conditions of the waveguide structure and assume that the waveguide structure is placed in a vacuum to calculate its dispersion characteristics. This assumption completely ignores the influence of boundary conditions on the dispersion characteristics of the waveguide structure. However, research shows that the boundary conditions of the waveguide structure often provide vertical, transverse, and longitudinal support stiffnesses, and the support stiffnesses will greatly affect the dispersion characteristics of the waveguide structure at low frequencies.

[0003] Therefore, for a waveguide structure under support stiffness conditions, how to accurately calculate its dispersion characteristics is a technical problem to be solved. Summary of the Invention

[0004] Based on this, in view of the defect that the prior art cannot accurately determine the dispersion characteristics of a waveguide structure under support stiffness conditions, it is necessary to provide a method, apparatus, storage medium, and electronic device for determining the dispersion characteristics of a waveguide structure.

[0005] In a first aspect, an embodiment of the present invention provides a method for determining the dispersion characteristics of a waveguide structure, the method including:

[0006] Obtain the longitudinal stiffness in the longitudinal direction, the transverse stiffness in the transverse direction, and the vertical stiffness in the vertical direction;

[0007] Based on the longitudinal stiffness, the transverse stiffness, and the vertical stiffness, distribute the stiffness to waveguide nodes and determine the node stiffness, where the node stiffness includes the longitudinal node stiffness in the longitudinal direction, the transverse node stiffness in the transverse direction, and the vertical node stiffness in the vertical direction;

[0008] Generate a support stiffness matrix based on the node stiffness;

[0009] Generate a wave control equation based on the support stiffness matrix;

[0010] Solve the wave control equation to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

[0011] Optionally, the generating a support stiffness matrix based on the node stiffness includes:

[0012] Generate a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal node stiffness;

[0013] Generate a global lateral stiffness matrix in the lateral direction based on the lateral node stiffness;

[0014] Generate a global vertical stiffness matrix in the vertical direction based on the vertical node stiffness;

[0015] Add the global longitudinal stiffness matrix, the global lateral stiffness matrix, and the global vertical stiffness matrix to generate the support stiffness matrix.

[0016] Optionally, before obtaining the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction, the method further includes:

[0017] Perform finite element discretization on the cross-section of the waveguide structure by the semi-analytical finite element method.

[0018] Optionally, the performing finite element discretization on the cross-section of the waveguide structure by the semi-analytical finite element method includes:

[0019] Perform domain discretization on the cross-section of the waveguide through a preset grid, dividing it into a first preset number of elements and a second preset number of nodes. The preset grid is a quadratic eight-node quadrilateral grid, and the high-order element corresponding to the quadratic eight-node quadrilateral grid is a quadratic eight-node high-order element, so as to fit the deformation of the waveguide boundary through the quadratic eight-node high-order element.

[0020] Optionally, the distributing the stiffness to the waveguide nodes based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness, and determining the node stiffness includes:

[0021] Determine the longitudinal node stiffness based on the longitudinal stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness;

[0022] Determine the lateral node stiffness based on the lateral stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness;

[0023] Determine the vertical node stiffness based on the vertical stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness.

[0024] Optionally, after solving the wave control equation to generate the dispersion curve of the waveguide structure, the method further includes:

[0025] Obtain a target formula, which is used to represent that when the wave numbers are the same, the calculation results between the same modal eigenvectors are not zero, and the calculation results between different modal eigenvectors are zero;

[0026] Each mode of the waveguide is separated by the target formula, and the wavenumber dispersion curve of mode separation is plotted based on each mode.

[0027] In a second aspect, an embodiment of the present invention provides a device for determining the dispersion characteristics of a waveguide structure. The device includes:

[0028] An acquisition module, configured to acquire the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction;

[0029] A distribution and determination module, configured to distribute the stiffness to waveguide nodes based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness, and determine the node stiffness, where the node stiffness includes: the longitudinal node stiffness in the longitudinal direction, the lateral node stiffness in the lateral direction, and the vertical node stiffness in the vertical direction;

[0030] A first generation module, configured to generate a support stiffness matrix based on the node stiffness;

[0031] A second generation module, configured to generate a wave control equation based on the support stiffness matrix;

[0032] A third generation module, configured to solve the wave control equation to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

[0033] Optionally, the first generation module is specifically configured to:

[0034] Generate a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal node stiffness;

[0035] Generate a lateral stiffness global matrix in the lateral direction based on the lateral node stiffness;

[0036] Generate a vertical stiffness global matrix in the vertical direction based on the vertical node stiffness;

[0037] Perform an addition process on the longitudinal stiffness global matrix, the lateral stiffness global matrix, and the vertical stiffness global matrix to generate the support stiffness matrix.

[0038] In a third aspect, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed in a computer, the computer is made to execute the method of the first aspect.

[0039] In a fourth aspect, an electronic device is provided, including a memory and a processor. An executable code is stored in the memory. When the processor executes the executable code, the method of the first aspect is implemented.

[0040] In an embodiment of the present invention, the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction are obtained; based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness, the stiffness is distributed to the waveguide nodes, and the node stiffness is determined, where the node stiffness includes the longitudinal node stiffness, the lateral node stiffness, and the vertical node stiffness; a support stiffness matrix is generated based on the node stiffness; a wave motion control equation of the waveguide considering the support stiffness is generated based on the support stiffness matrix; and the wave motion control equation is solved to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve. In the method for determining the dispersion characteristics of the waveguide structure provided by the embodiment of the present invention, since a support stiffness matrix is introduced, a wave motion control equation is generated based on the support stiffness matrix, and the wave motion control equation is solved to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve; therefore, through the determination method provided by the embodiment of the present invention, the dispersion characteristics of the waveguide structure under different support stiffness conditions can be accurately determined through the dispersion curve. Description of the Drawings

[0041] The exemplary embodiments of the present invention can be more fully understood by reference to the following drawings. The drawings are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention. In the drawings, the same reference numerals generally represent the same components or steps.

[0042] Figure 1 It is a flowchart of a method for determining the dispersion characteristics of a waveguide structure according to an exemplary embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the grid nodes of a 60 kg / m rail;

[0044] Figure 3 It is a schematic diagram of a first-order four-node first-order element;

[0045] Figure 4 It is a schematic diagram of a second-order eight-node high-order element;

[0046] Figure 5 It is a schematic diagram of the coordinates of a second-order eight-node element;

[0047] Figure 6 It is a schematic diagram of the rail support stiffness, where Figure 6 a is a schematic diagram of the longitudinal stiffness, Figure 6 b is a schematic diagram of the lateral stiffness and the vertical stiffness;

[0048] Figure 7 It is a schematic diagram of calculating the value of the support stiffness;

[0049] Figure 8 Schematic diagram of rail dispersion curve considering support stiffness;

[0050] Figure 9 Schematic diagram of the structure of a determining device 900 for the dispersion characteristics of a waveguide structure provided according to an exemplary embodiment of the present invention. Detailed implementation manners

[0051] Hereinafter, exemplary embodiments of the present disclosure will be described in more detail with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be completely conveyed to those skilled in the art.

[0052] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those skilled in the art to which the present invention belongs.

[0053] In addition, terms such as "first" and "second" are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products or devices.

[0054] Embodiments of the present invention provide a method and apparatus for determining the dispersion characteristics of a waveguide structure, a computer-readable medium, and an electronic device, which will be described below with reference to the accompanying drawings.

[0055] Please refer to Figure 1 , which shows a flowchart of a method for determining the dispersion characteristics of a waveguide structure provided by some embodiments of the present invention. As Figure 1 shown, the method for determining the dispersion characteristics of a waveguide structure may include the following steps:

[0056] Step S101: Obtain the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction.

[0057] In one example, before obtaining the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction, the method for determining the dispersion characteristics of a waveguide structure provided by embodiments of the present invention may further include the following steps:

[0058] Perform finite element discretization processing on the cross-section of the waveguide structure by the semi-analytical finite element method.

[0059] In one example, through the semi - analytical finite element method, finite element discretization is performed on the cross - section of the waveguide structure, including the following steps:

[0060] Through a preset grid, the cross - section of the waveguide is discretized in the domain, obtaining a first preset number of elements and a second preset number of nodes. The preset grid is a quadratic eight - node quadrilateral grid, and the high - order element corresponding to the quadratic eight - node quadrilateral grid is a quadratic eight - node high - order element, so as to fit the deformation of the waveguide boundary through the quadratic eight - node high - order element.

[0061] In one example, the first preset value is 562 and the second preset value is 1869.

[0062] In the semi - analytical finite element method, finite element discretization is performed on the cross - section of the waveguide structure, while the analytical method is used to solve the wave propagation direction. For example, the high - order element semi - analytical finite element method can be used to calculate the dispersion scatter plot of the rail cross - section in the frequency range of 100 kHz. Assuming that the elastic rail is homogeneous and isotropic, the x - direction is set as the wave propagation direction, and the y - and z - directions are the width and height directions of the rail cross - section respectively. The displacement of any point on the rail is represented by the spatial distribution function as follows:

[0063]

[0064] In formula (1): ξ is the wave number, ω is the angular frequency, and i is the imaginary unit

[0065] The cross - section of the rail is divided into a finite - element mesh to obtain a discrete domain. To facilitate the generation of high - quality hexahedral meshes in finite - element simulation, the rail cross - section is discretized in the domain using a quadratic eight - node quadrilateral grid, obtaining 562 elements and 1869 nodes, as Figure 2 shown.

[0066] Compared with the general first - order four - node first - order element, as Figure 2 shown, the quadratic eight - node high - order element (as Figure 4 shown) considers a node with degrees of freedom at the mid - point of each side of the quadrilateral grid, and uses a quadratic displacement equation to make the element boundary a curved shape. Therefore, using high - order elements can better fit the deformation of the rail boundary. As a result, the semi - analytical finite - element model will converge faster and have higher accuracy.

[0067] The displacement of any point inside the quadratic eight - node quadrilateral element can be expressed through the shape function as:

[0068]

[0069] In Equation (2), N(y, z) is the shape function matrix of a quadratic eight-node element, as shown in Equation (3).

[0070]

[0071] In the above Equation (3), N k (k = 1, 2…8) is the shape function corresponding to the k-th node, as shown in Equation (5).

[0072] q (e) is the nodal displacement vector of the quadratic eight-node element, as shown in Equation (4).

[0073] q (e) =[U x1 U y1 U z1 U x2 U y2 U z2 ...U x8 U y8 U z8 T

[0074] Equation (4);

[0075] In Equation (3), N k (k = 1, 2…8) is the shape function corresponding to the k-th node, as shown in Equation (5).

[0076]

[0077] In Equation (5), y and z are the coordinates of any point within the quadrilateral element, (y k , z k ) are the nodal coordinates of N k (k = 1, 2…8), as Figure 5 shown.

[0078] The strain vector of the element can be expressed in terms of the nodal displacements as follows:

[0079]

[0080]

[0081] In Equation (7): L x , L y , L z are the deformation component coefficients, B1 = L y N ,y + L z N ,z , B2 = L x N.

[0082] ​Step S102: Based on the longitudinal stiffness, lateral stiffness, and vertical stiffness, distribute the stiffness to the waveguide nodes and determine the nodal stiffness, where the nodal stiffness includes: the longitudinal nodal stiffness in the longitudinal direction, the lateral nodal stiffness in the lateral direction, and the vertical nodal stiffness in the vertical direction.

[0083] In one example, distributing the stiffness to the waveguide nodes and determining the nodal stiffness based on the longitudinal stiffness, lateral stiffness, and vertical stiffness includes:

[0084] Determine the longitudinal nodal stiffness based on the longitudinal stiffness, the number of nodes with distributed support stiffness, and the influence range of the support stiffness;

[0085] Determine the lateral nodal stiffness based on the lateral stiffness, the number of nodes with distributed support stiffness, and the influence range of the support stiffness;

[0086] Determine the vertical nodal stiffness based on the vertical stiffness, the number of nodes with distributed support stiffness, and the influence range of the support stiffness.

[0087] Step S103: Generate a support stiffness matrix based on the nodal stiffness, where the nodal stiffness includes: the longitudinal nodal stiffness in the longitudinal direction, the lateral nodal stiffness in the lateral direction, and the vertical nodal stiffness in the vertical direction.

[0088] In one example, generating a support stiffness matrix based on the nodal stiffness includes the following steps:

[0089] Generate a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal nodal stiffness;

[0090] Generate a lateral stiffness global matrix in the lateral direction based on the lateral nodal stiffness;

[0091] Generate a vertical stiffness global matrix in the vertical direction based on the vertical nodal stiffness;

[0092] Add the longitudinal stiffness global matrix, the lateral stiffness global matrix, and the vertical stiffness global matrix to generate a support stiffness matrix.

[0093] Step S104: Generate a wave control equation based on the support stiffness matrix.

[0094] Based on the principle of virtual work, the wave control equation for a standard cross-section rail without initial stress can be obtained:

[0095] [K1 + iξK2 + ξ 2 K3 - ω 2 M] M U = 0

[0096] Formula (8);

[0097]

[0098] In the above formula (9), and m (e) are the stiffness matrices of each element respectively, and n is the total number of sectional elements.

[0099]

[0100]

[0101]

[0102]

[0103] In formula (8), K1, K2, K3, and M are assembled from the corresponding element stiffness matrices, and the element stiffness matrix is expressed as formulas (10 - 13). and m (e) are the stiffness matrices of each element respectively, C e is the elastic constant matrix of the rail, Ω e is the quadrilateral element area domain after the rail cross-section is discretized, and ρ e is the material density.

[0104] The rail support stiffness considers the longitudinal, vertical, and lateral stiffnesses, as Figure 6 shown.

[0105] Assume that the longitudinal stiffness, lateral stiffness, and vertical stiffness are k x , k y , k z respectively. Then the stiffness distribution at the rail nodes is:

[0106] kk x = k x / (m * L), kk y = k y / (m * L), kk z = k z / (m * L)

[0107] Formula (14);

[0108] In formula (14), kk x , kk y , kk z are the longitudinal node stiffness, lateral node stiffness, and vertical node stiffness respectively, m is the number of nodes with the distributed support stiffness, and L is the influence range of the support stiffness.

[0109] According to the calculated node stiffnesses (longitudinal node stiffness, lateral node stiffness, and vertical node stiffness), the support stiffness matrix can be assembled:

[0110]

[0111]

[0112]

[0113] K4 = K x + K y + K z

[0114] Equation (18);

[0115] In Equation (18), K x , K y , K z are respectively the overall longitudinal stiffness matrix, the overall lateral stiffness matrix, and the overall vertical stiffness matrix. K4 is the support stiffness matrix introduced into the wave motion control equation.

[0116] By introducing the support stiffness matrix, the wave motion control equation of the rail considering the support stiffness can be obtained:

[0117] [K1 + iξK2 + ξ 2 K3 - ω 2 M + K4] M U = 0

[0118] Equation (19);

[0119] In Equation (19), ξ is the wave number and ω is the frequency. For any given frequency value ω, the corresponding wave number ξ can be solved. The positive and negative signs represent the forward or backward propagation in terms of physical meaning. The real part represents the wave number, and the imaginary part describes the attenuation characteristics. Usually, only the case where the wave number is real, that is, the imaginary part is 0, is concerned. Solving the wave motion control equation can obtain the dispersion curve of the waveguide structure, which describes the dispersion characteristics of the structure considering the support stiffness.

[0120] Step S105: Solve the wave motion control equation to generate the dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

[0121] By introducing the support stiffness matrix, the wave motion control equation of the rail considering the support stiffness can be obtained:

[0122] [K1 + iξK2 + ξ 2 K3 - ω 2 M + K4] M U = 0

[0123] Equation (19);

[0124] In Equation (19), ξ is the wave number and ω is the frequency. For any given frequency value ω, the corresponding wave number ξ can be solved.

[0125] Solving the wave control equation can obtain the dispersion curve of the waveguide structure, which describes the dispersion characteristics of the structure considering the support stiffness.

[0126] In one example, the dispersion characteristic data related to the dispersion characteristics includes: wave number dispersion data, phase velocity dispersion data, and group velocity dispersion data.

[0127] In the calculation, the vertical stiffness is taken as 25 kN / mm, the horizontal stiffness is taken as 15 kN / mm, and the longitudinal stiffness is taken as 0 kN / mm, that is, k x =0 kN / mm, k y =15 kN / mm, k z =25 kN / mm, as Figure 7 shown. The material density of the rail is taken as 7850 kg / m 3 , the elastic modulus is 210 GPa, and the Poisson's ratio is 0.3. The rail is assumed to be completely elastic and damping is not considered. According to formula (19), the frequency can be solved by the given wave number in the wave number range of 0-250 rad / m, and the analytical solution of the dispersion points in the range of 0-100 kHz can be calculated.

[0128] In one example, after solving the wave control equation to generate the dispersion curve of the waveguide structure, the method for determining the dispersion characteristics of the waveguide structure provided by the embodiments of the present invention may further include the following steps:

[0129] Obtain a target formula, which is used to represent that: when the wave numbers are the same, the calculation results between the same modal eigenvectors are not zero, and the calculation results between different modal eigenvectors are zero;

[0130] Separate each mode of the waveguide through the target formula, and draw the wave number dispersion curve of mode separation based on each mode.

[0131] In one example, the target formula may be:

[0132]

[0133] In formula (20), U is the eigenvector of the mode, and Uup is the upper half of the modal eigenvector.

[0134] In one example, according to the orthogonality between different modal eigenvectors, that is, formula (20), the modes can be separated. Formula (20) indicates that when the wave numbers are the same, the calculation results between the same modal eigenvectors are not zero, while the calculation results between different modal eigenvectors are zero. This rule still holds for the modal eigenvectors with very close wave numbers. According to this formula, each mode of the waveguide can be separated, and the wave number dispersion curve of mode separation drawn is as Figure 8 shown.

[0135]

[0136] In formula (20), U is the eigenvector of the mode, and Uup is the upper half of the eigenvector of the mode.

[0137] In the method for determining the dispersion characteristics of the waveguide structure provided by the embodiment of the present invention, due to the introduction of the support stiffness matrix, based on the support stiffness matrix, a wave control equation is generated, and the wave control equation is solved to generate the dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve; therefore, through the determination method provided by the embodiment of the present invention, the dispersion characteristics of the waveguide structure under different support stiffness conditions can be accurately determined through the dispersion curve.

[0138] In addition, the method for determining the dispersion characteristics of the waveguide structure provided by the embodiment of the present invention can calculate the dispersion characteristics of the waveguide structure under different support conditions in the actual situation, correct the calculation error of the dispersion characteristics in the low-frequency part in the traditional technology, and obtain a more realistic structural modal vibration mode and guided wave structure. Moreover, since high-order elements are used to replace the traditional first-order elements, its calculation efficiency is higher and the accuracy is also better.

[0139] In the above embodiment, a method for determining the dispersion characteristics of a waveguide structure is provided. Correspondingly, the present invention also provides a device for determining the dispersion characteristics of a waveguide structure. The device for determining the dispersion characteristics of the waveguide structure provided by the embodiment of the present invention can implement the method for determining the dispersion characteristics of the waveguide structure, and the device for determining the dispersion characteristics of the waveguide structure can be implemented in a software, hardware or a combination of software and hardware manner. For example, the device for determining the dispersion characteristics of the waveguide structure can include integrated or separate functional modules or units to execute the corresponding steps in the above methods.

[0140] Please refer to Figure 9 , which shows a schematic diagram of a device for determining the dispersion characteristics of a waveguide structure provided by some embodiments of the present invention. Since the device embodiment is basically similar to the method embodiment, the description is relatively simple, and for the related parts, please refer to the partial description of the method embodiment. The device embodiments described below are only illustrative.

[0141] As Figure 9 shown, the device 900 for determining the dispersion characteristics of the waveguide structure may include:

[0142] An acquisition module 901, configured to acquire the longitudinal stiffness in the longitudinal direction, the transverse stiffness in the transverse direction, and the vertical stiffness in the vertical direction;

[0143] A distribution and determination module 902, configured to distribute stiffness to waveguide nodes based on longitudinal stiffness, lateral stiffness, and vertical stiffness, and determine the node stiffness, where the node stiffness includes: a longitudinal node stiffness in the longitudinal direction, a lateral node stiffness in the lateral direction, and a vertical node stiffness in the vertical direction;

[0144] A first generation module 903, configured to generate a support stiffness matrix based on the node stiffness;

[0145] A second generation module 904, configured to generate a wave control equation based on the support stiffness matrix;

[0146] A third generation module 905, configured to solve the wave control equation to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

[0147] In some embodiments of the embodiments of the present invention, the first generation module 903 is specifically configured to:

[0148] Generate a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal node stiffness;

[0149] Generate a lateral stiffness global matrix in the lateral direction based on the lateral node stiffness;

[0150] Generate a vertical stiffness global matrix in the vertical direction based on the vertical node stiffness;

[0151] Perform an addition process on the longitudinal stiffness global matrix, the lateral stiffness global matrix, and the vertical stiffness global matrix to generate a support stiffness matrix.

[0152] In some embodiments of the embodiments of the present invention, the device 900 for determining the dispersion characteristics of the waveguide structure may further include:

[0153] A processing module (not shown in Figure 9 ), configured to perform finite element discretization processing on the cross-section of the waveguide structure by a semi-analytical finite element method before obtaining the longitudinal stiffness in the longitudinal direction, the lateral stiffness in the lateral direction, and the vertical stiffness in the vertical direction.

[0154] In some embodiments of the embodiments of the present invention, the processing module is specifically configured to:

[0155] Perform domain discretization processing on the cross-section of the waveguide through a preset grid, divide to obtain a first preset number of elements and a second preset number of nodes, the preset grid is a quadratic eight-node quadrilateral grid, and the high-order element corresponding to the quadratic eight-node quadrilateral grid is a quadratic eight-node high-order element, so as to fit the deformation of the waveguide boundary through the quadratic eight-node high-order element.

[0156] The distribution and determination module 902 is specifically configured to:

[0157] Based on the longitudinal stiffness, the number of nodes with the allocated support stiffness, and the influence range of the support stiffness, the longitudinal node stiffness is determined.

[0158] Based on the transverse stiffness, the number of nodes with the allocated support stiffness, and the influence range of the support stiffness, the transverse node stiffness is determined.

[0159] Based on the vertical stiffness, the number of nodes with the allocated support stiffness, and the influence range of the support stiffness, the vertical node stiffness is determined.

[0160] In some embodiments of the present invention, the apparatus 900 for determining the dispersion characteristics of the waveguide structure may further include:

[0161] A curve plotting module (not shown in Figure 9 ), which is configured to, after solving the wave control equation to generate the dispersion curve of the waveguide structure, obtain a target formula. The target formula is used to represent that, when the wave numbers are the same, the calculation results between the same modal eigenvectors are not zero, and the calculation results between different modal eigenvectors are zero; and to separate each mode of the waveguide through the target formula and plot the wave number dispersion curve with mode separation based on each mode.

[0162] In some embodiments of the present invention, in some embodiments of the present invention, the apparatus 900 for determining the dispersion characteristics of the waveguide structure provided by the embodiments of the present invention is based on the same inventive concept as the method for determining the dispersion characteristics of the waveguide structure provided by the foregoing embodiments of the present invention and has the same beneficial effects.

[0163] According to an embodiment of another aspect, there is also provided a computer-readable storage medium, on which a computer program is stored. When the computer program is executed in a computer, the computer is made to execute the method described in conjunction with Figure 1 .

[0164] According to an embodiment of still another aspect, there is also provided an electronic device, including a memory and a processor. An executable code is stored in the memory. When the processor executes the executable code, the method described in conjunction with Figure 1 is implemented.

[0165] Those skilled in the art should be able to realize that, in one or more of the above examples, the functions described in the present invention can be implemented by hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium.

[0166] The specific embodiments described above have further elaborated on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the dispersion characteristics of a waveguide structure, characterized in that The method includes: Obtaining a longitudinal stiffness in the longitudinal direction, a lateral stiffness in the lateral direction, and a vertical stiffness in the vertical direction; Based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness, distributing the stiffness to waveguide nodes and determining node stiffnesses, where the node stiffnesses include: a longitudinal node stiffness in the longitudinal direction, a lateral node stiffness in the lateral direction, and a vertical node stiffness in the vertical direction; Generating a support stiffness matrix based on the node stiffnesses; Generating a wave motion control equation based on the support stiffness matrix; Solving the wave motion control equation to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

2. The determination method according to claim 1, characterized in that, The generating a support stiffness matrix based on the node stiffnesses includes: Generating a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal node stiffness; Generating a lateral stiffness global matrix in the lateral direction based on the lateral node stiffness; Generating a vertical stiffness global matrix in the vertical direction based on the vertical node stiffness; Performing an addition process on the longitudinal stiffness global matrix, the lateral stiffness global matrix, and the vertical stiffness global matrix to generate the support stiffness matrix.

3. The determination method according to claim 1, wherein Before the obtaining a longitudinal stiffness in the longitudinal direction, a lateral stiffness in the lateral direction, and a vertical stiffness in the vertical direction, the method further includes: Performing a finite element discretization process on the cross-section of the waveguide structure by a semi-analytical finite element method.

4. The determination method according to claim 3, characterized in that, The performing a finite element discretization process on the cross-section of the waveguide structure by a semi-analytical finite element method includes: Performing a domain discretization process on the cross-section of the waveguide through a preset grid, dividing to obtain a first preset number of elements and a second preset number of nodes, where the preset grid is a quadratic eight-node quadrilateral grid, and the high-order element corresponding to the quadratic eight-node quadrilateral grid is a quadratic eight-node high-order element, so as to fit the deformation of the waveguide boundary through the quadratic eight-node high-order element.

5. The determination method according to claim 1, wherein The distributing the stiffness to waveguide nodes and determining node stiffnesses based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness includes: Determining the longitudinal node stiffness based on the longitudinal stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness; Determining the lateral node stiffness based on the lateral stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness; Determining the vertical node stiffness based on the vertical stiffness, the number of nodes of the distributed support stiffness, and the influence range of the support stiffness.

6. The determination method according to claim 1, wherein After the solving the wave motion control equation to generate a dispersion curve of the waveguide structure, the method further includes: Obtaining a target formula, where the target formula is used to represent that: when the wave numbers are the same, the calculation results between the same modal eigenvectors are not zero, and the calculation results between different modal eigenvectors are zero; Separating each mode of the waveguide through the target formula and drawing a wave number dispersion curve with mode separation based on the each mode.

7. An apparatus for determining the dispersion characteristics of a waveguide structure, characterized in that, The device includes: An obtaining module, configured to obtain a longitudinal stiffness in the longitudinal direction, a lateral stiffness in the lateral direction, and a vertical stiffness in the vertical direction; A distribution and determination module, configured to distribute stiffness to waveguide nodes based on the longitudinal stiffness, the lateral stiffness, and the vertical stiffness, and determine the node stiffness, where the node stiffness includes: a longitudinal node stiffness in the longitudinal direction, a lateral node stiffness in the lateral direction, and a vertical node stiffness in the vertical direction; A first generation module, configured to generate a support stiffness matrix based on the node stiffness; A second generation module, configured to generate a wave motion control equation based on the support stiffness matrix; A third generation module, configured to solve the wave motion control equation to generate a dispersion curve of the waveguide structure, so as to determine the dispersion characteristics of the waveguide structure under different support stiffness conditions through the dispersion curve.

8. The determination device according to claim 7, characterized in that, The first generation module is specifically configured to: Generate a longitudinal stiffness global matrix in the longitudinal direction based on the longitudinal node stiffness; Generate a lateral stiffness global matrix in the lateral direction based on the lateral node stiffness; Generate a vertical stiffness global matrix in the vertical direction based on the vertical node stiffness; Perform an addition process on the longitudinal stiffness global matrix, the lateral stiffness global matrix, and the vertical stiffness global matrix to generate the support stiffness matrix.

9. A computer-readable storage medium, characterized in that, A computer program is stored thereon, and when the computer program is executed on a computer, the computer is made to execute the method according to any one of claims 1 to 6.

10. An electronic device, characterized in that, It includes a memory and a processor, an executable code is stored in the memory, and when the processor executes the executable code, the method according to any one of claims 1 to 6 is implemented.

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