Method and system for forecasting vibration characteristics of magnetoelectric elastic structure based on overlapping finite element method

Abstract

The invention belongs to the field of vibration characteristics of magnetoelectric elastic structures, and particularly discloses a magnetoelectric elastic structure vibration characteristic forecasting method and system based on an overlapping finite element method, and the method comprises the steps: carrying out the discretization of physical field variables of a magnetoelectric elastic structure based on the overlapping finite element method, and enabling the physical field variables to comprise a displacement field, an electric potential field and a magnetic potential field; a weighted margin method is adopted, a Galerkin weak form of a dynamic control equation of the magnetoelectric elastic structure is obtained through derivation, and an overlapped finite element dynamic discrete linear equation set of the magnetoelectric elastic structure is obtained in combination with the discretized physical field variables; and reducing the degree of freedom of the discrete linear equation set of the overlapped finite element dynamics by adopting a static cohesion method to obtain an overlapped finite element control equation so as to realize vibration characteristic prediction of the magnetoelectric elastic structure. According to the method, accurate prediction of the inherent frequency, the modal shape and the multi-physics field harmonic response under external excitation of the structure is achieved, and compared with a traditional finite element method, the method has remarkable advantages in calculation accuracy and efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of magneto-electro-elastic structure vibration characteristics, and more specifically, relates to a magneto-electro-elastic structure vibration characteristics prediction method and system based on overlapping finite element method. Background Art

[0002] Magneto-electroelastic materials are advanced smart materials made of piezoelectric materials and piezomagnetic materials. The materials integrate the interactive conversion of electric field, magnetic field and mechanical stress, and show extraordinary multi-physical field coupling performance. They can not only generate magnetic response when the electric field changes, or induce electrical signals when the magnetic field changes, but also regulate electromagnetic properties through mechanical stress, and vice versa. This unique physical property makes magneto-electroelastic materials show immeasurable importance in many fields. At present, researchers have proposed many magneto-electroelastic smart devices such as sensors, energy collectors, etc., and magneto-electroelastic materials have become one of the hot spots in the current field of materials science research.

[0003] In the early research of magneto-electroelastic materials, researchers often used analytical methods to study magneto-electroelastic structures with simple geometric features. Such methods are based on the basic governing equations of magneto-electroelastic materials and can produce very reliable results through calculations. However, when solving the dynamic problems of complex magneto-electroelastic structures, analytical methods are often no longer applicable. At this time, scholars prefer to use numerical methods for in-depth analysis.

[0004] The finite element method is a stable and efficient numerical method. It is widely used in engineering practice and can handle various complex physical fields and coupling problems. Therefore, the finite element method is also used to predict the dynamic characteristics of magneto-electro-elastic structures. At present, many scholars have used the finite element method to study magneto-electro-elastic structures and achieved important results. However, it is worth noting that although the finite element method is a powerful analysis tool, its solution accuracy is limited to a certain extent by the degree of mesh refinement. Therefore, in order to ensure the reliability and accuracy of the results, a fine mesh division strategy is usually required. This means that when dealing with complex structures, researchers need to spend a lot of effort to obtain a satisfactory mesh. Therefore, it is necessary to study a higher-precision and more efficient magneto-electro-elastic structure dynamic prediction model to provide technical support for theoretical research and engineering practice. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a method and system for predicting the vibration characteristics of a magneto-electro-elastic structure based on the overlapping finite element method, the purpose of which is to achieve high-precision and high-efficiency prediction of the vibration characteristics of a magneto-electro-elastic structure.

[0006] To achieve the above object, according to one aspect of the present invention, a method for predicting vibration characteristics of a magneto-electroelastic structure based on an overlapping finite element method is proposed, comprising the following steps:

[0007] Discretizing the physical field variables of the magneto-electroelastic structure based on an overlapping finite element method, wherein the physical field variables include a displacement field, an electric potential field, and a magnetic potential field;

[0008] The weighted residual method is used to derive the Galerkin weak form of the dynamics control equation of the magneto-electroelastic structure. Combined with the discretized physical field variables, the overlapping finite element dynamics discrete linear equations of the magneto-electroelastic structure are obtained.

[0009] The static condensation method is used to reduce the degrees of freedom of the overlapping finite element dynamics discrete linear equations and obtain the overlapping finite element control equations.

[0010] Dynamic analysis is performed based on overlapping finite element governing equations, and the vibration characteristic parameters of the magneto-electroelastic structure are obtained.

[0011] As a further preferred embodiment, the physical field variables of the magneto-electroelastic structure are discretized based on the overlapping finite element method, which is expressed as:

[0012]

[0013] Among them, u d , φ, ψ represent the displacement field, electric potential field, and magnetic potential field of the magneto-electroelastic structure, respectively; Nn represents the total number of nodes after the magneto-electroelastic structure is meshed; are node values, representing the displacement, electric potential, and magnetic potential corresponding to node J; γ J Represents the overlapping finite element method interpolation function corresponding to node J.

[0014] As a further preferred embodiment, the overlapping finite element method interpolation function is constructed as follows:

[0015]

[0016] Where Ne represents the number of nodes in an overlapping finite element, h I is the finite element method linear unit shape function corresponding to node I; virtual nodes are introduced at the midpoint of each edge of the overlapping finite element to form a secondary unit, is the virtual node construction parameter; Nh is the number of nodes in a quadratic unit, is the finite element method quadratic element shape function corresponding to node i, yes The corresponding weight coefficient.

[0017] As a further preferred embodiment, the overlapping finite element method interpolation function γ corresponding to node J J Specifically:

[0018]

[0019] Where K is the node directly connected to node J in the overlapping finite element, β represents the adjustable coefficient, represents the quadratic element shape function corresponding to the virtual node between nodes J and K, h J 、h K They represent the linear element shape functions corresponding to nodes J and K respectively.

[0020] As a further preferred embodiment, the node value is based on the basis function p J and the unknown variable a J It indicates that the basis function adopts a first-order complete polynomial basis function.

[0021] As a further preferred embodiment, the discretized physical field variables are expressed in matrix form:

[0022] u d =N u u,φ=N φ φ, ψ=N ψ ψ

[0023] N u =[N1 N1x N1z]

[0024] N φ =[N2 N2x N2z]

[0025] N ψ =[N2 N2x N2z]

[0026] N1=[γ1I e γ2I e ...γ Nn I e ],

[0027] N2=[γ1γ2...γ Nn ]

[0028] Among them, u, φ, and ψ represent the responses of displacement field, electric potential field, and magnetic potential field, respectively, all of which contain unknown variables a J vector; a plane rectangular coordinate system is constructed with the y-axis perpendicular to the plane of the magneto-electroelastic structure, and x and z represent coordinate variables; γ1,γ2…γ Nn They represent the overlapping finite element method interpolation functions corresponding to nodes 1, 2…Nn respectively.

[0029] As a further preferred embodiment, the overlapping finite element dynamics discrete linear equations for determining the magneto-electroelastic structure include:

[0030] The weighted residual method is used to determine the weighted residual formula according to the dynamic control equation of the magneto-electroelastic structure. Then, the Green's divergence theorem is applied, the preset boundary conditions are considered, and the matrix form of the physical field variables after discretization is combined to obtain the overlapping finite element dynamic discrete linear equations of the magneto-electroelastic structure, which can be expressed as:

[0031]

[0032] in:

[0033]

[0034] Gradient matrix B u , B φ , B ψ It is expressed as:

[0035] B u =L u N u , B φ =L φ N φ , B ψ =L ψ N ψ

[0036]

[0037] in, represents the second-order derivative of u with respect to the time variable, Ω and Γ represent the computational domain and boundary of the magneto-electroelastic structure, respectively. They represent the applied traction, charge, and magnetic induction boundary conditions respectively, ρ represents the density, and the matrices C, e, q, m, ε, and μ correspond to the elastic, piezoelectric, piezomagnetic, dielectric, magnetoelectric, and permeability constants respectively; x, y, and z represent coordinate variables.

[0038] As a further preferred embodiment, when the external excitation force is not considered and the magneto-electroelastic structure is subjected to free vibration analysis, the overlapping finite element control equation is expressed as:

[0039]

[0040] When an external excitation force is applied to perform harmonic response analysis on the magneto-electroelastic structure, the overlapping finite element control equation is expressed as:

[0041]

[0042] in:

[0043]

[0044] As a further preferred embodiment, dynamic analysis is performed based on overlapping finite element control equations to obtain vibration characteristic parameters of the magneto-electroelastic structure, including:

[0045] Based on the overlapping finite element governing equations, the free vibration analysis of the magneto-electro-elastic structure is carried out to obtain the natural frequency and mode shape of the magneto-electro-elastic structure.

[0046] Based on the overlapping finite element governing equations, the harmonic response analysis of the magneto-electro-elastic structure is carried out to obtain the displacement harmonic response of the magneto-electro-elastic structure. Then, the electric potential and magnetic potential response of the magneto-electro-elastic structure are obtained according to the displacement harmonic response.

[0047] According to another aspect of the present invention, a magneto-electro-elastic structure vibration characteristic prediction system based on overlapping finite element method is provided, comprising a processor, wherein the processor is used to execute the magneto-electro-elastic structure vibration characteristic prediction method based on overlapping finite element method.

[0048] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0049] 1. The present invention uses overlapping finite elements to discretely model the magneto-electro-elastic structure, and combines the structural dynamics control equations to construct a magneto-electro-elastic structure dynamics calculation model based on overlapping finite elements, thereby realizing accurate prediction of the natural frequency, modal vibration shape and multi-physical field harmonic response of the magneto-electro-elastic structure under external excitation. Compared with the traditional finite element method, it has significant advantages in calculation accuracy and efficiency, and can provide technical support for the theoretical research and engineering application of magneto-electro-elastic composite materials.

[0050] 2. The present invention interpolates and simulates the magnetic field, electric field and displacement field of the magneto-electroelastic structure based on the overlapping finite element method, and adopts the first-order complete polynomial basis function as the local field approximation to enhance the overlapping finite element performance, so that even with relatively coarse grid division, accurate simulation of the structural vibration characteristics can be achieved, further improving the efficiency of the dynamic simulation of magneto-electroelastic materials.

[0051] 3. The method of the present invention can perform calculations based on the finite element grid commonly used in engineering practice and can be easily integrated into existing finite element analysis software, thereby reducing technical barriers and promotion costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of a method for predicting vibration characteristics of a magneto-electroelastic structure based on an overlapping finite element method according to an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of a magneto-electroelastic cantilever beam model according to an embodiment of the present invention;

[0054] Figure 3Schematic diagram of finite element mesh division of the magneto-electroelastic cantilever beam model according to an embodiment of the present invention, wherein (a) is mesh 1 and (b) is mesh 2;

[0055] Figure 4 Graphs of multi-physics field harmonic response at observation points of a magneto-electroelastic cantilever beam structure under unit harmonic force excitation according to an embodiment of the present invention, wherein (a) is a displacement harmonic response, (b) is an electric potential harmonic response, and (c) is a magnetic potential harmonic response. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0057] The present invention provides a method for predicting the vibration characteristics of a magneto-electroelastic structure based on an overlapping finite element method, such as Figure 1 As shown, the following steps are included:

[0058] S1: Obtain the mesh data of the magneto-electroelastic structure and set the corresponding material parameters; based on the mesh data, use the overlapping finite element method to discretize the magnetic field, electric field and displacement field of the magneto-electroelastic structure, and combine the magneto-electroelastic material dynamics control equations to derive the overlapping finite element dynamics discrete linear equations of the constructed structure, and set the boundary conditions according to the model situation.

[0059] Furthermore, the specific steps of step S1 are as follows:

[0060] S11: Based on the overlapping finite element method, the three physical field variables in the magneto-electroelastic structure are discretized as follows:

[0061]

[0062] Where u d , φ, ψ represent the displacement field, electric potential field, and magnetic potential field in the calculation domain of the magneto-electroelastic structure, respectively; are unknown node values, representing the displacement, electric potential, and magnetic potential corresponding to the grid node J; Nn represents the total number of grid nodes of the magneto-electroelastic structure; γ J represents the overlapping finite element method interpolation function corresponding to the mesh node J, γ J The expression is:

[0063]

[0064] Where h Iis the interpolation function used in the traditional finite element method, i.e., the linear finite element shape function; Ne represents the number of nodes in an overlapping finite element; In the construction of , virtual nodes are introduced, that is, virtual nodes are introduced at the midpoint of each edge of the overlapping finite element:

[0065]

[0066] In the formula is the interpolation function after the introduction of virtual nodes, i.e., the quadratic finite element shape function; Nh is the number of nodes in a quadratic finite element; is the interpolation function The corresponding weight coefficient includes an adjustable coefficient β for controlling the higher-order term, and in this embodiment, β=0.01. For example, if the initial division is into quadrilateral meshes, each finite element unit has 4 nodes, that is, Ne=4; after the introduction of virtual nodes, an 8-node quadrilateral unit is formed, that is, Nh=8.

[0067] Combining formulas (2) and (3), we can get the interpolation function:

[0068]

[0069] The other part of formula (1), the node value is composed of various basis functions p n and the unknown variable a Jn to form; to For example, It can be expressed as:

[0070]

[0071] Considering the calculation accuracy and efficiency, combined with engineering practice, the first-order complete polynomial basis function is selected as the local approximation:

[0072] p J =[1,x,z] (6)

[0073] In this embodiment, a plane where the magneto-electroelastic structure is located is taken as the xoz plane, and a plane rectangular coordinate system is constructed with the direction perpendicular to the plane of the magneto-electroelastic structure as the y-axis; that is, (x, z) are coordinate variables.

[0074] Combining equations (2)-(6), equation (1) can be simplified into matrix form:

[0075]

[0076] In the formula, the matrix N u 、N φ and N ψ By the interpolation function and the basis function p J constitute

[0077] N u =[N1 N1x N1y] (8)

[0078] N φ =[N2 N2x N2y] (9)

[0079] N ψ =[N2 N2x N2y] (10)

[0080]

[0081] N2=[γ1γ2γ3γ4] (12)

[0082] u, φ and ψ are the unknown variables a that need to be solved Jn The vectors describe the responses of the three physical fields respectively.

[0083] S12: Using the weighted residual method, the Galerkin weak form of the dynamic control equation of the magneto-electroelastic material is derived, and then combined with formula (7), the overlapping finite element dynamic discrete model for solving the vibration characteristics of the magneto-electroelastic structure is obtained. The specific steps are as follows:

[0084] The two-dimensional magneto-electroelastic material satisfies the following constitutive relations (i.e., dynamic control equations):

[0085]

[0086] Wherein, σ, D and B represent stress, electric displacement and magnetic induction respectively, S, E and H represent the corresponding strain field, electric field and magnetic field respectively, and C, e, q, ε, m and μ represent elastic, piezoelectric, piezomagnetic, dielectric, magnetoelectric and permeability constants respectively (i.e., the magneto-electroelastic material parameters set in step S1); subscripts i, j, k, l correspond to the x or z axis. For example, when i and j both represent x, σ ij That is σ xx , represents the stress in the x direction. In addition, in formula (15), D i,i Indicates D i Find the partial derivative of i, B i,i Indicates B i Find the partial derivative with respect to i, ρ is the density, is the acceleration.

[0087] In addition, the boundary conditions imposed by the magneto-electroelastic structure are expressed as follows:

[0088]

[0089] In the formula, and represent the applied displacement, electric potential, magnetic potential, traction, charge and magnetic induction boundary conditions, Γ u, Γ φ , Γ ψ , Γ T , Γ E and Γ M is the corresponding boundary.

[0090] Consider a magneto-electroelastic structure with a computational domain of Ω and a boundary of Γ. By combining the test function t with equation (15) and integrating it over Ω, we can obtain the weighted residual formula:

[0091]

[0092] Applying Green's divergence theorem and considering the boundary conditions, we can get:

[0093]

[0094] Then, from formulas (13), (14), (19) and the overlapping finite element discretization format (7), the discrete Galerkin weak form of the governing equations of the two-dimensional magneto-electroelastic dynamics problem based on overlapping finite elements is obtained:

[0095]

[0096] In the formula

[0097] The matrices C, e, q, m, ε, and μ contain the material constants in equation (13), and the gradient matrix B u , B φ and B ψ It is expressed as:

[0098] B u =L u N u , B φ =L φ N φ , B ψ =L ψ N ψ , (twenty one)

[0099]

[0100] The above equation (20) is the set of overlapping finite element dynamic discrete linear equations of the magneto-electroelastic structure.

[0101] S2: For the derived overlapping finite element dynamic discrete linear equations, the static condensation method is used to reduce the degrees of freedom of the linear equations, and an overlapping finite element control equation related only to the displacement field is obtained.

[0102] Furthermore, the specific steps of step S2 are as follows:

[0103] 1) In the free vibration analysis of magneto-electroelastic structure, the external excitation force, i.e. f u =0,f φ =0,f ψ =0, from the second and third equations in equation (20), we get:

[0104]

[0105] Substituting equation (24) into the second equation of equation (20) and equation (23) into the third equation of equation (20), we get:

[0106]

[0107] Substituting formulas (25) and (26) into the first formula of formula (20), we obtain the overlapping finite element control equation:

[0108]

[0109] In the formula

[0110]

[0111] 2) When an external mechanical excitation force is applied to perform harmonic response analysis on the magneto-electroelastic structure, f φ =0,f ψ =0, then the overlapping finite element governing equation is expressed as:

[0112]

[0113] The above equations (27) and (33) are the overlapping finite element governing equations related only to the displacement field.

[0114] S3: By solving the overlapping finite element control equations according to the problem, the natural frequency, modal vibration shape, and displacement harmonic response of the magneto-electroelastic structure can be obtained; the electric potential and magnetic potential response of the structure can be inversely calculated from the obtained displacement harmonic response results to obtain all the results related to the vibration characteristics of the magneto-electroelastic structure.

[0115] Specifically, based on the overlapping finite element control equation (27), the magneto-electro-elastic structure is subjected to free vibration analysis to obtain the natural frequency and modal vibration shape; based on the overlapping finite element control equation (33), the magneto-electro-elastic structure is subjected to harmonic response analysis to obtain the displacement harmonic response, and then the electric potential and magnetic potential response are obtained.

[0116] The following is a detailed description with specific embodiments:

[0117] For a magneto-electroelastic cantilever beam with a fixed support on the left end and a unit harmonic force on the top of the right end, as Figure 2As shown, the beam is 0.3m long, 0.02m wide and 0.001m thick, and the magneto-electroelastic material used is BaTiO3-CoFe2O4, wherein BaTiO3 is a piezoelectric material with a volume ratio of 60%, and CoFe2O4 is a piezomagnetic material with a corresponding volume ratio of 40%. Although the accompanying drawings show exemplary embodiments of the present disclosure, it should be understood that the present disclosure can be used for various two-dimensional magneto-electroelastic structures and should not be limited by the embodiments described herein. The present disclosure can effectively predict the vibration characteristics of various two-dimensional magneto-electroelastic structures (such as beams, plates and other structures, and different magneto-electroelastic materials).

[0118] In S1, first import the finite element mesh of the cantilever beam, using mesh 1: 2×30=60 elements, such as Figure 3 As shown in (a); in addition, the material parameters are determined. The magneto-electroelastic material parameters used in this embodiment are shown in Table 1.

[0119] Table 1 BaTiO3 (60%) -CoFe2O4 (40%) material parameters

[0120]

[0121] Then, according to grid 1, the magnetic field, electric field and displacement field of the magneto-electroelastic structure are discretized based on overlapping finite elements, and combined with the dynamic control equations of the magneto-electroelastic material, an overlapping finite element dynamic discrete model of the structure is derived and constructed, the finite element stiffness and mass matrix of the cantilever beam model are obtained, and the boundary conditions are set according to the model conditions.

[0122] In S2, the static condensation method is used to eliminate the magnetic and electric terms in the equation, and a magneto-electroelastic structure control equation related only to the displacement is obtained.

[0123] In S3, the natural frequency of the magneto-electroelastic material cantilever beam is first solved based on the overlapping finite element method, as shown in Table 2. At the same time, Table 2 also gives the numerical solution and reference solution obtained by the traditional finite element method. For the numerical solution, the grid 2: 8×120=960 units is used, as shown in Table 2. Figure 3 As shown in (b), the reference solution is obtained by using an extremely fine grid. As shown in Table 2, compared with the traditional finite element method, the overlapping finite element method only requires a coarser grid and a shorter time to obtain a more accurate solution. Therefore, the overlapping finite element model proposed in the present invention can realize an efficient analysis of the dynamic characteristics of the magneto-electroelastic structure.

[0124] Table 2 The natural frequencies of the magneto-electroelastic cantilever beam obtained by different methods and the required numerical cost

[0125]

[0126] In addition, the displacement harmonic response of the observation point of the magneto-electroelastic cantilever beam under the action of unit harmonic force is calculated based on the overlapping finite element method, and compared with the traditional finite element method (the results of both methods are based on grid 1), as shown in Figure 4 As shown in (a).

[0127] Then, by applying formulas (25) and (26), the harmonic responses of the two physical fields of magneto-electroelastic structure observation point are calculated, as follows: Figure 4 As shown in (b) and (c) in the figure, it can be seen from the comparison of the curves that the overlapping finite element method is more accurate than the traditional finite element method.

[0128] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting vibration characteristics of magneto-electroelastic structures based on overlapping finite element method, characterized in that: The steps include: Discretizing the physical field variables of the magneto-electroelastic structure based on an overlapping finite element method, wherein the physical field variables include a displacement field, an electric potential field, and a magnetic potential field; The weighted residual method is used to derive the Galerkin weak form of the dynamics control equation of the magneto-electroelastic structure. Combined with the discretized physical field variables, the overlapping finite element dynamics discrete linear equations of the magneto-electroelastic structure are obtained. The static condensation method is used to reduce the degrees of freedom of the overlapping finite element dynamics discrete linear equations and obtain the overlapping finite element control equations. Dynamic analysis is performed based on overlapping finite element governing equations, and the vibration characteristic parameters of the magneto-electroelastic structure are obtained.

2. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 1, characterized in that: Based on the overlapping finite element method, the physical field variables of the magneto-electroelastic structure are discretized and expressed as: Among them, u d , φ, ψ represent the displacement field, electric potential field, and magnetic potential field of the magneto-electroelastic structure, respectively; Nn represents the total number of nodes after the magneto-electroelastic structure is meshed; are node values, representing the displacement, electric potential, and magnetic potential corresponding to node J; γ J Represents the overlapping finite element method interpolation function corresponding to node J.

3. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 2, characterized in that: The overlapping finite element method interpolation function is constructed as follows: Where Ne represents the number of nodes in an overlapping finite element, h I is the finite element method linear unit shape function corresponding to node I; virtual nodes are introduced at the midpoint of each edge of the overlapping finite element to form a secondary unit, is the virtual node construction parameter; Nh is the number of nodes in a quadratic unit, is the finite element method quadratic element shape function corresponding to node i, yes The corresponding weight coefficient.

4. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 3, characterized in that: Overlapping finite element method interpolation function γ corresponding to node J J Specifically: Where K is the node directly connected to node J in the overlapping finite element, β represents the adjustable coefficient, represents the quadratic element shape function corresponding to the virtual node between nodes J and K, h J 、h K They represent the linear element shape functions corresponding to nodes J and K respectively.

5. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 4, characterized in that: The node value is based on the basis function p J and the unknown variable a J It indicates that the basis function adopts a first-order complete polynomial basis function.

6. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 5, characterized in that: The discretized physical field variables are expressed in matrix form: you d =N u u,φ=N φ φ,ψ=N ψ ψ N u =[N1 N1x N1z] N φ =[N2 N2x N2z] N ψ =[N2 N2x N2z] N1=[γ1I e c2I e ...c Nn I e ], N2=[γ1γ2...γ Nn ] Among them, u, φ, and ψ represent the responses of displacement field, electric potential field, and magnetic potential field, respectively, all of which contain unknown variables a J vector; a plane rectangular coordinate system is constructed with the y-axis perpendicular to the plane of the magneto-electroelastic structure, and x and z represent coordinate variables; γ1,γ2…γ Nn They represent the overlapping finite element method interpolation functions corresponding to nodes 1, 2…Nn respectively.

7. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 6, characterized in that: The system of linear equations discretized to determine the overlapping finite element dynamics of the magneto-electroelastic structure includes: The weighted residual method is used to determine the weighted residual formula according to the dynamic control equation of the magneto-electroelastic structure. Then, the Green's divergence theorem is applied, the preset boundary conditions are considered, and the matrix form of the physical field variables after discretization is combined to obtain the overlapping finite element dynamic discrete linear equations of the magneto-electroelastic structure, which can be expressed as: in: Gradient matrix B u , B φ , B ψ It is expressed as: B u =L u N u ,B φ =L φ N φ ,B ψ =L ψ N ψ Where u represents the second-order derivative of u with respect to the time variable, Ω and Γ represent the computational domain and boundary of the magneto-electroelastic structure, respectively. They represent the applied traction, charge, and magnetic induction boundary conditions respectively, ρ represents the density, and the matrices C, e, q, m, ε, and μ correspond to the elastic, piezoelectric, piezomagnetic, dielectric, magnetoelectric, and permeability constants respectively; x, y, and z represent coordinate variables.

8. The magneto-electroelastic structure vibration characteristic prediction method based on overlapping finite element method according to claim 7, characterized in that: When the external excitation force is not considered and the free vibration analysis of the magneto-electroelastic structure is performed, the overlapping finite element control equation is expressed as: Mu+K eq u=0 When an external excitation force is applied to perform harmonic response analysis on the magneto-electroelastic structure, the overlapping finite element control equation is expressed as: Mu+K eq u=f u in:

9. The method for predicting vibration characteristics of a magneto-electroelastic structure based on overlapping finite element method according to any one of claims 1 to 8, characterized in that: Based on the overlapping finite element governing equations, dynamic analysis is performed to obtain the vibration characteristic parameters of the magneto-electroelastic structure, including: Based on the overlapping finite element governing equations, the free vibration analysis of the magneto-electro-elastic structure is carried out to obtain the natural frequency and mode shape of the magneto-electro-elastic structure. Based on the overlapping finite element governing equations, the harmonic response analysis of the magneto-electro-elastic structure is carried out to obtain the displacement harmonic response of the magneto-electro-elastic structure. Then, the electric potential and magnetic potential response of the magneto-electro-elastic structure are obtained according to the displacement harmonic response.

10. A magneto-electro-elastic structure vibration characteristic prediction system based on overlapping finite element method, characterized in that: It includes a processor, which is used to execute the magneto-electroelastic structure vibration characteristic prediction method based on the overlapping finite element method as described in any one of claims 1 to 9.

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