A method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna

Abstract

The present invention discloses a method for analyzing the electrostatic-force-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna. The method comprises the following steps: establishing a geometric model of the three-dimensional low-frequency magnetoelectric antenna and setting material parameters and boundary conditions to establish a finite element model of the three-dimensional low-frequency magnetoelectric antenna; segmenting the finite element model to obtain a cellular structure; constructing an electrostatic-force-magnetostatic coupling equation set based on the cellular structure; wherein the electrostatic-force-magnetostatic coupling equation set includes a piezoelectric constitutive equation, an electrostatic field equation, a mechanical equation of motion, a piezomagnetic constitutive equation, and a static magnetic field equation; and solving the electrostatic-force-magnetostatic coupling equation set using an FDTD algorithm to obtain physical parameters at each position. Based on the physical parameters at each position, the magnetic flux density, radiation efficiency, directivity coefficient, and gain of the three-dimensional low-frequency magnetoelectric antenna are obtained. The present invention can effectively improve the speed and accuracy of electrostatic-force-magnetostatic coupling analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of bulk acoustic wave magnetoelectric antenna simulation, and in particular to a method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna. Background Art

[0002] Bulk acoustic wave magnetoelectric antennas typically employ a magnetoelectric hybrid structure, utilizing the inverse piezoelectric effect to convert electrical signals into acoustic signals, i.e., mechanical resonance. These signals are then converted into radiated waves through the magnetostrictive and magnetoelectric effects, involving mechanisms such as acoustic resonance and ferromagnetic resonance. By rationally utilizing existing mechanisms and designing bulk acoustic wave magnetoelectric antennas with different structures, different operating effects can be achieved, such as dual-band operation. Nan's team at Northeastern University in the United States has developed an acoustically excited magnetoelectric antenna, depositing ferromagnetic and piezoelectric materials in layers on a substrate with a hollowed-out bottom, forming a magnetoelectric heterostructure. This structure utilizes the magnetoelectric effect at acoustic resonance to transmit and receive electromagnetic waves. In 2018, Hwaider's team, building on the bulk acoustic wave magnetoelectric antenna structure proposed by Nan's team, replaced the upper magnetostrictive material with conductive aluminum. Experimental results showed that the replaced model had no obvious resonance peaks, and the transmission and reception parameters at the resonance point were 20dB lower than those of the antenna using a magnetoelectric laminated structure radiating unit. This shows that in the radiation process of the bulk acoustic wave magnetoelectric antenna, the "magnetic current" radiation source generated by the magnetostrictive material is the main radiation source compared to the "electric current" radiation source generated by the piezoelectric material, which also proves that the magnetostrictive layer plays an important role.

[0003] Currently, research on bulk acoustic wave magnetoelectric antennas primarily relies on COMSOL multiphysics simulation software, but this software cannot accurately obtain radiation results, such as radiation efficiency, all at once. Furthermore, the model's long simulation times and low accuracy significantly hinder in-depth research on this type of antenna.

[0004] To solve this problem, in 2015, Yao's team used the constitutive equations of magnetoelectric materials to couple Maxwell's equations with Newton's equations, and used algorithms to intuitively analyze the influence of various parameters on device results, such as stress magnitude. In 2016, Yao's team took into account surface effects and eddy current losses and innovated the algorithm tools, but still needed to construct the radiation model from a field perspective. In 2017, Yao's team proposed an improved implicit finite-difference time-domain algorithm (ADIFDTD). This algorithm uses special boundary conditions to fully consider the effect of demagnetization and has special advantages in dealing with fine details. In 2021, Yao's team continued to consider the dynamic magnetic field problem and modified the ADIFDTD algorithm to more realistically analyze the dynamic working conditions of the bulk acoustic wave magnetoelectric antenna. By applying the finite-difference time-domain algorithm, the team solved the problem of not being able to directly obtain the far-field radiation performance of the bulk acoustic wave magnetoelectric antenna, and gradually considered more actual environmental factors, with higher accuracy. However, such a solution requires high requirements for algorithm writing and solution condition setting, and is labor-intensive, and cannot quickly obtain parameter results for the BAW magnetoelectric antenna. Some university research teams, based on the working principle of the BAW magnetoelectric antenna, use the equivalent substitution method to analyze the output unit area stress value on the magnetostrictive layer to equivalently analyze the relationship between radiation performance and various parameters. Their simulation results qualitatively provide the law of how the radiation performance of the BAW magnetoelectric antenna is affected by parameters, but lack quantitative far-field radiation results and conclusions, which is of little guiding significance for actual processing and testing.

[0005] In summary, while researchers have made some progress in the study of BAW magnetoelectric antennas, their mechanism analysis and model design have primarily relied on theory, validated through physical fabrication, and lacking effective simulation results. While COMSOL multiphysics simulation software can yield constrained BAW magnetoelectric antenna multiphysics models and qualitative conclusions about radiation performance, the results are imprecise and the solution time is lengthy. Therefore, further improvements are urgently needed in the electrostatic-mechanical-magnetostatic coupling analysis of low-frequency magnetoelectric antennas. Summary of the Invention

[0006] In order to solve the technical problems existing in the background technology, the present invention proposes a method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna.

[0007] The present invention proposes a method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna, comprising:

[0008] Establish a three-dimensional geometric model of low-frequency magnetoelectric antenna;

[0009] Set the material parameters and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna;

[0010] Based on the geometric model, material parameters and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna, a finite element model of the three-dimensional low-frequency magnetoelectric antenna is established;

[0011] The 3D low-frequency magnetoelectric antenna finite element model is partitioned using hexahedral meshes to obtain a cellular structure.

[0012] Based on the cellular structure, the electrostatic-mechanical-magnetostatic coupling equations are constructed; the electrostatic-mechanical-magnetostatic coupling equations include the piezoelectric constitutive equation, the electrostatic field equation, the mechanical motion equation, the piezomagnetic constitutive equation, and the static magnetic field equation.

[0013] The FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna;

[0014] According to the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna, the radiation efficiency, directivity coefficient and gain of the three-dimensional low-frequency magnetoelectric antenna are obtained.

[0015] Preferably, the piezoelectric constitutive equation is

[0016]

[0017] Where, is the piezoelectric stress vector, is the piezoelectric strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoelectric stress constant, for The transpose of is the electric field strength, is the electric displacement vector, is the second-order tensor of relative permittivity.

[0018] Preferably, the electrostatic field equation is

[0019] ;

[0020] Where, represents the electric potential, is the electric field strength, is the electric displacement vector, is the Laplace operator.

[0021] Preferably, the mechanical equation of motion is

[0022] ;

[0023] Where, is the strain vector, is a symmetric gradient operator, is the spatial displacement vector, is the density, is the divergence operator, is the stress vector.

[0024] Preferably, the piezomagnetic constitutive equation is

[0025]

[0026] Where, is the piezomagnetic stress vector, is the piezomagnetic strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoresistance constant, for The transpose of is the magnetic field strength, is the magnetic flux density, is the second-order magnetic permeability tensor.

[0027] Preferably, the static magnetic field equation is

[0028] ;

[0029] Where, represents the magnetic potential, is the magnetic field strength; is the magnetic flux density, is the Laplace operator.

[0030] Preferably, the three-dimensional low-frequency magnetoelectric antenna finite element model includes a first magnetostrictive material piezomagnetic layer, an aluminum nitride piezoelectric layer, and a second magnetostrictive material piezomagnetic layer arranged in sequence from top to bottom.

[0031] Preferably, the equation that the aluminum nitride piezoelectric layer needs to satisfy is

[0032] Where, is the piezoelectric stress vector, is the piezoelectric strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoelectric stress constant, for The transpose of is the electric field strength, is the electric displacement vector, is the second-order tensor of relative permittivity, is the spatial displacement vector, represents the electric potential, is the Laplace operator, is the density, is a symmetric gradient operator, is the divergence operator, For time;

[0033] Among them, the equations that the first and second magnetostrictive material piezomagnetic layers need to satisfy are:

[0034]

[0035] Where, is the piezomagnetic stress vector, is the piezomagnetic strain vector, is the second-order tensor of the piezoresistance constant, for The transpose of is the second-order magnetic permeability tensor, is the second-order tensor of elastic constants, is the density, Represents magnetic potential.

[0036] Preferably, the FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the three-dimensional low-frequency magnetoelectric antenna finite element model, specifically including:

[0037] The FDTD algorithm is used to express the differential of space and time variables in differential form, and the calculation is performed directly through the differential equation; when the time step iteration starts, the piezoelectric area is represented by the displacement vector According to the mechanical motion equation, the piezoelectric strain vector is obtained , the piezoelectric strain vector Substitute into the electrostatic field equation to solve for the electric potential , the potential and the piezoelectric strain vector Substituting into the piezoelectric constitutive equation, we can obtain the piezoelectric stress vector , the piezoelectric stress vector Substitute into the mechanical motion equation to get the displacement vector at the next moment ; The displacement vector of the piezomagnetic region is obtained by the boundary conditions , given by the displacement vector According to the mechanical motion equation, the piezomagnetic strain vector is obtained , the piezomagnetic strain vector Substitute into the static magnetic field equation to solve the magnetic potential , the magnetic potential and the piezomagnetic strain vector Substituting into the piezomagnetic constitutive equation, we can obtain the piezomagnetic stress vector , the piezomagnetic stress vector Substitute into the mechanical motion equation to obtain the displacement vector at the next moment , and then iteratively calculates over time until the preset time is reached.

[0038] Preferably, the calculation formula for magnetic flux density is

[0039] ;

[0040] Where, is the magnetic flux density, is the piezomagnetic strain vector, is the second-order tensor of the piezoresistance constant, is the magnetic field strength, is the second-order magnetic permeability tensor.

[0041] Preferably, the calculation formula of the radiation power P is

[0042] ;

[0043] Among them, the radiation efficiency The calculation formula is

[0044] ;

[0045] Among them, the directivity coefficient The calculation formula is

[0046] ;

[0047] Among them, the calculation formula of gain G is

[0048] ;

[0049] Where, is the free space wave impedance, is the operating frequency, is the piezomagnetic coefficient, is the stress amplitude in the piezoresistance layer, is the cross-sectional area, is the wave number when the piezomagnetic layer resonates, is the thickness of the piezomagnetic material, is the radiation efficiency, is the input power, is the angle.

[0050] In the present invention, the proposed method for analyzing the electrostatic-force-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna is constructed by constructing a finite element model of the three-dimensional low-frequency magnetoelectric antenna, performing a hexahedral decomposition on the finite element model of the three-dimensional low-frequency magnetoelectric antenna, and constructing an electrostatic-force-magnetostatic coupling equation group based on the cellular structure obtained by the decomposition; wherein the electrostatic-force-magnetostatic coupling equation group includes a piezoelectric constitutive equation, an electrostatic field equation, a mechanical equation of motion, a piezomagnetic constitutive equation, and a static magnetic field equation; the electrostatic-force-magnetostatic coupling equation group is solved using an FDTD algorithm to obtain the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna; thereby facilitating the calculation of the magnetic flux density, radiation efficiency, directivity coefficient, and gain of the three-dimensional low-frequency magnetoelectric antenna based on the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna. The present invention can effectively improve the calculation speed and accuracy of the calculation results of the electrostatic-force-magnetostatic coupling analysis of the electrostatic-force-magnetostatic coupling analysis, and is more conducive to handling complex problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a flow chart of a method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna in an example proposed by the present invention.

[0052] Figure 2 This is a schematic structural diagram of a finite element model of a three-dimensional low-frequency magnetoelectric antenna in an example proposed by the present invention.

[0053] Figure 3 A schematic diagram of the antenna magnetic flux density of a three-dimensional low-frequency magnetoelectric antenna finite element model in an example proposed by the present invention. DETAILED DESCRIPTION

[0054] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0055] Reference Figure 1 The present invention proposes a method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna, comprising:

[0056] Establish a three-dimensional geometric model of low-frequency magnetoelectric antenna;

[0057] Set the material parameters and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna;

[0058] Based on the geometric model, material parameters and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna, a finite element model of the three-dimensional low-frequency magnetoelectric antenna is established;

[0059] The 3D low-frequency magnetoelectric antenna finite element model is partitioned using hexahedral meshes to obtain a cellular structure.

[0060] Based on the cellular structure, the electrostatic-mechanical-magnetostatic coupling equations are constructed; the electrostatic-mechanical-magnetostatic coupling equations include the piezoelectric constitutive equation, the electrostatic field equation, the mechanical motion equation, the piezomagnetic constitutive equation, and the static magnetic field equation.

[0061] The FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna;

[0062] According to the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna, the magnetic flux density, radiation efficiency, directivity coefficient and gain of the three-dimensional low-frequency magnetoelectric antenna are obtained.

[0063] Finite element method (FEM) and finite difference method are commonly used in existing technologies to solve complex mathematical models. The finite element method divides the solution area into interconnected and non-overlapping units, uses basis functions to approximate the solution in each unit, and constructs the final solution through the approximate solutions of these units in the entire area. In contrast, the finite difference method divides the computational domain into a grid, with a finite number of nodes representing the continuous computational domain. The accuracy of the finite difference method depends only on the mesh completeness condition, while the finite element method requires additional supplementary conditions to ensure convergence. In addition, the upper bound of the discretization error of the finite difference method is usually lower than the upper bound of the discretization error achieved by the approximation theorem used in the accuracy analysis of the finite element method. In the finite difference time domain (FDTD) algorithm, the field components are updated by differencing the time and space variables. This method directly uses the difference equation for calculation, avoiding the need to solve the matrix inverse problem, thereby simplifying the calculation process.

[0064] In the specific implementation of the present invention, a three-dimensional low-frequency magnetoelectric antenna finite element model is constructed, and the three-dimensional low-frequency magnetoelectric antenna finite element model is hexahedron-decomposed, and an electrostatic-force-magnetostatic coupling equation group is constructed based on the cellular structure obtained by the decomposition; wherein, the electrostatic-force-magnetostatic coupling equation group includes a piezoelectric constitutive equation, an electrostatic field equation, a mechanical motion equation, a piezomagnetic constitutive equation and a static magnetic field equation; the electrostatic-force-magnetostatic coupling equation group is solved using the FDTD algorithm to obtain the physical parameters of each position in the three-dimensional low-frequency magnetoelectric antenna finite element model; thereby facilitating the calculation of the magnetic flux density, radiation efficiency, directivity coefficient and gain of the three-dimensional low-frequency magnetoelectric antenna based on the physical parameters of each position in the three-dimensional low-frequency magnetoelectric antenna finite element model.

[0065] The design of magnetoelectric antennas typically involves more than just the coupling of multiple physical fields, such as mechanical and thermal fields, but also electromagnetic fields. This invention adds a new physical field, the magnetic field, to the existing multi-physics electro-mechanical coupling equations to precisely describe the physical properties and operating principles of magnetoelectric antennas. However, the addition of the magnetic field complicates the multi-physics coupling and imposes stricter time step restrictions. To address this issue, the present invention further constructs an electrostatic-mechanical-magnetostatic coupling equation set to accurately describe the physical properties and operating principles of magnetoelectric antennas. This facilitates optimization of magnetoelectric antenna design while also enabling adjustments to the magnetoelectric antenna's geometry and material selection based on specific design requirements (such as frequency response, bandwidth, and gain), thereby improving magnetoelectric antenna performance. This transforms complex electromagnetic field problems into a form that can be efficiently solved using numerical methods. This makes predicting magnetoelectric antenna performance in practical engineering more feasible and efficient, effectively improving both the computational speed and accuracy of electrostatic-mechanical-magnetostatic coupling analysis, and further facilitating the handling of complex problems. The present invention simultaneously considers these physical effects, providing a more comprehensive analysis of the magnetoelectric antenna's overall performance.

[0066] In this embodiment, the piezoelectric constitutive equation is Where, is the piezoelectric stress vector, is the piezoelectric strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoelectric stress constant, for The transpose of is the electric field strength, is the electric displacement vector, is the second-order tensor of relative permittivity.

[0067] In this embodiment, the electrostatic field equation is ;

[0068] Where, is the electric potential, is the electric field strength, is the electric displacement vector, is the Laplace operator.

[0069] In this embodiment, the mechanical motion equation is ;in, ;

[0070] Where, is the strain vector, is a symmetric gradient operator, is the spatial displacement vector, is the density, is the divergence operator, is the stress vector, For time.

[0071] In this embodiment, the piezomagnetic constitutive equation is Where, is the piezomagnetic stress vector, is the piezomagnetic strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoresistance constant, is the magnetic field strength, is the magnetic flux density vector, is the second-order magnetic permeability tensor.

[0072] In this embodiment, the static magnetic field equation is ;

[0073] Where, is the magnetic potential, is the magnetic field strength, is the magnetic flux density vector, is the Laplace operator.

[0074] like Figure 2 As shown, in this embodiment, the three-dimensional low-frequency magnetoelectric antenna finite element model is divided into three layers, from top to bottom: a first magnetostrictive material piezomagnetic layer, an aluminum nitride (AlN) piezoelectric layer, and a second magnetostrictive material piezomagnetic layer.

[0075] Among them, the piezoelectric region needs to satisfy the electrostatic field equation, piezoelectric constitutive equation and mechanical motion equation; the piezomagnetic region needs to satisfy the static magnetic field equation, piezomagnetic constitutive equation and mechanical motion equation.

[0076] The equation that the piezoelectric material region (piezoelectric layer) in this embodiment needs to satisfy is The equation that the piezomagnetic material region (piezomagnetic layer) in this embodiment needs to satisfy is Among them, the physical parameters of each position include displacement , electric potential , the piezoelectric stress vector in the piezoelectric region , the piezoelectric strain vector of the piezoelectric region and the piezomagnetic stress vector in the piezomagnetic region , the piezomagnetic strain vector of the piezomagnetic region , magnetic potential .

[0077] In this embodiment, the FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna, including:

[0078] The FDTD algorithm is used to express the differential of space and time variables in differential form, and the calculation is performed directly through the differential equation; when the time step iteration starts, the piezoelectric area is represented by the displacement vector According to the mechanical motion equation, the piezoelectric strain vector is obtained , the piezoelectric strain vector Substitute into the electrostatic field equation to solve for the electric potential , the potential and the strain tensor Substituting into the piezoelectric constitutive equation, we can obtain the piezoelectric stress vector , the piezoelectric stress vector Substitute into the mechanical motion equation to obtain the displacement vector at the next moment ; The displacement vector of the piezomagnetic region is obtained by the boundary conditions , given by the displacement vector According to the mechanical motion equation, the piezomagnetic strain vector is obtained , the piezomagnetic strain vector Substitute into the static magnetic field equation to solve the magnetic potential , the magnetic potential and the piezomagnetic strain vector Substituting into the piezomagnetic constitutive equation, we can obtain the piezomagnetic stress vector , the piezomagnetic stress vector Substitute into the mechanical motion equation to obtain the displacement vector at the next moment , and then iteratively calculates over time until the preset time is reached.

[0079] It's important to understand that magnetic flux density refers to the strength of the magnetic field at a specific point when an antenna radiates or receives electromagnetic waves. It's a key parameter in electromagnetic field theory, often used to describe the propagation characteristics of electromagnetic waves.

[0080] Radiation efficiency refers to the ratio of the antenna's radiated power to its input active power, and its value ranges from 0 to 1.

[0081] The directivity coefficient is used to evaluate the degree of energy concentration of an antenna in a certain radiation direction.

[0082] Gain is used to measure the ability of an antenna to radiate electromagnetic wave signals in a specific direction. The greater the gain, the longer the radiation distance.

[0083] The polarization of an antenna is an indicator used to describe the vector space direction of the electromagnetic field. Common antenna polarization modes include linear polarization, circular polarization, and elliptical polarization.

[0084] The calculation formula for magnetic flux density is: ;

[0085] Where, is the magnetic flux density, is the piezomagnetic strain vector, is the second-order tensor of the piezoresistance constant, is the magnetic field strength, is the second-order magnetic permeability tensor.

[0086] Among them, the calculation formula of radiation power P is ;

[0087] Among them, the radiation efficiency The calculation formula is ;

[0088] Among them, the directivity coefficient The calculation formula is ;

[0089] Among them, the gain The calculation formula is ;

[0090] Where, is the free space wave impedance, is the operating frequency, is the piezomagnetic coefficient, is the stress amplitude in the piezoresistance layer, is the cross-sectional area, is the wave number when the piezomagnetic layer resonates, is the thickness of the piezomagnetic material, is the radiation efficiency, is the input power, is the angle.

[0091] In one specific embodiment, the thickness of the first magnetostrictive material piezomagnetic layer 1 of the three-dimensional low-frequency magnetoelectric antenna finite element model is 1 mm, the thickness of the aluminum nitride (AlN) piezoelectric layer 2 is 1 mm, and the thickness of the second magnetostrictive material piezomagnetic layer 3 is 1 mm. Through COMSOL simulation, the operating frequency of the three-dimensional low-frequency magnetoelectric antenna finite element model is 228 kHz, and the magnetic flux density obtained is as follows: Figure 3 shown.

[0092] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna, characterized in that: include: Establish a three-dimensional geometric model of low-frequency magnetoelectric antenna; Set the material parameters and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna; A finite element model of the three-dimensional low-frequency magnetoelectric antenna is established based on the geometric model, material parameters, and boundary conditions of the three-dimensional low-frequency magnetoelectric antenna. The finite element model includes a first piezomagnetic layer of magnetostrictive material, an aluminum nitride piezoelectric layer, and a second piezomagnetic layer of magnetostrictive material, arranged in order from top to bottom. The 3D low-frequency magnetoelectric antenna finite element model is partitioned using hexahedral meshes to obtain a cellular structure. Based on the cellular structure, the electrostatic-mechanical-magnetostatic coupling equations are constructed; the electrostatic-mechanical-magnetostatic coupling equations include the piezoelectric constitutive equation, the electrostatic field equation, the mechanical motion equation, the piezomagnetic constitutive equation, and the static magnetic field equation. The FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna; According to the physical parameters of each position in the finite element model of the three-dimensional low-frequency magnetoelectric antenna, the magnetic flux density, radiation efficiency, directivity coefficient and gain of the three-dimensional low-frequency magnetoelectric antenna are obtained.

2. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The piezoelectric constitutive equation is Where, is the piezoelectric stress vector, is the piezoelectric strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoelectric stress constant, for The transpose of is the electric field strength, is the electric displacement vector, is the second-order tensor of relative permittivity.

3. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The electrostatic field equation is Where, represents the electric potential, is the electric field strength, is the electric displacement vector, is the Laplace operator.

4. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, wherein: The mechanical equation of motion is Where, is the strain vector, is a symmetric gradient operator, is the spatial displacement vector, is the density, is the divergence operator, is the stress vector.

5. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The piezomagnetic constitutive equation is Where, is the piezomagnetic stress vector, is the piezomagnetic strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoresistance constant, for The transpose of is the magnetic field strength, is the magnetic flux density vector, is the second-order magnetic permeability tensor.

6. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The static magnetic field equation is Where, represents the magnetic potential, is the magnetic field strength; is the magnetic flux density, is the Laplace operator.

7. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The equation that the aluminum nitride piezoelectric layer needs to satisfy is Where, is the piezoelectric stress vector, is the piezoelectric strain vector, is the second-order tensor of elastic constants, is the second-order tensor of the piezoelectric stress constant, for The transpose of is the electric field strength, is the electric displacement vector, is the second-order tensor of relative permittivity, is the spatial displacement vector, represents the electric potential, is the Laplace operator, is the density, is a symmetric gradient operator, is the divergence operator, For time; Among them, the equations that the first and second magnetostrictive material piezomagnetic layers need to satisfy are: Where, is the piezomagnetic stress vector, is the piezomagnetic strain vector, is the second-order tensor of the piezoresistance constant, for The transpose of is the second-order magnetic permeability tensor, is the second-order tensor of elastic constants, is the density, Represents magnetic potential.

8. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, wherein: The FDTD algorithm is used to solve the electrostatic-mechanical-magnetostatic coupling equations to obtain the physical parameters of each position in the 3D low-frequency magnetoelectric antenna finite element model, including: The FDTD algorithm is used to express the differential of space and time variables in differential form, and the calculation is performed directly through the differential equation; when the time step iteration starts, the piezoelectric area is represented by the displacement vector According to the mechanical motion equation, the piezoelectric strain vector is obtained , the piezoelectric strain vector Substitute into the electrostatic field equation to solve for the electric potential , the potential and the piezoelectric strain vector Substituting into the piezoelectric constitutive equation, we can obtain the piezoelectric stress vector , the piezoelectric stress vector Substitute into the mechanical motion equation to obtain the displacement vector at the next moment ; The displacement vector of the piezomagnetic region is obtained by the boundary conditions , given by the displacement vector According to the mechanical motion equation, the piezomagnetic strain vector is obtained , the piezomagnetic strain vector Substitute into the static magnetic field equation to solve the magnetic potential , the magnetic potential and the piezomagnetic strain vector Substituting into the piezomagnetic constitutive equation, we can obtain the piezomagnetic stress vector , the piezomagnetic stress vector Substitute into the mechanical motion equation to obtain the displacement vector at the next moment , and then iteratively calculates over time until the preset time is reached.

9. The method for analyzing the electrostatic-mechanical-magnetostatic coupling characteristics of a three-dimensional low-frequency magnetoelectric antenna according to claim 1, characterized in that: The calculation formula for magnetic flux density is: ; Where, is the magnetic flux density, is the piezomagnetic strain vector, is the second-order tensor of the piezoresistance constant, is the magnetic field strength, is the second-order tensor of magnetic permeability; The calculation formula for radiation efficiency is: ; Where, is the free space wave impedance, is the operating frequency, is the piezomagnetic coefficient, is the stress amplitude in the piezoresistance layer, is the cross-sectional area, is the wave number when the piezomagnetic layer resonates, is the thickness of the piezomagnetic material, is the radiation efficiency, is the input power, is the radiated power, is the angle; The calculation formula of the directivity coefficient is: ; Where, is the directivity coefficient, is the wave number when the piezomagnetic layer resonates, is the thickness of the piezomagnetic material; The calculation formula of gain is: ; Where, For gain, is the radiation efficiency, is the directivity coefficient.

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