Micro electro mechanical system performance optimization method based on anisotropic elastic waves of wave function

Abstract

The invention discloses a wave function-based anisotropic elastic wave micro-electro-mechanical system performance optimization method, which comprises the following steps of: establishing an anisotropic elastic wave differential system model of a microstructure and a thin film material in a micro-electro-mechanical system, and performing grid discrete division on the model to obtain a plurality of convex sub-regions; constructing a local solution in a wave function form, and performing solution parameter estimation by applying a weighted residual formula; an elastic modulus approximate solution is obtained, and numerical simulation is completed; and finally, on the basis of a numerical simulation result, an optimization algorithm is adopted to enable the system performance parameter index to be optimal. The method is based on semi-analytical calculation, programming is simple, parametric modeling is flexible, calculation efficiency is high, and compared with a traditional finite difference method, the method has higher precision and stability. The key point of the method lies in accurate vector field discretization and grid structure optimization, multi-frequency modulus calculation can be rapidly coped with, and research results can provide reference for practical problems such as device design and performance improvement.

Description

Technical Field

[0001] The invention belongs to the technical field of micro-electromechanical systems, and in particular relates to a micro-electromechanical system performance optimization method based on anisotropic elastic waves of wave functions. Background Art

[0002] Anisotropic elastic wave calculation and simulation based on wave function mainly involves the computational simulation of elastic wave propagation characteristics in complex media, and has wide applications in geophysics, materials science, nondestructive testing, micro-electromechanical systems and other fields. The microstructures and thin film materials in micro-electromechanical systems have anisotropic mechanical and elastic properties. Traditional performance optimization methods are mostly based on macroscopic and isotropic assumptions, which are difficult to accurately describe physical phenomena at the microscopic scale. Therefore, there is an urgent need for a method that can optimize the performance of micro-electromechanical systems (MEMS) based on numerical simulation of anisotropic elastic waves. In order to numerically calculate the wave equation of elastic wave propagation in anisotropic media, the continuous wave equation needs to be discretized into a differential equation or an integral equation. Commonly used traditional methods include finite difference method (FDM), finite element method (FEM) or spectral element method (SEM). These methods have their own advantages and disadvantages, and the choice should be based on the complexity of the specific problem and the computing resources. At the same time, traditional numerical methods generally cannot obtain accurate analytical solutions, and often have complex algorithms, large calculations and poor stability. The wave function method can often give a clear mathematical expression of the solution, which can describe the propagation characteristics of elastic waves more accurately, making the problem-solving process clearer and more systematic. This clear mathematical expression is not only easy to understand and analyze, but also provides a solid foundation for subsequent numerical calculations and simulations. In particular, in some cases with regular geometric shapes and uniform medium characteristics, accurate analytical solutions can be obtained with high calculation accuracy and stability.

[0003] In summary, studying the calculation and numerical simulation of elastic waves under complex media and boundary conditions using the wave function method to optimize the performance of MEMS systems is an urgent problem that needs to be solved and has important research value. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a micro-electromechanical system performance optimization method based on anisotropic elastic waves of wave functions, which can better optimize the performance of the MEMS system.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions, comprising the following steps:

[0006] S1. Based on the anisotropic elastic constants of the microstructure materials in the MEMS, an anisotropic elastic wave differential system model of the microstructure and thin film materials in the MEMS is established, and the model is meshed and discretized to obtain a number of convex sub-regions;

[0007] S2. Construct the local solution of the anisotropic elastic wave equation in each convex sub-region in the form of wave function, and use the weighted residual formula to estimate the parameters of the solution to obtain the wave field value at each moment;

[0008] S3. Determine the calculation area of ​​each grid according to the vector field value, partition it and perform integral calculation on the partition boundary data to complete the anisotropic elastic wave calculation and numerical simulation calculation;

[0009] S4. Based on the numerical simulation results, an optimization algorithm is used to obtain the optimal parameter indicators of system performance.

[0010] Furthermore, in the aforementioned step S1, the anisotropic elastic constants of the microstructure material in the micro-electromechanical system include: values ​​of the elastic modulus in different directions, density, and Poisson's ratio;

[0011] Furthermore, in the aforementioned step S1, the model is grid-discretely divided to obtain a number of convex sub-regions, and the convex sub-regions are characterized in that the computational domain is divided into non-overlapping convex sub-domains to ensure that the boundaries The two adjacent sub-regions Ω (α) and Ω (β) The compatibility of displacement and stress, imposing boundary continuity conditions, ensures the convergence of the constructed wave function:

[0012]

[0013] Among them, u n (x) = u 1 n 1 +u 2 n 2 ,u τ (x) = u 1 τ 1 +u 2 τ 2 , n=(n 1 ,n 2 ) T and τ=(τ 1 ,τ 2 ) T =(n 2 ,-n 1 ) T Represent the normal vector and tangent vector of the boundary, u 1 and u 2 They are x 1 and x 2Displacement in the direction; t n (x) = t 1 n 1 +t 2 n 2 , t τ (x) = t 1 τ 1 +t 2 τ 2 , t 1 =σ 11 n 1 +σ 12 n 2 , t 2 =σ 21 n 1 +σ 22 n 2 , σ ij (i,j=1,2) are stress field components.

[0014] Furthermore, in the aforementioned step S2, in each convex subregion, the domain variables are approximately represented by the following four groups of basis functions, which are represented by superscripts a, b, c and d:

[0015]

[0016] in, and is the wave function; and is the unknown contribution factor of the wave function to be determined; and is the number of wave functions.

[0017] Furthermore, in the aforementioned step S2, the wave function is the product of the trigonometric function and the preset unknown function, which is in the following four forms:

[0018]

[0019] in, and is about the variable x 2 The unknown function of is about the variable x 1 The unknown function of and Represents the convex domain Ω (α) The minimum rectangular box size.

[0020] Furthermore, in the aforementioned step S2, the weighted residual formula is used to estimate the parameters of the solution to obtain the wave field value at each moment, as shown in the following formula:

[0021]

[0022] in, m=1,2,…,n (α) , n=(n 1 ,n 2 ) T and τ=(τ 1 ,τ 2 ) T =(n 2 ,-n 1 ) T denote the normal vector and tangent vector of the boundary respectively; · denotes superscript a, b, c, d.

[0023] Furthermore, in the aforementioned step S3, the calculation area of ​​each grid is determined according to the vector field value, partitioned, and the partition boundary data is integrally calculated, as follows:

[0024] Du=0 (7)

[0025]

[0026] Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency,

[0027] get:

[0028] in, δ 2 =2C 11 C 26 -2C 12 C 16 , δ 4 =2C 22 C 16 -2C 12 C 26 , δ 6 =(C 11 +C 66 )ρω 2 , δ 7 =2(C 16 +C 26 )ρω 2 , δ 8 =(C 22 +C 66 )ρω 2 and δ 9 =ρ 2 ω 4 ;

[0029] The following approximate solution and basis function are obtained to complete the elastic wave numerical simulation.

[0030]

[0031] in,

[0032]

[0033]

[0034] and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound of the unknown coefficient subscript, Represents an imaginary unit.

[0035] Furthermore, the expression characteristics of the wave function in the aforementioned anisotropic elastic wave numerical simulation system include truncation of the infinite basis function. When simulating elastic waves in the calculation area, the number of truncation terms k of the wave function is calculated by the following formula:

[0036]

[0037] in,

[0038] D 1 (θ)=[(C 11 -C 66 )cos 2 θ+(C 22 -C 66 )sin 2 θ] 2 -4Θcos 2 θsin 2 θ,

[0039] D 2 (θ) = C 11 C 66 cos 4 θ+C 22 C 66 sin 4 θ+[(C 11 +C 22 )C 66 +Θ]cos 2 θsin 2 θ,

[0040] Θ=(C 11 -C 66 )(C 22 -C 66)-(C 12 +C 66 ) 2 , θ is the angle of incidence.

[0041] Furthermore, the aforementioned method for optimizing the performance of a MEMS based on anisotropic elastic waves of wave functions substitutes the simulation system on a rectangular area into the elastic system equation for calculation to obtain the elastic stress results and vector field values ​​at each moment.

[0042] Furthermore, the aforementioned optimization algorithm includes one of a genetic algorithm and a particle swarm optimization algorithm.

[0043] Compared with the prior art, the beneficial technical effects of the above technical solution adopted by the present invention are as follows: In quantum mechanics, the wave function is a function of space and time, and is a complex function, which can be expressed as Ψ=Ψ(x, y, z, t). In the study of elastic wave calculation, the wave function can be used to describe the propagation state of elastic waves in the medium, including its amplitude, phase, frequency and other characteristics. The wave function calculation method in the square calculation area on the two-dimensional plane provided by the present invention is solved and numerically simulated based on the following method:

[0044] Establish the wave equation: Establish the corresponding wave equation based on the boundary characteristics of the square area, the elastic wave propagation characteristics and the medium properties.

[0045] Select the wave function form: According to the characteristics of the wave equation and the solution requirements, select the appropriate wave function form for expansion. The product form of the sine and cosine functions and the metric function is used in the present invention.

[0046] Solving the wave equation: Using wave function expansion technology and the method of undetermined parameters, the wave equation is solved to obtain the analytical solution of elastic waves.

[0047] Verification and error analysis: Use the weighted residual formula to perform error analysis to verify and analyze the solution results, discuss the influence of different parameters (such as different frequencies, etc.) on the propagation characteristics of elastic waves, perform numerical simulation, and compare with traditional methods (such as finite element, etc.).

[0048] It can be seen from the above description that the method provided by the present invention can accurately and stably express and numerically simulate elastic wave field values. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic flow chart of the method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves according to the present invention.

[0050] Figure 2 A diagram describing the problem for a square area.

[0051] Figure 3 Figure 2 is the WBM convergence curve diagram of displacement and stress at different frequencies in the square area; Figure (a) is the WBM convergence curve diagram of displacement at different frequencies, and (b) is the WBM convergence curve diagram of stress at different frequencies.

[0052] Figure 4 Figure 2 shows the stress contour map generated by WBM in the square area and the exact solution result map at different frequencies. (a) is the stress contour map generated by WBM at 2kHz, (b) is the exact solution result map at 2kHz, (c) is the stress contour map generated by WBM at 10.5kHz, (d) is the exact solution result map at 10.5kHz, (e) is the stress contour map generated by WBM at 15kHz, and (f) is the exact solution result map at 15kHz. DETAILED DESCRIPTION

[0053] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings.

[0054] Various aspects of the invention are described herein with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the invention are not limited to those described in the accompanying drawings. It should be understood that the invention is implemented by any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in the invention are not limited to any implementation. In addition, some aspects disclosed in the invention may be used alone or in any appropriate combination with other aspects disclosed in the invention.

[0055] refer to Figure 1 The present invention provides a method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions, comprising the following steps:

[0056] S1. Based on the anisotropic elastic constants of the microstructure materials in the MEMS, an anisotropic elastic wave differential system model of the microstructure and thin film materials in the MEMS is established, and the model is meshed and discretized to obtain a number of convex sub-regions;

[0057] S2. Construct the local solution of the anisotropic elastic wave equation in each convex sub-region in the form of wave function, and use the weighted residual formula to estimate the parameters of the solution to obtain the wave field value at each moment;

[0058] S3. Determine the calculation area of ​​each grid according to the vector field value, partition it and perform integral calculation on the partition boundary data to complete the anisotropic elastic wave calculation and numerical simulation calculation;

[0059] S4. Based on the numerical simulation results, an optimization algorithm is used to obtain the optimal parameter indicators of system performance.

[0060] In step S1, specifically, by querying the material database, basic parameters such as anisotropic elastic constants (such as the values ​​of elastic modulus in different directions), density, Poisson's ratio, etc. of the microstructure materials in MEMS are obtained. According to the background conditions of the problem, data, elastic wave theory and the characteristics of anisotropic media, an elastic wave equation suitable for anisotropic media is constructed.

[0061] For non-convex domain division, the computational domain is divided into non-overlapping convex sub-domains to ensure the boundary The two adjacent sub-regions Ω (α) and Ω (β) The compatibility of displacement and stress, imposing boundary continuity conditions:

[0062]

[0063] Among them, u n (x) = u 1 n 1 +u 2 n 2 ,u τ (x) = u 1 τ 1 +u 2 τ 2 , n=(n 1 ,n 2 ) T and τ=(τ 1 ,τ 2 ) T =(n 2 ,-n 1 ) T Represent the normal vector and tangent vector of the boundary, u 1 and u 2 They are x 1 and x 2 Displacement in the direction; t n (x) = t 1 n 1 +t 2 n 2 , t τ (x) = t 1 τ 1 +t 2 τ 2 , t 1 =σ 11 n 1 +σ 12 n 2 , t 2 =σ 21 n 1 +σ 22 n 2 , σij (i,j=1,2) are stress field components.

[0064] In step S2, a local solution of the anisotropic elastic wave equation in each sub-region is constructed in the form of a wave function, and the parameters of the solution are estimated using a weighted residual formula to obtain the wave field value at each moment.

[0065] Specifically, in each subdomain Ω (α) In the above formula, the domain variables are approximately represented by the following four sets of basis functions, which are represented by superscripts a, b, c and d:

[0066]

[0067] in, and is the wave function; and is the unknown contribution factor of the wave function to be determined; and is the number of wave functions.

[0068] The local solution is expressed in the form of a wave function on the convex subcomputation region, while satisfying the control equation, avoiding the computational divergence problem after regional discretization in traditional algorithms. Specifically, assuming that the wave function is the product of a trigonometric function and a part of the preset unknown function, it is often expressed in the following four forms:

[0069]

[0070] in, and is about the variable x 2 The unknown function of is about the variable x 1 The unknown function of and Represents the convex domain Ω (α) The minimum rectangular box size.

[0071] For each subdomain Ω (α) , using the weighted function and Minimize the residual:

[0072]

[0073] in, m=1,2,…,n (α) , n=(n 1 ,n 2 ) T and τ=(τ 1 ,τ2 ) T =(n 2 ,-n 1 ) T denote the normal vector and tangent vector of the boundary respectively; · denotes superscript a, b, c, d.

[0074] Step S3, determining the calculation area of ​​each grid point according to the vector field value, partitioning and performing integral calculation on the partition boundary data, and completing the anisotropic elastic wave calculation and numerical simulation.

[0075] Specifically, the anisotropic elastic equation is processed and all wave field values ​​in the calculation area of ​​each grid point are decomposed:

[0076] Du=0

[0077]

[0078] Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency,

[0079] So, we get:

[0080] in, δ 2 =2C 11 C 26 -2C 12 C 16 , δ 4 =2C 22 C 16 -2C 12 C 26 , δ 6 =(C 11 +C 66 )ρω 2 , δ 7 =2(C 16 +C 26 )ρω 2 , δ 8 =(C 22 +C 66 )ρω 2 and δ 9 =ρ 2 ω 4 ;

[0081] The following approximate solution and basis function are obtained to complete the elastic wave numerical simulation:

[0082]

[0083] in,

[0084]

[0085] and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound of the unknown coefficient subscript, Represents an imaginary unit.

[0086] The expression characteristics of the wave function in the anisotropic elastic wave numerical simulation system include truncation of the infinite basis function. For the convenience of numerical implementation, when simulating elastic waves in the calculation area, the number of wave function truncation terms k is calculated by the following formula:

[0087]

[0088] in,

[0089] D 1 (θ)=[(C 11 -C 66 )cos 2 θ+(C 22 -C 66 )sin 2 θ] 2 -4Θcos 2 θsin 2 θ,

[0090] D 2 (θ) = C 11 C 66 cos 4 θ+C 22 C 66 sin 4 θ+[(C 11 +C 22 )C 66 +Θ]cos 2 θsin 2 θ,

[0091] Θ=(C 11 -C 66 )(C 22 -C 66 )-(C 12 +C 66 ) 2 , θ is the angle of incidence.

[0092] Specifically, a square area is taken as an example to illustrate the accuracy and efficiency of the method.

[0093] Material properties: E 1 =161.3GPa, E 2 =8.82GPa, G 12 =5.331GPa, v 12 =0.33,ρ=1580kg / m 3

[0094] The boundary conditions are:

[0095]

[0096] in, The exact solution is derived as follows:

[0097] Function f(x 1 ) can be expressed in the following Fourier form:

[0098]

[0099] In order to obtain an exact solution, we first consider the following boundary conditions:

[0100]

[0101] Among them, Γ 1 , Γ 2 , Γ 3 and Γ 4 like Figure 2 As shown, the displacement of the problem with boundary conditions can be expressed as:

[0102]

[0103] Among them, Λ i (i=1,2,3,4) are unknown coefficients.

[0104] stress and The relationship can be used to obtain:

[0105]

[0106]

[0107] Figure 3 The WBM convergence curves of displacement (left) and stress (right) at 4, 14.5 and 25kHz. In order to verify that WBM can accurately characterize the vibration characteristics of anisotropic materials, the stress contours and their exact solutions generated by WBM at 2, 10.5 and 15kHz are plotted, as shown in Figure 2. Figure 4As shown in the figure, (a) is the stress contour map generated by WBM at 2kHz, (b) is the exact solution result map at 2kHz, (c) is the stress contour map generated by WBM at 10.5kHz, (d) is the exact solution result map at 10.5kHz, (e) is the stress contour map generated by WBM at 15kHz, and (f) is the exact solution result map at 15kHz.

[0108] It can be seen from the above description that the method provided by the present invention can accurately express the wave vector and stress calculation results of the plane calculation area under different frequency parameters, and improve the accuracy of numerical simulation.

[0109] Step S4 uses an optimization algorithm based on the numerical simulation results to optimize the system performance parameter indicators. When optimizing the performance of the micro-electromechanical system based on numerical simulation, the algorithm adopted is the particle swarm optimization algorithm. The specific steps are as follows: Step 1: Initialization

[0110] (1) Population initialization: Randomly initialize the position and velocity of each particle in the particle swarm. The position is usually randomly generated in the solution space of the problem, and the velocity is also randomly set within a certain range.

[0111] (2) Initialization of individual optimal solution and global optimal solution: For each particle, its initial position is set as the individual optimal position, and then the one with the best fitness is selected from the individual optimal positions of all particles as the global optimal position. The fitness here is calculated based on the standard function and is used to measure the quality of the solution.

[0112] Step 2: Update speed and position

[0113] (1) Speed ​​update formula:

[0114] v i (t+1)=ω×v i (t)+c 1 × 1 ×(pbest i -x i (t))+c 2 × 2 ×(gbest-x i (t))

[0115] Among them, v i (t) is the velocity of particle i at time t, v i (t+1) is the velocity at the next moment; ω is the inertia weight, which is used to balance the global and local search capabilities of the particle; c 1 and c 2 are learning factors, which represent the particle’s ability to learn from its own experience and group experience; r 1 and r2 is a random number between [0,1]; pbest i is the individual optimal position of particle i, x i (t) is the position of particle i at time t, and gbest is the global optimal position.

[0116] (2) Position update formula:

[0117] x i (t+1)=x i (t)+v i (t+1)

[0118] Step 3: Calculate the fitness value of each particle's new position based on the objective function

[0119] Step 4: Update individual optimal solutions and global optimal solutions

[0120] For each particle, if the fitness value of its new position is better than the fitness value of the current individual optimal position, the individual optimal position is updated. Then, the best fitness is selected from the individual optimal positions of all particles to update the global optimal position.

[0121] Step 5: Termination condition judgment

[0122] The termination conditions of the particle swarm optimization algorithm usually include reaching the maximum number of iterations, the fitness of the global optimal solution reaching a certain threshold, etc. If the termination conditions are met, the global optimal solution is output; otherwise, the update speed and position step is returned to continue the iteration.

[0123] Although the present invention has been described above with preferred embodiments, it is not intended to limit the present invention. A person skilled in the art of the present invention may make various modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the definition of the claims.

Claims

1. A method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions, characterized in that: The following steps are involved: S1. Based on the anisotropic elastic constants of the microstructure materials in the MEMS, an anisotropic elastic wave differential system model of the microstructure and thin film materials in the MEMS is established, and the model is meshed and discretized to obtain a number of convex sub-regions; S2. Construct the local solution of the anisotropic elastic wave equation in each convex sub-region in the form of wave function, and use the weighted residual formula to estimate the parameters of the solution to obtain the wave field value at each moment; S3. Determine the calculation area of ​​each grid according to the vector field value, partition it and perform integral calculation on the partition boundary data to complete the anisotropic elastic wave calculation and numerical simulation calculation; S4. Based on the numerical simulation results, an optimization algorithm is used to obtain the optimal parameter indicators of system performance.

2. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S1 , the anisotropic elastic constants of the microstructure material in the micro-electromechanical system include: values ​​of the elastic modulus in different directions, density, and Poisson's ratio.

3. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S1, the model is grid-discretely divided into several convex sub-regions. The characteristic of the divided convex sub-regions is that the computational domain is divided into non-overlapping convex sub-domains to ensure the boundary The two adjacent sub-regions Ω (α) and Ω (β) The compatibility of displacement and stress, imposing boundary continuity conditions, ensures the convergence of the constructed wave function: Among them, u n (x)=u1n1+u2n2,u τ (x)=u1τ1+u2τ2, n=(n1,n2) T and τ=(τ1,τ2) T =(n2,-n1) T They represent the normal vector and tangent vector of the boundary respectively, u1 and u2 are the displacements in the x1 and x2 directions respectively; t n (x) = t1n1 + t2n2, t τ (x) = t1τ1 + t2τ2, t1 = σ 11 n1+σ 12 n2, t2 = σ 21 n1+σ 22 n2,σ ij (i,j=1,2) are stress field components.

4. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S2, in each convex subregion, the domain variables are approximately represented by the following four sets of basis functions, which are represented by superscripts a, b, c and d: in, and is the wave function; and is the unknown contribution factor of the wave function to be determined; and is the number of wave functions.

5. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S2, the wave function is the product of the trigonometric function and the preset unknown function, which can be in the following four forms: in, and is an unknown function of the variable x2, is an unknown function of the variable x1, and Represents the convex domain Ω (α) The minimum rectangular box size.

6. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S2, the weighted residual formula is used to estimate the parameters of the solution to obtain the wave field value at each moment, as shown in the following formula: in, m=1,2,…,n (α) , n=(n1,n2) T and τ=(τ1,τ2) T =(n2,-n1) T denote the normal vector and tangent vector of the boundary respectively; · denotes superscript a, b, c, d.

7. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S3, the calculation area of ​​each grid is determined according to the vector field value, partitioned, and the integral calculation is performed on the partition boundary data, as follows: Du=0(7) Among them, C m,n (m,n=1,2,6) represents the anisotropic material parameters, ρ is the density, ω=2πf is the angular frequency, f is the frequency, get: Among them, δ2=2C 11 C 26 -2C 12 C 16 , δ4=2C 22 C 16 -2C 12 C 26 , δ6=(C 11 +C 66 I am 2 ,δ7=2(C 16 +C 26 I am 2 ,δ8=(C 22 +C 66 I am 2 and δ9=ρ 2 oh 4 ; The following approximate solution and basis function are obtained to complete the elastic wave numerical simulation. in, and is the unknown wave number component to be determined, and is the unknown coefficient, and is the upper bound of the unknown coefficient subscript, Represents an imaginary unit.

8. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: The expression characteristics of the wave function in the anisotropic elastic wave numerical simulation system include truncation of the infinite basis function. When simulating elastic waves in the calculation area, the number of truncation terms k of the wave function is calculated by the following formula: in, D1(θ)=[(C 11 -C 66 )cos 2 θ+(C 22 -C 66 )sin 2 [i] 2 -4Θcos 2 θsin 2 I, D2(θ)=C 11 C 66 cos 4 θ+C 22 C 66 sin 4 θ+[(C 11 +C 22 )C 66 +Θ]cos 2 θsin 2 I, Θ=(C 11 -C 66 )(C 22 -C 66 )-(C 12 +C 66 ) 2 , θ is the angle of incidence.

9. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: The simulation system on the rectangular area is substituted into the elastic system equation for calculation to obtain the elastic stress results and vector field values ​​at each moment.

10. The method for optimizing the performance of a micro-electromechanical system based on anisotropic elastic waves of wave functions according to claim 1, characterized in that: In step S4, the optimization algorithm includes one of a genetic algorithm and a particle swarm optimization algorithm.

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