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自考论文范文-静电力作用下微梁静态特性分析

来源:浙江自学考试专业查询平台 2020-11-24 14:39

摘 要

微机电系统(MEMS)自20世纪80年代中期发展至今一直受到世界各发达国家的广泛重视,被认为是一项面向21世纪可以广泛应用的新兴技术。而微机电系统中都采用了微梁结构,因此对微梁的研究对微机电系统的系统设计有重要意义。本文考虑了静电力边缘效应的影响,通过薄板大挠度弯曲微分方程退化建立了微梁大挠度变形的一阶控制方程组,并采用打靶法将微梁大挠度变形的边值问题转化为初值问题,借助高精度迭代修正齐次扩容精细积分法建立了一种原理简单、应用广泛的分析微梁大挠度变形的计算模型与方法。为了保证在非线性代数方程组求根时的收敛性和稳定性,本文根据微梁的受力特点提出了一种增量迭代的算法。分析了边缘效应和大挠度变形对微梁静态特性的影响。数值算例表明,本文所提出的方法具有较高的精度和稳定性,是分析微梁大挠度变形的一种有效方法。

关键词:微梁;大挠度;打靶法;精细积分;增量迭代

Abstract

Since the mid-1980s, Micro Electromechanical System has attracted an extensive attention by the developed countries, which is considered an emerging technology can be broadly applied in the 21st century. The micro beam structures are used in Micro Electromechanical System, so the study of micro-beam is important on the MEMS system design. Considering the influence of electrostatic force edge effect, first order control equations of a large deflection bending micro beam was deduced by degenerate differential equations of a large deflection bending thin plate. The large deflection deformation of a micro beam is a boundary value problem. In this paper, the shooting method was adopted to change the boundary value into initial value problem. By means of the high precision iterative refinement extended homogeneous capacity integration method, a simple and wide use computational model and method was established to analyze the deformation of a large deflection bending micro beam. In order to guarantee the convergence and stability in solving nonlinear algebraic equations, an incremental iterative algorithm was put forward according the load characteristic. The effect of an edge effects and large deflection deformation to static characteristics of the micro-beam were analyzed. Numerical calculated results show that the proposed method is more accurate and stable, which is an effective method to analyze the large deflection deformation of a micro beam.

Key words: micro beam;large deflect;shooting method;high precision direct integration;incremental iterative

目 录

1 绪 论 ..........................................................................1

1.1 课题研究的目的和意义 ............................................................1

1.1.1 MEMS概述 ......................................................................1

1.1.2 选题的目的和意义 ..............................................................2

1.2 国内外研究概况 ..................................................................3

1.2.1 微机电系统研究概况 ............................................................3

1.2.2 静电驱动微梁结构研究现状 ......................................................4

1.3 课题研究内容 ....................................................................5

2 迭代修正齐次扩容精细积分法 .......................................................6

2.1 引言 ............................................................................6

2.2 齐次扩容精细积分法 ..............................................................6

2.2.1 精细积分法 ....................................................................6

2.2.2 齐次扩容精细积分法 ............................................................8

2.3 迭代修正齐次扩容精细积分法 ......................................................9

2.3.1 非线性动力方程的齐次扩容精细积分法 ............................................9

2.3.2 迭代修正齐次扩容精细积分法 ....................................................11

2.3.3 数值算例 ......................................................................12

2.4 本章小结 ........................................................................13

3 拟牛顿法 .........................................................................15

3.1 引言 ............................................................................15

3.2 拟牛顿法 ........................................................................15

3.2.1 拟牛顿法的基本思想 ............................................................15

3.2.2 秩1拟牛顿法与Broyden方法 ......................................................16

3.3 本章小结 ........................................................................19

4 打靶法 ...........................................................................20

4.1 打靶法的基本原理 ................................................................20

4.2 本章小结 ........................................................................21

5 微梁的静力学模型及计算方法 .......................................................22

5.1 微梁计算模型 ....................................................................22

5.2 计及边缘效应的微梁静力学方程 ....................................................23

5.3 数值计算方法 ....................................................................24

5.4 本章小结 ........................................................................26

6 微梁静态特性分析 .................................................................27

6.1 边缘效应对微梁静态特性的影响 ....................................................27

6.2 大挠度变形对微梁静态特性的影响 ..................................................28

6.3 微梁自身参数对微梁静态特性的影响 ................................................30

6.3.1 微梁长度对微梁静态特性的影响 ..................................................30

6.3.2 微梁自身宽度对微梁静态特性的影响 ..............................................31

6.3.3 微梁自身厚度对微梁静态特性的影响 ..............................................31

6.3.4 改变梁与固定极板的距离对微梁静态特性的影响 ....................................32

6.3 本章小结 ........................................................................32

7 结 论 ...........................................................................33

参 考 文献 .........................................................................34

致 谢 .............................................................................36

附录 ................................................................................37

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