靜電力作用下微梁靜態特性分析

此份畢業設計包括,開題報告,畢業論文,大摘要,小摘要,目錄,和外文原文,翻譯.      論文編號:LX001  字數:18790,頁數:47

摘  要
微機電系統（MEMS）自20世紀80年代中期發展至今一直受到世界各發達國家的廣泛重視，被認為是一項面向21世紀可以廣泛應用的新興技術。而微機電系統中都采用了微梁結構，因此對微梁的研究對微機電系統的系統設計有重要意義。本文考慮了靜電力邊緣效應的影響，通過薄板大撓度彎曲微分方程退化建立了微梁大撓度變形的一階控制方程組，并采用打靶法將微梁大撓度變形的邊值問題轉化為初值問題，借助高精度迭代修正齊次擴容精細積分法建立了一種原理簡單、應用廣泛的分析微梁大撓度變形的計算模型與方法。為了保證在非線性代數方程組求根時的收斂性和穩定性，本文根據微梁的受力特點提出了一種增量迭代的算法。分析了邊緣效應和大撓度變形對微梁靜態特性的影響。數值算例表明，本文所提出的方法具有較高的精度和穩定性，是分析微梁大撓度變形的一種有效方法。

關鍵詞：微梁；大撓度；打靶法；精細積分；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  錄
1  緒   論 ..........................................................................1
1.1 課題研究的目的和意義 ............................................................1
1.1.1 MEMS概述 ......................................................................1
1.1.2 選題的目的和意義 ..............................................................2
1.2 國內外研究概況 ..................................................................3
1.2.1 微機電系統研究概況 ............................................................3
1.2.2 靜電驅動微梁結構研究現狀 ......................................................4
1.3 課題研究內容 ....................................................................5
2  迭代修正齊次擴容精細積分法 .......................................................6
2.1 引言 ............................................................................6
2.2 齊次擴容精細積分法 ..............................................................6
2.2.1 精細積分法 ....................................................................6
2.2.2 齊次擴容精細積分法 ............................................................8
2.3 迭代修正齊次擴容精細積分法 ......................................................9
2.3.1 非線性動力方程的齊次擴容精細積分法 ............................................9
2.3.2 迭代修正齊次擴容精細積分法 ....................................................11
2.3.3 數值算例 ......................................................................12
2.4 本章小結 ........................................................................13
3  擬牛頓法 .........................................................................15
3.1 引言 ............................................................................15
3.2 擬牛頓法 ........................................................................15
3.2.1 擬牛頓法的基本思想 ............................................................15
3.2.2 秩1擬牛頓法與Broyden方法 ......................................................16
3.3 本章小結 ........................................................................19
4  打靶法 ...........................................................................20
4.1 打靶法的基本原理 ................................................................20
4.2 本章小結 ........................................................................21
5  微梁的靜力學模型及計算方法 .......................................................22
5.1 微梁計算模型 ....................................................................22
5.2 計及邊緣效應的微梁靜力學方程 ....................................................23
5.3 數值計算方法 ....................................................................24
5.4 本章小結 ........................................................................26
6  微梁靜態特性分析 .................................................................27
6.1 邊緣效應對微梁靜態特性的影響 ....................................................27
6.2 大撓度變形對微梁靜態特性的影響 ..................................................28
6.3 微梁自身參數對微梁靜態特性的影響 ................................................30
6.3.1 微梁長度對微梁靜態特性的影響 ..................................................30
6.3.2 微梁自身寬度對微梁靜態特性的影響 ..............................................31
6.3.3 微梁自身厚度對微梁靜態特性的影響 ..............................................31
6.3.4 改變梁與固定極板的距離對微梁靜態特性的影響 ....................................32
6.3 本章小結 ........................................................................32
7  結  論 ...........................................................................33
參 考 文獻 .........................................................................34
致   謝 .............................................................................36
附錄 ................................................................................37