静电驱动MEMS微结构非线性吸合特性研究- - 理论和数值方法

项目名称： 静电驱动MEMS微结构非线性吸合特性研究- - 理论和数值方法

项目编号： No.11202117

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王炳雷

作者单位： 山东大学

项目金额： 25万元

中文摘要： 吸合特性是静电驱动微机电系统（MEMS）的重要特征，合理建立力学模型是研究MEMS吸合特性的前提。MEMS有如下特点：首先，对结构尺寸在微米或亚微米量级的MEMS结构，它表现出明显的尺寸效应，传统连续介质理论无法表征；其次，在MEMS微结构工作过程中存在各种影响因素：几何非线性而引起的中面伸长效应；加工工艺等因素而使结构中存在残余应力；空气阻尼引起变形的滞后效应以及极板边缘静电场等。以上特点都为精确建立理论模型带来了困难。因此，本研究将基于哈密顿原理和应变梯度弹性理论，不仅考虑微结构的尺寸效应、而且综合考虑各种影响因素，分别建立一维非线性梁模型和二维非线性板模型，并建立相应的有限单元方法。在此基础上，研究MEMS微结构的静态和动态非线性吸合特性及其尺寸效应现象，揭示微尺度下结构的力学、电学及其耦合机理，为静电驱动MEMS微结构的精确表征和优化设计提供理论依据。

中文关键词： 尺寸效应；微机械系统；吸合电压；有限元；应变梯度理论

英文摘要： Pull-in instability is an important characteristic for electrostatically actuated MEMS, which requires developing reasonable model to precisely characteristic such pull-in instability. MEMS has the following features: firstly, size effect is prominent when it is in micron or sub-micron, which cannot be predicted by the classical continuum theory; the second is the various effects in MEMS: the midplane stretching caused by large displacement; the presence of residual stress of microstructures, which is generated during the deposition; the nonlinear squeeze film damping and the fringing filed effect between the two electrodes. The above features bring difficulties for accurately modeling MEMS. The proposal is aimed to develop the nonlinear microbeam model and nonlinear microplate model based on Hamilton's principle and strain gradient elasticity theory, with the incorporation of size effect and various nonlinearities. The corresponding higher-order finite element method will also be developed. The static and dynamic nonlinear pull-in instabilities are then studied to uncover the mechanism in MEMS and to meet the purpose of developing the theoretical model and numerical method. The research may provide help in characterizing the mechanical and electrical properties of electrostatically actuated MEMS, or guiding the

英文关键词： Size effect；MEMS；Pull-in voltage；Finite element method；Strain gradient Theory