【作者】 陶志军；

【导师】 吴志强；

【作者基本信息】 天津大学 ， 一般力学与力学基础， 2004， 硕士

【摘要】 微型电子机械系统(MEMS)采用与集成电路(Integrated Circuits,IC)技术相兼容的加工技术，制造出尺寸达到微米甚至纳米级的机械，尺寸效应和表面效应及相关的科学问题导致了其中存在诸多非线性因素,如微机械元件的几何非线性﹑所用特殊材料的非线性﹑磁场力与气隙的非线性等等,往往导致基于线性动力学的设计失效。初步研究表明:非线性对微机械电子系统动力学行为有着严重的重要的影响。本文研究了一种微静电开关的双模态非线性行为。本文对一种典型结构的微静电开关，在考虑机械﹑静电以及挤压气隙等三部分因素所建立的偏微分方程的基础上，导出了系统两自由度常微分运动方程，第三章从数值和理论两个方面研究了该系统在1：2内共振时的动力学特性，第四章则根据原系统导出的平均方程的结构对模型方程进行了简化，然后用约束分岔理论对简化方程进行了奇异性分析。研究表明：在系统存在1：2内共振时，当电压值比较小时，系统不稳定，若此时同时有发生外激共振发生则系统达到稳定的时间增长；在非内共振情况发生外激共振时，系统中存在着丰富的分岔行为。更多还原

【Abstract】 Micro-Electro-Mechanical Systems(MEMS) is a promising technology based on intergrated Circuits. The size of the microstructures can be up to micron and even nanometer, and then they are integrated with the circuits to compose systems. There are many nonlinear factors existing in Micro-Electro-Mechanical systems (MEMS) caused by size and suface effects and some other factors, such as nonlinearity of geometrics, special material, electrostatic force and squeeze-film damping force, that often lead to the invalid design based on linear dynamics. The research indicates that nonlinearity has a very important effect on the dynamical behavior of MEMS system. In this paper, we firstly studied the 1:2 internal resonance by numerical simulation of a typical micromachined switch which was fixed at both ends by numerical simulation, considering the three factors, which are mechanism, electrostatic force and squeeze-film damping force, and on the condition that voltage changing, then studied the birfurcation with constraints of the simplified system.It is shown that, in the case of 1:2 internal resonance, there are complicated dynamical behaviors in the system while the voltage is small and the pull-in time will be greatly increased with the external excited resonance; in the case of external resonance without internal resonance, there are boundant with bifurcation behaviors in the system.更多还原