一种微机电非线性耦合系统奇点稳定性研究

Stability of Equilibrium Points of a Micro-Electromechanical Nonlinear Coupling System

工程中许多微机电系统都采用电容驱动原理 ,这类结构实际上存在着强烈的静电和机械两个物理场的非线性耦合 ,因此系统的动态特性比较复杂。本文基于一种扭转微镜系统 ,通过数值分析方法 ,研究其非线性动态特性 ,根据理论分析和数值计算证明该系统在相平面中存在两个奇点 ,一个是稳定中心 ,一个是鞍点 ,且两个奇点位置均随施加电压的变化而逐渐靠近 ,从而得出系统的静态分叉点 ;同时分析了有阻尼和无阻尼时电压的变化对相轨道的影响 ,以及阻尼对吸合电压的影响 ,吸合电压随阻尼的增大而提高 ,这些研究结果不仅对扭转微镜的设计和应用提供了理论和方法 。

In engineering ,the dynamic characteristics of a micro-electromechanical coupling system is very complicated, by the fact that there are two physical domains, micro-electromechanical with nonlinear coupling between them. In this paper, by numerical methods, a DMD micromirror system is discussed. Some nonlinear phenomena are observed, i.e., the stable property of equilibrium points are studied in the phase space, and the larger the voltage amplitude applied to the micromirror, the further is the equilibrium position .And the effect of damping is analysed on the pull-in voltage. The results of study are helpful to design torsion micromirror systems and extend the usage of a micromirror system.