静电微梁器件的降阶模型及其动态Pull-in不稳定性研究

Study on Dynamic Pull- in Instability of Electrostatically Actuated Micro-beam Devices

微器件的设计需要利用计算机技术快速准确仿真其动态特性。以器件中结构件的模态振型函数作为基函数,结合Galerkin映射建立静电-结构耦合微梁器件的自由度缩减模型,该降阶模型能考虑初始轴向载荷、大变形几何非线性效应对器件基频及动态特性的影响。在Simulink中建立单模态模型,并对器件的Pull-in过程进行动态仿真,分析了有阻尼和无阻尼情况下,静电器件动态Pull-in的分叉现象。

The dynamic characteristics of micro-devices need to be fully understood by using fast and accurate simulation technology during the stage of prototype design and operation. The Galerkin＇s decomposition method was utilized to set up the order reduced model of the electrostatic-structural coupling systems,where the normal modes of beam were used as basic functions. The contribution of initial axial stress,electrostatic softening and the mid-plane scratch stiffening to the device＇s natural frequency can be described by the reduced model. A single mode model was constructed in Simulinkenvironment for studying the dynamic Pullin process of the device. The bifurcation based on phase portraits was conducted to derive the dynamic pull-in instability under considering the damping effect or not.