基于Galerkin方法构建MEMS器件宏模型

将器件结构单元的线性模态振型函数(或是本征正交模态)作为全局基函数集合,结合Galerkin方法,获得具有足够仿真精度的微机电系统(MEMS)器件自由度缩减模型.宏模型中相关的状态变量数目很少,可以被快速计算,便于植入系统仿真器中进行模拟.文中分别阐述了这两种自由度缩减模型构造方法的优缺点及存在的问题,认为宏模型研究的重点将是器件非线性特性的有效表达以及建模过程自动化的计算机实现;并对非线性MEMS器件宏模型的研究发展给出了建议.

Investigation of Macromodeling Methods for MEMS Devices Based on Galerkin's Procedure

The various order reduction strategies for transient simulation of MEMS-based devices are reviewed.Combed with the Galerkin method,the linear normal modes or proper orthogonal modes of structural elements in MEMS devices can be used as a global set of basis function for rewriting the system equations in the terms of few domain-wide modes.Therefore,the order of MEMS devices model can be enormously reduced.The equivalent models(macromodels) can be easily inserted into system simulator and evaluated effectively.The major contributions and the advantages and disadvantages of each approach are summarized and discussed.The two keystones in model order reduction are the representation of the original system's nonlinear characteristics and the realization of automatic model reduction.Some suggestions for the development of nonlinear MEMS devices macro-modeling are proposed.