静电力作用下微梁变形分析与计算

Analysis and Computation of a Deformation of a Microbeam Driven by Electrostatic Force

机电耦合问题是微机电系统结构分析中的重要内容之一,目前多采用有限元方法求解。作为结构分析的有限元方法从精度上来说是令人满意的,但对于结构设计来说计算效率低、费用高。本文在对微梁结构控制方程中的静电力和梁伸长拉力公式进行校正的基础上,给出一种易于实现的不需要求解方程组的数值计算方法,通过计算实例证明,该方法与有限元方法计算的结果误差在2%以内。

Electromechanical coupling is one of the most critical issues in microelectromechanical systems (MEMS). Finite element(FE) methods are widely used in current commercial MEMS CADs to perform analysis. FE methods can meet the demands in accuracy, but it can be computationally expensive and complex in structural design. In this paper, the electrostatic load applied to microbeam and axial tension load induced by deflection are modified. The modified controlling equation can be solved by a novel numerical algorithm. The examples show that the errors are within 2% between the numerical algorithm and FE methods with typical physical structures.