Finite Element Analysis Using Hierarchal Decomposition for Interaction of Structural, Fluidic and Electrostatic Fields in MEMS Structural Components

Abstract

In this study a finite element analysis using hierarchal decompositions for the interaction of structural, fluidic and electrostatic fields is applied for vibration analyses of a MEMS structural component. The interaction is partitioned into the electrostatic field and the fluid-structure interaction (FSI) using the block Gauss-Seidel method. The FSI is split into the pressure field and the other using a projection method, where the intermediate state variables are used for the splitting without generating computationally expensive Schur complement matrices. The developed finite element analysis is applied for a micro cantilever beam actuated by the step electrostatic force in vacuum and air. It was demonstrated from the comparisons among the numerical and experimental results that the proposed analyses provide the results consistent with the experimental results. It follows from the present results that the numerical analyses taking into account the interaction of the structural, fluidic and electrostatic fields are required for the accurate predictions of the vibration characteristics of the MEMS structural components.