Numerical analysis of fluid–structure interaction effects on vibrations of cantilever microstructure

The operation of microelectromechanical systems (MEMS) with movable parts is often strongly affected by a fluid–structure interaction. Microelectromechanical devices often operate in ambient pressure, therefore air functions as an important working fluid. The influence of air in MEMS devices manifests as viscous air damping, which can be divided into two categories: slide-film damping and squeeze-film damping. The former occurs in laterally moving devices (e.g. comb drives), while the latter is characteristic for MEMS devices, in which a microstructure moves or bends towards a rigid surface with a thin air film in-between (as in microswitch). This paper reports results of numerical analysis of squeeze-film damping effects on free and forced vibrations of cantilever microstructure. Three separate finite element models are used for simulations. Each model is based on different form of Reynolds equation: nonlinear, linearized and linearized incompressible. Squeeze-film damping is associated with displacements of microstructure by using weak formulations of the equations that are coupled to lower surface of the microstructure, which is represented in three-dimensional (3D) and is treated as flexible in the analysis. Both small- and large-amplitude motions are considered. Comparison of results obtained with different models is presented and suggestions are given regarding the usage of particular form of Reynolds equation for modelling air-damping effects in the case of developed electrostatic microswitch.