Analysis of fluid-structure interaction for predicting resonant frequencies and quality factors of a microcantilever on a squeeze-film

The dynamic behavior of a flexible microcantilever vibrating above a substrate such as the cantilever-based structure of a radio frequency microelectromechanical switch is strongly affected by the motion of gas between the microcantilever and the substrate. In this paper, parameter studies to investigate the effects of geometry, material properties of a microcantilever, and ambient pressure on the resonant frequencies and quality factors of the microcantilever are described. A Reynolds-equation-based continuum model is used to derive the gas force reflecting the gas rarefaction effect due to the size effect of MEMS packed at low ambient pressure. The frequency response function of an inertially-excited microcantilever is developed using the mode superposition method. One interaction parameter, including information on geometry, material properties of a microcantilever, and ambient pressure, is defined to investigate the fluid-structure interaction in a microcantilever vibrating on a squeeze-film. The quality factors of the first three bending modes increase with the decreasing interaction parameter. The changing trend of associated resonant frequencies depends on the order of the bending mode.