Stabilization of electrostatically actuated microstructures using parametric excitation

Abstract

Electrostatically actuated microstructures are inherently nonlinear and can become unstable. Pull-in instability is encountered as a basic instability mechanism. We demonstrate that the parametric excitation of a microstructure by periodic (ac) voltages may have a stabilizing effect and permits an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. An elastic string as well as a cantilever beam are considered in order to illustrate the influence of fast-scale excitation on the slow-scale behavior. The main conclusions about the stability are drawn using the simplest model of a parametrically excited system described by Mathieu and Hill's equations. Theoretical results are verified by numerical analysis of microstructure subject to nonlinear electrostatic forces and performed by using Galerkin decomposition with undamped linear modes as base functions. The parametric stabilization of a cantilever beam is demonstrated experimentally.