Table of Contents
Journal of Nonlinear Dynamics
Volume 2014 (2014), Article ID 735712, 10 pages
http://dx.doi.org/10.1155/2014/735712
Research Article

Multimode Analysis of the Dynamics and Integrity of Electrically Actuated MEMS Resonators

Department of Physics, Higher Teachers Training College Bambili, The University of Bamenda, P.O. Box 39, Bamenda, Cameroon

Received 25 June 2014; Revised 6 September 2014; Accepted 8 September 2014; Published 25 September 2014

Academic Editor: Sebastien Poncet

Copyright © 2014 Serge Bruno Yamgoué and Alain Juvenal Tchiegang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a theoretical investigation of the dynamic behavior of a microelectromechanical system (in brief, MEMS) device modelled as a clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. We use the Galerkin projection technique to reduce the partial integro-differential equation governing the dynamics of the microbeam to a system of coupled ordinary differential equations which describe the interactions of the linear mode shapes of the microbeam. Analytical solutions are derived and their stability is studied for the simplest reduced-order model which takes into account only the first linear mode in the Galerkin procedure. We further investigate the influence of the first few higher modes on the Galerkin procedure, and hence its convergence, by analysing the boundaries between pull-in and pull-in-free vibrations domains in the space of actuation parameters. These are determined for the various multimode combinations using direct numerical time integration. Our results show that unsafe domains form V-like shapes for actuation frequencies close to the superharmonic, fundamental, and subharmonic resonances. They also reveal that the single first-mode reduced model usually considered underestimates the left branches and overestimates the right branches of these boundaries.