Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 173459, 14 pages
Research Article

Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever

1State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
2Department of Mechanics, Sun Yat-Sen University, Guangzhou 510275, China

Received 21 May 2010; Revised 8 November 2010; Accepted 30 November 2010

Academic Editor: Marcelo Messias

Copyright © 2011 Y. M. Chen et al. 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.


The homotopy analysis method (HAM) is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.