Numerical investigation into nonlinear dynamic behavior of electrically-actuated clamped–clamped micro-beam with squeeze-film damping effect

• Published in: Applied mathematical modelling Vol. 38; no. 13; pp. 3269 - 3280
• Main Authors: Liu, Chin-Chia, Wang, Cheng-Chi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2014
• Subjects: Clamps; Deflection; Differential transformation; Electric potential; Finite difference method; Mathematical analysis; Mathematical models; MEMS; Nonlinear dynamics; Nonlinearity; Pull-in voltage; Reynolds equation; Squeeze film damping effect; Voltage; MEMS; Pull-in voltage; Differential transformation; Squeeze film damping effect; Reynolds equation; Finite difference method
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2013.11.048

A numerical investigation is performed into the nonlinear dynamic behavior of a clamped–clamped micro-beam actuated by a combined DC/AC voltage and subject to a squeeze-film damping effect. An analytical model based on a nonlinear deflection equation and a linearized Reynolds equation is proposed to describe the deflection of the micro-beam under the effects of the electrostatic actuating force. The deflection of the micro-beam is investigated under various actuating conditions by solving the analytical model using a hybrid numerical scheme comprising the differential transformation method and the finite difference approximation method. It is shown that the numerical results for the dynamic pull-in voltage of the clamped–clamped micro-beam deviate by no more than 2.04% from those presented in the literature based on the conventional finite difference scheme. The effects of the AC voltage amplitude, excitation frequency, residual stress, and ambient pressure on the center-point displacement of the micro-beam are systematically explored. Moreover, the actuation conditions which ensure the stability of the micro-beam are identified by means of phase portraits. Overall, the results presented in this study confirm that the hybrid numerical method provides an accurate means of analyzing the complex nonlinear behavior of common electrostatically-actuated microstructures.