Size-dependent behaviour of electrically actuated microcantilever-based MEMS
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Size-dependent behaviour of electrically actuated microcantilever-based MEMS Hamed Farokhi • Mergen H. Ghayesh
Received: 11 October 2014 / Accepted: 9 February 2015 Ó Springer Science+Business Media Dordrecht 2015
Abstract In this paper, the nonlinear size-dependent static and dynamic behaviours of a microelectromechanical system under an electric excitation are investigated. A microcantilever is considered for the modelling of the deformable electrode of the MEMS. The governing equation of motion is derived based on the modified couple stress theory (MCST), a nonclassical model capable of capturing small-size effects. With the aid of a high-dimensional Galerkin scheme, the nonlinear partial differential equation governing the motion of the deformable electrode is converted into a reduced-order model of the system. Then, the pseudo-arclength continuation technique is used to solve the governing equations. In order to investigate the static behaviour and static pull-in instabilities, the system is excited only by the electrostatic actuation (i.e., a DC voltage). The results obtained for the static pull-in instability predicted by both the classical theory and MCST are compared. In the second stage of analysis, the nonlinear dynamic behaviour of the deformable electrode due to the AC
H. Farokhi Department of Mechanical Engineering, McGill University, Montreal, QC H3A 0C3, Canada e-mail: [email protected] M. H. Ghayesh (&) School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, Wollongong, NSW 2522, Australia e-mail: [email protected]
harmonic actuation is investigated around the deflected configuration, incorporating size dependence. Keywords Microcantilever Electrically actuated Pull-in instability Modified couple stress theory Nonlinear dynamics Size-dependent behaviour
1 Introduction The superior applications of microstructures in the area of microelectromechanical systems (MEMS) have inspired scientists to comprehend all mechanical features associated with these mechanical systems (Ghayesh et al. 2013c; Ghayesh and Farokhi 2013). Among them, electrically actuated microstructures have received a considerable attention in development of MEMS. Electrically excited microstructures (e.g., the deformable electrode of a MEMS resonator) undergo both DC and AC voltages in two steps; first, under the electrostatic actuation (i.e., the DC voltage), the microstructure (i.e., the deformable electrode in this paper) is deflected to a new non-trivial equilibrium configuration. Then, by applying the AC excitation, it oscillates around the new non-trivial configuration. One of the concerns associated with electrically actuated microstructures is pull-in instability phenomenon, i.e., a discontinuity related to the interaction of the mechanical restoring force of the microstructure and the electric forces; when the applied electric
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potential difference exceeds a critical value known as the pull-in voltage, the microstructure fails to establis
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