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Modelling and Simulation in Engineering
Volume 2016, Article ID 8543616, 6 pages
Research Article

Numerical Investigation of Pull-In Instability in a Micro-Switch MEMS Device through the Pseudo-Spectral Method

Dipartimento di Scienze e Metodi dell’Ingegneria (DISMI), Universitá degli Studi di Modena e Reggio Emilia, Via G. Amendola 2, 42122 Reggio Emilia, Italy

Received 4 December 2015; Revised 10 May 2016; Accepted 5 October 2016

Academic Editor: Julius Kaplunov

Copyright © 2016 P. Di Maida and G. Bianchi. 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.


A pseudo-spectral approximation is presented to solve the problem of pull-in instability in a cantilever micro-switch. As well known, pull-in instability arises when the acting force reaches a critical threshold beyond which equilibrium is no longer possible. In particular, Coulomb electrostatic force is considered, although the method can be easily generalized to account for fringe as well as Casimir effects. A numerical comparison is presented between a pseudo-spectral and a Finite Element (FE) approximation of the problem, both methods employing the same number of degrees of freedom. It is shown that the pseudo-spectral method appears more effective in accurately approximating the behavior of the cantilever near its tip. This fact is crucial to capturing the threshold voltage on the verge of pull-in. Conversely, the FE approximation presents rapid successions of attracting/repulsing regions along the cantilever, which are not restricted to the near pull-in regime.