Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors

N. Kacem, S. Baguet, S. Hentz, R. Dufour
Université de Lyon, CNRS INSA-Lyon, LaMCoS UMR5259, F-69621 Villeurbanne, France, Received 11 May 2010; revised 21 December 2010; Accepted 26 December 2010. Available online 4 January 2011.


Abstract

Large-amplitude non-linear vibrations of micro- and nano-electromechanical resonant sensors around their primary resonance are investigated. A comprehensive multiphysics model based on the Galerkin decomposition method coupled with the averaging method is developed in the case of electrostatically actuated clamped–clamped resonators. The model is purely analytical and includes the main sources of non-linearities as well as fringing field effects. The influence of the higher modes and the validation of the model is demonstrated with respect to the shooting method as well as the harmonic balance coupled with the asymptotic numerical method. This model allows designers to investigate the sensitivity variation of resonant sensors in the non-linear regime with respect to the electrostatic forcing.

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