MEMS: From Micro Devices to Wireless Systems

Vol. 7, Special Issue, October 2009, pp.125-135

A Multiscale Model of Cantilever Arrays and its Updating

Michel LENCZNER, Emmanuel PILLET, Scott COGAN and Hui HUI

 FEMTO-ST, 26 Chemin de l'épitaphe, 25000 Besançon, France

Tel.: +33 (0)3 81 83 26 69, fax: +33 (0)3 81 85 39 98

E-mail: michel.lenczner@utbm.fr, manu.pillet@gmail.com, scott.cogan@univ-fcomte.fr, hui.hui@femto-st.fr

Received: 28 August 2009   /Accepted: 28 September 2009   /Published: 12 October 2009

Abstract: We present a simplified model of mechanical behavior of large cantilever arrays with discoupled rows in the dynamic operating regime. Since the supporting bases are assumed to be elastic, cross-talk effect between cantilevers is taken into account. The mathematical derivation combines a thin plate asymptotic theory and the two-scale approximation theory, devoted to strongly heterogeneous periodic systems. The model is not standard, so we present some of its features. We explain how each eigenmode is decomposed into a product of a base mode with a cantilever mode. We explain the method used for its discretization, and report results of its numerical validation with full three-dimensional Finite Element simulations. Finally, we provide a short description of parameter updating and identification techniques developed for the model.

Keywords: Cantilever arrays, Multiscale modeling, Homogenization, Strongly Heterogeneous homogenization, Parameter identification

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