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Proceedings Paper

Modeling of electromechanical coupling problem using the finite element formulation
Author(s): Véronique Rochus; Daniel Rixen; Jean-Claude Golinval
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Paper Abstract

A modeling procedure is proposed to handle the strong electro-mechanical coupling appearing in micro-electro-mechanical systems (MEMS). The finite element method is used to discretize simultaneously the electrostatic and mechanical fields. The formulation is consistently derived from variational principles based on the electro-mechanical free energy. In classical weakly coupled formulations staggered iteration is used between the electro-static and the mechanical domain. Therefore, in those approaches, linear stiffness is evaluated by finite differences and equilibrium is reached typically by relaxation techniques. The strong coupling formulation presented here allows to derive exact tangent matrices of the electro-mechanical system. Thus it allows to compute non-linear equilibrium positions using Newton-Raphson type of iterations combined with adaptive meshing in case of large displacements. Furthermore, the tangent matrix obtained in the method exposed in this paper greatly simplifies the computation of vibration modes and frequencies of the coupled system around equilibrium configurations. The non-linear variation of frequencies with respect to voltage and stiffness can then be investigated until pull-in appears. In order to illustrate the effectiveness of the proposed formulation numerical results are shown first for the reference problem of a simple flexible capacitor, then for the model of a micro-bridge.

Paper Details

Date Published: 1 August 2003
PDF: 12 pages
Proc. SPIE 5049, Smart Structures and Materials 2003: Modeling, Signal Processing, and Control, (1 August 2003); doi: 10.1117/12.482820
Show Author Affiliations
Véronique Rochus, Univ. de Liège (Belgium)
Daniel Rixen, Delft Univ. of Technology (Netherlands)
Jean-Claude Golinval, Univ. de Liège (Belgium)

Published in SPIE Proceedings Vol. 5049:
Smart Structures and Materials 2003: Modeling, Signal Processing, and Control
Ralph C. Smith, Editor(s)

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