2007 NSTI Nanotechnology Conference and Trade Show - Nanotech 2007 - 10th Annual

Perturbation Stochastic Finite Element Analysis of Thermoelastic Quality Factor of Micro-Resonators

S. Lepage and J.C. Golinval
University of Liege, BE

thermoelastic damping, Stochastic finite element method, Random parameter

MEMS are subject to inevitable and inherent uncertainty that leads to variability in their performance. The effects of these variations have to be considered and modeled to ensure required MEMS performance under uncertainties. In the design of high-Q micro-resonators, one of the major dissipation phenomena to consider is thermoelastic damping. The purpose of this paper is to develop a numerical method to analyze the effects of geometric and material property random variations on the thermoelastic quality factor of MEMS. Since the deterministic thermoelastic finite element problem is well defined and characterized, uncertainties can be added into the model. The perturbation Stochastic Finite Element Method is used to determine the mean and the variance of the thermoelastic quality factor. The originality of this work is the extension of SFEM to the analysis of strongly coupled multiphysic phenomena. The perturbation SFEM is applied on the analysis of the thermoelastic quality factor of a micro-beam whose elastic modulus and length are considered as random. Therefore, using the proposed SFEM, a numerical method is available to quantify the influence of uncertain geometric and material property variations on the thermoelastic quality factor of micro-resonators, making available a new efficient numerical tool to MEMS designers.

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