Stochastic finite element modeling of thermoelastic quality factor of micro-beams

Abstract

In the design of micro-electromechanical systems (MEMS) such as micro-resonators, one of the major dissipation phenomena to consider is thermoelastic damping. The performance of such MEMS is directly related to their thermoelastic quality factor which has to be predicted acurately. Moreover, the performance of MEMS depends on manufacturing processes which cause substantial uncertainty in the geometry and in the material properties of the device. The aim of this paper is to provide a framework to account for uncertainties in the hnite element analysis of thermoelastic damping in MEMS. Four stochastic methods are investigated: perturbation stochastic finite element method (SFEM), spectral SFEM, projection method and Monte-Carlo method. Due to the nature of the thermoelastic problem, these stochastic methods are extended to the resolution of non-symmetric damped eigenproblems. The methods are applied on the analysis of the thermoelastic quality factor of a micro-beam whose elastic modulus is considered as random.