Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach

This paper aims at accounting for the uncertainties due to material structure and surface topology of microbeams in a stochastic multiscale model. For micro-resonators made of anisotropic polycrystalline materials, micro-scale uncertainties are due to the grain size, grain orientation, and to the surface profile. First, microscale realizations of stochastic volume elements (SVEs) are obtained based on experimental measurements. To account for the surface roughness, the SVEs are defined as a volume element having the same thickness as the MEMS, with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso-scale, through a second-order homogenization procedure.From the meso-scale plate resultant material property realizations, a spatially correlated random field of the in plane, out of plane, and cross resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS-scale problems can be defined on a plate finite element model. Samples of the macro-scale quantity of interest can then be computed by relying on a Monte-Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro-beams is investigated for different uncertainty cases, such as grain preferred orientations and surface roughness effects.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) and by the Romanian UEFISCDI Agency contract ERA-NET MNT no 7-063/2012 (20122015) in the context of the ERA-NET MNT framework; Computational resources have been provided by the supercomputing facilities of the Consortium des Equipements de Calcul Intensif en Federation Wallonie Bruxelles (CECI) funded by the Fond de la Recherche Scientifique de Belgique (FRS-FNRS)