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 because of material structure and surface topology of micro‐beams in a stochastic multi‐scale model. For micro‐resonators made of anisotropic polycrystalline materials, micro‐scale uncertainties exist because of the grain size, grain orientation, and the surface profile. First, micro‐scale realizations of stochastic volume elements are obtained based on experimental measurements. To account for the surface roughness, the stochastic volume elements are defined as a volume element having the same thickness as the microelectromechanical system (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. Copyright © 2016 John Wiley & Sons, Ltd.