LAUSR

Summary 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.