Uncertainty Quantification in Nonlinear Resonant MEMS

Abstract

This work is focused on Uncertainty Quantification (UQ) in a nonlinear MEMS T-beam structure exhibiting 1:2 autoparametric internal resonance. The study is presented by elaborating on the sources of uncertainty in fabrication and operation of the device and their quantification. Nonlinear response of the system is formulated by using a two-mode model constructed with lowest two linear modes of the structure in conjunction with the nonlinear Lagrangian representing the dynamics of the beam structure as well as the excitation mechanism. Thus UQ for the nonlinear resonant MEMS is carried out in two steps. First, propagation and quantification in linear analysis outputs namely mode shapes, natural frequencies and tuning, and secondly, UQ on nonlinear response obtained from averaged equations determined by the averaged Lagrangian. In this paper, applications of UQ techniques on linear part are presented and effects of various parameteric uncertainties on model output are brought out. Sensitivity analysis is performed to reduce the number of parameters and a comparison of sensitivity analysis with sampling is done to establish the accuracy of the method. Response surface analysis is performed using generalized polynomial chaos (gPC) to generate an analytical expression for multi-dimensional uncertainty. A detailed description of the gPC collocation method is also presented. A comparison of response surface method with direct sampling is done to illustrate the efficiency and accuracy of gPC collocation technique for up to 5 uncertain parameters.