Mass sensing by symmetry breaking and localization of motion in an array of electrostatically coupled nonlinear MEMS resonators

Abstract

This paper investigates the global dynamics of an array of electrostatically coupled nonlinear MEMS resonators before and after a symmetry breaking event by means of nonlinear normal modes, nonlinear forced responses curves and bifurcation analysis. The possible coexistence of isolated solutions is explained by means of energy balance and limit point tracking. The results show that the energy balance method and limit point tracking can be used equivalently to detect the birth of isolated solutions, but only the limit point tracking can predict accurately their merging. Moreover, the localization of motion and the merging of isolated solutions resulting from a symmetry breaking of the underlying nonlinear normal mode can be exploited to provide alternative mass detection methods. The amount of mass that can be detected by this method is directly related to the initial level of asymmetry.