Nonlinear analysis and effectiveness of weakly coupled microbeams for mass sensing applications

Abstract

In this work, we develop a general model of a mass sensor made of N weakly mechanically coupled microbeams subject to electric actuation. The developed model is verified by comparing the simulated pull-in voltages, natural frequencies, and frequency response of a two-weakly coupled beam system against their experimental counterparts reported in the literature. The sensitivity of the mass sensor in terms of frequency shift is observed to significantly increase when enlarging the size of the beams array. The simulation results reveal a clear transformation of the frequency response from a nearly linear to nonlinear behavior as result of the deposition of a small mass on the coupled system. As such, we show the potential use of bifurcations that result in an abrupt jump to a large-amplitude motion for sensing purposes. Furthermore, by exploiting the mode localization effect, the nonlinear response can be triggered on one of the beams when an added masses is introduced, allowing for an amplitude-based mass detection mechanism of the device. The proposed sensing method has the possibility to operate in bifurcation mode for mass threshold detection that can be tuned using the AC actuation or in continuous mode based on extracting the added mass from the amplitude of the sensing beam’s oscillations.