Size-dependent pull-in voltage and nonlinear dynamics of electrically actuated microcantilever-based MEMS: A full nonlinear analysis

This paper aims to develop a size-dependent nonlinear model for electrically actuated microcantilever-based MEMS based on the modified couple stress theory. The pull-in instability and nonlinear dynamics of the microcantilever are explored considering the full nonlinear equation of motion. The discretized equations are obtained using Galerkin method. It has been demonstrated that the material's small length scale parameter and geometric nonlinearities significantly influence the static and dynamic pull-in behaviors of the microcantilever-based MEMS. In the presence of the length-scale parameter, the pull-in voltage is found to be size-dependent. If a time-dependent harmonic component is superposed on the DC voltage, the primary resonances of the micro-cantilever are observed. When the dimensionless length-scale parameter is relatively large, the frequency-response curves indicate that the dynamic responses of the microbeam can evolve from softening-type to hardening-type nonlinear behaviors; the combined effects of length-scale parameter and geometric nonlinearities on the pull-in band of frequencies may be remarkable.