Abstract
This paper deals with the frequency-amplitude response of parametric resonance of alternating current (AC) electrostatically actuated nonuniform micro-electromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever of linear thickness and constant width, parallel to a ground plate, and under AC voltage producing soft excitations. AC frequency is near first natural frequency of the cantilever. The fringe effect is included in the electrostatic force. Two reduced-order models (ROMs), namely ROMs using one and two modes of vibration, are developed. Two methods are used to solve these ROMs: the method of multiple scales (MMS), and numerical integration. The frequency-amplitude response shows a softening effect and two bifurcation points, one subcritical and another one supercritical. The two bifurcation points occur at zero amplitude. Three branches of steady-state solutions are predicted, one zero amplitude branch, and two non-zero amplitude branches, one stable and one unstable. Pull-in occurs for constant frequency with initial amplitudes above the unstable branches, or when the frequency is swept down from frequencies larger than supercritical bifurcation frequency. The range of frequencies between the bifurcation points decreases as damping increases and/or voltage and fringe effect decrease. Between the two bifurcation points, damping, voltage, and fringe effect have the greatest effect on the subcritical bifurcation point.
