Parametric resonance and Hopf bifurcation analysis for a MEMS resonator (Q544099)

The response of a MEMS resonator, driven in an in-plane length-extensional mode of excitation, is studied. It is observed that the amplitude of the resulting vibration has an upper bound, i.e., the response shows saturation. A model for this phenomenon, incorporating interaction with a bending mode, is presented in terms of the equation of motion. It is demonstrated that this model accurately describes the observed phenomena. The in-plane (so-called ``trivial'') mode is shown to be stable up to a critical value of the amplitude of the excitation. At this value, a new ``bending'' branch of solutions bifurcates. For appropriate values of the parameters, a subsequent Hopf bifurcation causes a beating phenomenon, in accordance with experimental observations.