Superharmonic resonance of an electrically actuated resonant microsensor

We investigate the response of a microbeam-based resonant sensor to a superharmonic electric actuation. The model incorporates the nonlinearities associated with moderately large displacements and electric forces. The method of multiple scales is used to obtain two first-order nonlinear ordinary-differential equations that describe the modulation of the amplitude and phase of the response and its stability. We present typical microsensor frequency-response and force-response curves. The curves demonstrate the existence of multivalued. solutions. These curves consist of three branches which meet at two saddle-node bifurcation points. The results provide an analytical tool to predict the microsensor response to superharmonic excitations, specifically the locations of sudden jumps and regions of hysteretic behavior, thereby enabling designers to safely use this frequency as a measurement signal.