Secondary resonances of electrically actuated resonant microsensors

We investigate the response of a microbeam-based resonant sensor to superharmonic and subharmonic electric actuations using a model that incorporates the nonlinearities associated with moderately large displacements and electric forces. The method of multiple scales is used, in each case, 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 frequency-response and force-response curves demonstrating, in both cases, the coexistence of multivalued solutions. The solution corresponding to a superharmonic excitation consists of three branches, which meet at two saddle-node bifurcation points. The solution corresponding to a subharmonic excitation consists of two branches meeting a branch of trivial solutions at two pitchfork bifurcation points. One of these bifurcation points is supercritical and the other is subcritical. The results provide an analytical tool to predict the microsensor response to superharmonic and subharmonic excitations, specifically the locations of sudden jumps and regions of hysteretic behavior, thereby enabling designers to safely use these frequencies as measurement signals. They also allow designers to examine the impact of various design parameters on the device behavior.