Parametric resonance and pattern selection in an array of microcantilevers interacting through fringing electrostatic fields

We investigate collective resonant dynamics of an array of microcantilevers coupled elastically, through a flexible overhang, and electrostatically, through fringing fields. Time-harmonic modulation of the effective coupling stiffness parameterized by voltage results in excitation of the parametric resonance accompanied by modal pattern switching during an actuating signal frequency sweep. Using the two-stage Galerkin projection, the equations governing the array's dynamics are reduced to two nonlinearly coupled Mathieu-Duffing equations, which are then analyzed numerically and asymptotically. At sufficiently high actuating voltages, the regions of the parametric resonance associated with different modes of the array overlap, resulting in an abrupt switching between the modes previously observed in the experiments.