On the response of MEMS resonators under generic electrostatic loadings: theoretical analysis

We present an investigation of the dynamic behavior of an electrostatically actuated resonant structure, resonator, under the simultaneous excitation of primary and subharmonic resonances. A comprehensive analytical solution is obtained via the method of Multiple Time Scales (MTS), which is applicable for generic electrostatic loading cases. Results using different MTS scaling methods in the equations of motion and loading conditions are compared. These results are further verified against results obtained using direct time integration of the equation of motion. It is observed that for a generic parallel-plate electrostatic loading case, the direct forcing component at the excitation frequency, and the direct and parametric excitation components at double the excitation frequency must be considered for accurate prediction of the structure’s response. Further, the case of simultaneous excitations of primary and subharmonic resonance, where both excitations are of comparable strength, is examined under various electrostatic loading conditions. We show mixed behaviors of the resonator transiting from a subharmonic-dominated response, characterized by the sudden jumps in amplitude and smaller monostable regime, to primary-dominated response exhibiting gradual amplitude increase and larger monostable regimes. This transition behavior can be potentially used for applications, such as electrometers.