A reduced-order dynamic model is presented for nonlinear devices subjected to in-plane oscillatory motion. Comparisons between numerical and finite element results demonstrate that the nonlinear behavior of a planar resonator can be predicted accurately by the derived dynamic model with significantly less computation. Simulation results illustrate the effects of nonlinear stiffness, damping ratio, electrostatic driving force, and device dimensions on the nonlinear dynamic behavior. The analysis yields two possible stable responses, depending on the initial rotation angle and rotation rate. The present dynamic model can be easily modified to analyze the nonlinear response of various planar resonators.

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