On Nonlinear Response Near-half Natural Frequency of Electrostatically Actuated Microresonators

This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A first_order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The influences of damping, actuation, and fringe effect on the resonator response are found.