Reduced order model of parametric resonance of electrostatically actuated MEMS cantilever resonators

• This work deals with electrostatically actuated MEMS cantilever resonators.
• Parametric resonance due to soft AC near natural frequency and weak nonlinearities.
• Reduced order model method and the method of multiple scales are used.
• Five terms ROM is accurate for both small and high amplitudes of the system.
• Damping, voltage, and fringe effects are found using five term ROM.

This paper deals with parametric resonance of microelectromechanical (MEMS) cantilever resonators under soft damping, and soft alternating current (AC) electrostatic actuation to include fringing effect. A comparison between the Reduced Order Model (ROM) method and the Method of Multiple Scales (MMS) for both small and large amplitudes is reported. The actuation is parametric non-linear. It includes non-linear terms with periodic coefficients. The AC frequency is near resonator׳s natural frequency. The amplitude frequency response is investigated using ROM. Damping, voltage, and fringe effects on the response are also reported. It is showed that five terms ROM accurately predicts the behavior of the resonator at all amplitudes, while MMS is accurate only for small amplitudes.