Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency

This paper deals with nonlinear-parametric frequency response of alternating current (AC) near natural frequency electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators. The model includes fringe and Casimir effects, and damping. Method of multiple scales (MMS) and reduced order model (ROM) method are used to investigate the case of weak nonlinearities. It is reported for uniform resonators: (1) an excellent agreement between the two methods for amplitudes less than half of the gap, (2) a significant influence of fringe effect and damping on bifurcation frequencies and phase-frequency response, respectively, (3) an increase of nonzero amplitudes' frequency range with voltage increase and damping decrease, and (4) a negligible Casimir effect at microscale.