Casimir Effect on Amplitude-Frequency Response of Parametric Resonance of Electrostatically Actuated NEMS Cantilever Resonators

Abstract

This paper deals with the effect of Casimir force on the amplitudefrequency response of parametric resonance of electrostatically actuated nanoresonators. The resonator is actuated by using an electrostatic force to include a first order fringe correction. Casimir force and viscous damping force are included in the model, as well. Both electrostatic and Casimir forces are nonlinear. The behavior of the resonator is investigated using two methods, the Method of Multiple Scales (MMS) for a Reduced Order Model (ROM) using one mode of vibration, and numerical integration of ROMs using up to five modes of vibration. ROM is based on the application of a Galerkin procedure that uses the undamped mode shapes of the cantilevered beam as the basis of functions. The amplitude-frequency response consists of two bifurcations, namely subcritical and supercritical. The increase of Casimir effect shows an increase of the interval of frequencies of the unstable zero steady-state solutions, and a larger range of frequencies for which the system has stable steady-state solutions for amplitudes larger than 0.5 of the gap.