Quantum Dynamics Effects on Amplitude-Frequency Response of Superharmonic Resonance of Second-Order of Electrostatically Actuated NEMS Circular Plates

This work deals with the effects of Casimir and/or van der Waals forces (quantum dynamics phenomena) on the amplitude-frequency response of the superharmonic resonance of second-order of axisymmetric vibrations of electrostatically actuated nanoelectromechanical systems (NEMS) clamped circular plates. Electrostatic actuation consists of alternating current (AC) voltage of magnitude to produce hard excitations and of frequency near one fourth the natural frequency of the clamped circular plate. The intermolecular forces Casimir and van derWaals, damping force, and electrostatic force are the forces acting on the NEMS plate. Six Reduced Order Models (ROMs) with one and up to 6 modes of vibration are used. The ROM with one mode of vibration is solved using the Method of Multiple Scales (MMS) in which the hard excitations are modeled using first-order and second-order models of hard excitations electrostatic force. Also, Taylor polynomials up to 25th degree are used to approximate the electrostatic, Casimir and van der Waals forces in the ROM with one mode of vibration. MMS predicts the amplitude-frequency response (bifurcation diagram) of the resonance. The other ROMs, using from two to six modes of vibration are solved using two methods, namely continuation and bifurcation using AUTO software package to predict the amplitude-frequency response, and numerical integration using Matlab to predict time responses of the NEMS plate. The amplitude-frequency response predicts a softening effect, and the existence of three branches, two stable and one unstable. A saddle-node bifurcation point of amplitude of 0.24 of the gap, and end points of amplitudes of 0.66 and 0.75 of the gap of unstable and stable branches, respectively, are predicted. The increase of Casimir and/or van der Waals forces shifts the branches, bifurcation points, and endpoints to lower frequencies.