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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 hardexcitationsandoffrequencynearonefourththenaturalfrequencyoftheclamped circular plate. The intermolecular forces Casimir and van der Waals, 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 ROMwithone modeof 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 AUTOsoftwarepackagetopredicttheamplitude-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.


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Theoretical Analyses, Computations, and Experiments of Multiscale Materials, Series: Advanced Structured Materials

Available for download on Wednesday, April 03, 2024