Impact of nanostructures on the superharmonic resonance characteristics of nanobeam-based capacitors: Analytical approach

Abstract

In this paper, the nonlinear vibration of a size-dependent doubly clamped NEMS has been investigated based on the consistent couple-stress theory and Euler-Bernoulli beam theory. The impact of surface elasticity, dispersion Casimir force, and fringing field effect are considered in the nonlinear model. Here, the nanobeam is supposed to be under a single-side electrostatic actuation, which is a combination of DC and AC voltages. The governing differential equation of motion is derived using the extended Hamilton’s principle and discretized to a nonlinear ODE using Galerkin’s procedure. The multiple time scales method is applied to the reduced-order model in order to analytically obtain the nanobeam frequency–response curves under hard AC load. The influence of the small-scale parameter, Casimir force, and surface effect are investigated on both the static pull-in and the superharmonic resonance characteristics of the system. It is shown that the application of non-classical continuum theory effectively shifts the saddle-node bifurcation point’s loci to lower frequencies, and diminishes the maximum amplitude of the system response without changing the system stiffness. Moreover, it is concluded that the influence of surface energy on the system dynamic behavior depends on the value of DC voltage load. To validate the results obtained from perturbation analysis, the shooting method is schemed through numerical integration of the reduced-order model equation.