Analytical Primary Resonance of Size-Dependent Electrostatically Actuated Nanoresonator Under the Effects of Surface Energy and Casmir Force

Abstract

This paper investigates the nonlinear vibration of a size-dependent doubly clamped nanoresonator based on modified indeterminate couple-stress theory and Euler–Bernoulli beam theory. Surface effects, dispersion Casimir force, and fringing field effects are considered in the nonlinear model. The electrostatic actuation is a combination of DC and AC voltages and imposed on the nanobeam through one electrode. 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 scale method is applied to the reduced-order model in order to obtain the nanobeam frequency-response curves analytically under small AC voltage loads. The influences of the mentioned parameters are investigated on the primary resonance characteristics of the nanoresonator. It is shown that the application of non-classical continuum theory results in a softening effect on the dynamic response of the system near primary resonance. Moreover, it is concluded that the influence of surface energy on the system dynamic behavior depends on the value of DC voltage load.