Size-dependent resonant response of a double-layered viscoelastic nanoresonator under electrostatic and piezoelectric actuations incorporating surface effects and Casimir regime

Abstract

Nonlinear dynamics of a double-layer viscoelastic nanobeam embedded into an electromechanical system is investigated in this paper. The nanoelectromechanical system (NEMS) consists of two piezoelectric and Kelvin–Voigt viscoelastic nanobeams with visco-Pasternak medium in between. An electrostatic force which is the combination of DC and AC voltages is applied to the lower nanobeam through the fixed electrode. Taking into account both the small-scale effect and surface energy effect, the modified couple-stress theory together with Gurtin–Murdoch elasticity theory is implemented. As intermolecular interactions between the fixed and lower electrodes, the influence of Casimir regime on the dynamic behavior of the NEMS device is also included in the proposed model. The differential motion’s equations are derived by means of Hamilton’s principle and discretized to a set of nonlinear ODEs through Galerkin’s decomposition procedure. In order to capture the steady-state dynamic response of the system, a combined shooting and arclength continuation method is schemed. A comprehensive study has been carried out on the impact of viscoelasticity, size-dependency, surface effects, direct and alternating current voltages, piezoelectric voltage and visco-Pasternak parameters on the frequency-response behavior of the system near primary resonance. Furthermore, some bifurcation points in the frequency-response curves are addressed. The combined hardening–softening-type behaviors are observed in the dynamic response of the system. It has been shown that the nonlinear characteristics of the motion of the proposed NEMS device have sensitive-dependence on some of the mentioned parameters.