Nonlinear dual frequency excited vibration of viscoelastic graphene sheets exposed to thermo-magnetic field

Abstract

Nonlinear forced vibration of a single layer graphene sheets (SLGSs) resting on a visco-Pasternak foundation and exposed to a dual frequency excitation and a thermo-magnetic field is the main objective of the present study. To obtain this goal, based on nonlocal elasticity theory, Kelvin–Voigt model, nonlinear strain-displacement relations are used to model the geometrical nonlinearity and governing equation of motion is derived. Then, applying Galerkin technique, the partial differential equation is transformed to the ordinary differential one. Derived equation of motion is analyzed and solved using multiple time scales method. Finally, modulation equation under sub-harmonic and super-harmonic stimulation are studied. Emphasizing the effect of nonlinearity, great attention is given to dual frequency excitation and results for nonlinear frequency response with respect to amplitude, the phase angle and force amplitude for SLGS are also plotted. At the end, results of this article are compared with results in the other researches. The results emphasize that the multi-frequency excitation intensifies resonance behavior and jump phenomenon in SLGS.