Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet under 1:1 and 3:1 Internal Resonance

Abstract

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on Kirchhoff’s plate theory and nonlinearity of von Karman type is considered in strain–displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included, and some of the material properties are assumed to be temperature-dependent. A coupled system of equations is derived and a new semi-analytical solution is obtained using multiple time-scale methods. The effects of variation of small-scale parameter on the natural frequencies, deflections and response curve of DLGS are analyzed, and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics (MD) simulations are used to investigate different vibration behaviors of DLGS and calibration of the small-scale coefficient. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, environmental damping, length and thermal load are presented. The stability and occurrence of internal resonance between vibration modes around a stable buckled configuration are investigated.