A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects

In this study, nonlocal strain gradient theory (NSGT) is applied to examine the dynamic instability of embedded viscoelastic graphene sheet under periodic axial load including thermal effects. The foundation is simulated by visco-Pasternak model containing springs, dampers and a shear layer. The motion equations are derived according to the four-variable refined shear deformation plate theory and via Hamilton's principle. The equations are converted into a linear system of Mathieu-Hill equations by means of Navier's method. Afterwards, Bolotin's approach is utilized to determine the principle unstable region of graphene sheet. The influences of nonlocal parameter, structural damping coefficient, length scale parameter, static load factor, temperature variation, foundation type as well as aspect ratio on the dynamic stability of graphene sheet are investigated. Based on the numerical results, it is indicated that with enlarging the nonlocal parameter, static load factor and temperature change, the excitation frequency decreases and so, instability region shifts to left side while the effect of length scale parameter is on the contrary. Additionally, it is indicated that when the length scale parameter enhances, the effects of temperature and foundation on the instability region of graphene sheet reduce.