On the dynamic stability of viscoelastic graphene sheets

Due to their extraordinary and unique properties, graphene sheets have been attracted tremendous attention in recent years. This paper is concerned with the dynamic stability of an embedded orthotropic single layer graphene sheet (SLGS) subjected to periodic excitation compressive load with various boundary conditions. In order to obtain more accurate results, the material properties of graphene sheet are assumed to be viscoelastic using Kelvin-Voigt model. The surrounding medium is described by visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. Adopting the first order shear deformation theory (FSDT) in the framework of Eringen's differential constitutive model, the governing equations of motion are obtained via energy method and Hamilton's principle which are then solved numerically via Ritz method in conjunction with Bolotin method. The parametric studies are carried out to explore the effects of the static load factor, structural damping, nonlocal parameter, stiffness and damping coefficients of the foundation and aspect ratio on the dynamic instability region (DIR) of SLGS for each of the boundary conditions separately. Results indicate that with increasing the structural damping coefficient, the dimensionless pulsation frequency decreases and DIR moves to left, consequently. Moreover, it is observed that when one edge of the nanoplate changes from free to simply supported or from simply supported to clamped, the dimensionless pulsation frequency enhances.