Transient behavior of an orthotropic graphene sheet resting on orthotropic visco-Pasternak foundation

This paper deals with transient analysis of simply-supported orthotropic single-layered graphene sheet (SLGS) resting on orthotropic visco-Pasternak foundation subjected to dynamic loads. The size effect is taken into account using Eringen's nonlocal theory due to its simplicity and accuracy. In order to present a realistic model, the material properties of graphene sheet are supposed viscoelastic using Kelvin–Voigt model. Based on the first order shear deformation theory (FSDT), equations of motion are derived using Hamilton's principle which are then solved analytically by means of Fourier series-Laplace transform method. The present results are found to be in good agreement with those available in the literature. Some numerical results are presented to indicate the influences of size effect, elastic foundation type, structural damping, orthotropy directions and damping coefficient of the foundation, modulus ratio, length to thickness ratio and aspect ratio on the dynamic behavior of rectangular SLGS. Results depict that the structural and foundation damping coefficients are effective parameters on the transient response, particularly for large damping coefficients, where response of SLGS is damped rapidly.