A new approach for time-dependent response of viscoelastic graphene sheets embedded in visco-Pasternak foundation based on nonlocal FSDT and MHSDT theories

Abstract

In this paper, the thermo-mechanical dynamic response of annular/circular viscoelastic graphene plates embedded in visco-Pasternak foundation has been investigated using nonlocal first and modified higher-order shear deformation theories. The modified higher-order shear deformation theory is assumed to obtain the results of thick (high ratio of thickness to size) plates too. Also, the sheet is considered in thermal environment in order to study the thermal effects on the viscoelastic analysis. The viscoelastic behavior of the plate is simulated based on the Kelvin–Voigt model and the nonlinear von Karman strains have been considered. The dynamic governing equations have been derived using the Hamilton stationary of minimum potential energy based on the nonlocal first and modified higher-order shear theories and have been solved applying semi-analytical polynomial method solving method. The solving methodology is unique and has not been used in any other dynamic analysis before and its ability for solving the dynamic governing equations has also been confirmed. The time-dependent deflection of the sheet under uniform and non-uniform loads has been obtained. Different effects on the problem, including boundary conditions, damping coefficient of visco-Pasternak foundation, viscoelastic coefficient of the plate, small-scale effects, loading, and nonlinear effects have been discussed more precisely.