Geometrically nonlinear free vibration of FG-GPLRC circular plate on the nonlinear elastic foundation

The current article deals with the nonlinear free vibration of nanocomposite circular plates reinforced with graphene platelets (GPL). The functionally graded (FG) plate is considered over a three parameter non-linear elastic foundation. In this research, three types of gradings are assumed for reinforcing the plate by GPLs. The Halpin-Tsai micromechanical rule is exploited to obtain the elastic modulus of the plate. The first order shear deformation plate theory associated with the nonlinear strain-displacement relations are applied to extract the governing motion equations. The generalized differential quadrature (GDQ) method is implemented to solve the equations of motion in the plate domain. Furthermore, an iterative displacement control technique associated with the weighted residual technique are used to linearize the present problem and obtain the linear and nonlinear frequencies. After examining the validation study, some parametric studies are tabulated and plotted to recognize the effects of the boundary condition, distribution types of GPL, GPL weight fraction, geometrical parameters, and elastic foundation parameters on the linear and non-linear free vibration behaviour of structure. It is shown that maximum frequencies of the plate belong to the FG-X case and the minimum ones are obtained in FG-O type.