Saeidreza Mohebpour

The nonlinear vibrational characteristics of functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal shell panels in contact with nonlinear elastic foundation under internal pressure and thermal environment is investigated using the finite element method (FEM). The panel edges are restrained by rotational springs to simulate more realistically the edge boundary conditions. The toroidal panels are composed of several perfectly bonded individual layers, which are built by dispersing graphene platelets (GPLs) uniformly and with a random direction in a polymer matrix. The governing equations are derived in the context of the first-order shear deformation theory (FSDT) of shells along with von Kármán nonlinear geometric assumptions using nine-noded elements with five degrees of freedom per node. Results are presented in the graphical and tabulated forms to illustrate the effects of geometric and elastic foundation parameters, initial stresses and different patterns of distributions of GPLs on the nonlinear treatments of composite toroidal panels. It is shown that when the internal pressure and temperature difference increase the ratio of the nonlinear to linear frequency ratio increases as well.