Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments

This paper studies the small and large amplitude vibration behaviors of graphene-reinforced composite (GRC) laminated cylindrical panels supported by an elastic foundation under thermal environmental conditions. The temperature dependent material properties of GRC are assumed to be functionally graded in a piece-wise pattern by changing the volume fraction of graphene in the panel thickness direction and are estimated by the extended Halpin-Tsai micromechanical model. The motion equations for the nonlinear vibration problem of the panels are obtained from the higher order shear deformation shell theory and take into consideration of the effects of the von Kármán geometric nonlinearity, the elastic foundation and the temperature change. The nonlinear vibration solutions for the FG-GRC laminated cylindrical panels can be obtained by applying a two-step perturbation technique. We observe that the natural frequencies of FG-GRC panel with symmetrical distribution of graphene reinforcements are higher, whereas the nonlinear to linear frequency ratios of the same panel are lower than those of panels with uniform or unsymmetrical distribution of graphene reinforcements.