The aim of this study is the development of geometrically non-linear vibration and Green–Naghdi-based coupled thermo-elasticity analysis with energy dissipation in a functionally graded multilayer cylinder reinforced by graphene platelets subjected to mechanical and thermal shock loadings. The mechanical and thermal properties of each graphene platelets-reinforced layer are estimated using the modified Halpin–Tsai model and rule of mixture. The meshless local Petrov–Galerkin method based on total Lagrangian approach is developed to derive the non-linear discrete system of governing equation with respect to the initial configuration. The obtained non-linear dynamic equations are solved analytically using the iterative Newmark/Newton–Raphson technique. The obtained results by the proposed method for isotropic homogeneous cylinder are verified by results of finite element method with very fine meshing and good agreement is achieved. The effect of some parameters, such as number of layers, stacking sequences of layers and volume fraction exponent on dynamic characteristics of FG multilayer cylinder, is discussed in details. The results show that the volume fraction of graphene platelets in each layer and stacking sequences of layers have significant effect on non-linear dynamic behavior of cylinder.

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