Stress wave propagation and natural frequency analysis of functionally graded graphene platelet-reinforced porous joined conical-cylindrical-conical shell

Stress wave propagation and free vibration response of functionally graded graphene platelet (FG-GPL)-reinforced porous joined truncated conical-cylindrical-conical shell are investigated in this paper. The shell is constructed of a metallic matrix reinforced by three types of distribution of GPLs in open-cell interior pores. The modified Halpin-Tsai estimation and the generalized rule of the mixture are employed to calculate the effective mechanical properties of the structure. Three different distributions for porosity are assumed along with the shell thickness: two kinds of symmetric FG distributions and uniform distribution of porosity. The Rayleigh-Ritz energy method, accompanied by the Finite element method, has been used to solve 2D-axisymmetric elasticity equations. Furthermore, the Newmark direct integration method is applied to obtain time responses and stress wave propagation of shells subjected to an internal impulse loading. A comparative and detailed investigation is also conducted to indicate the effects of different boundary conditions, geometries, the weight fraction of GPLs, porosity coefficient, distribution of porosity and dispersion pattern of GPLs on the natural frequencies, mode shapes and time histories of displacement and stresses of the shell.