Vibration Analysis of Functionally Graded Graphene Reinforced Porous Nanocomposite Shells

Abstract

In this study, the vibration of functionally graded porous truncated conical shell reinforced with graphene platelets (GPLs) is investigated. The GPLs nanofillers and pores are considered to be uniform and nonuniform throughout the thickness direction. Using Hamilton’s principle, the governing equations are derived based on Love’s first approximation theory. The generalized differential quadrature method is applied to solve the governing equations of motion and to obtain the natural frequencies of the shells for various boundary conditions. Applying the Halpin–Tsai model and the rule of mixture, the effective elastic modulus, the Poisson’s ratio and the density of nanocomposite shell reinforced with GPLs are computed. The effects of porosity coefficients, distribution patterns of porosity, GPL weight fraction, geometry and size of GPLs, semi-vertex angle as well as boundary conditions on the natural frequency of the system are analyzed. It was observed in the results that the shells with symmetric porosity distribution reinforced by graphene platelet pattern A predict the highest natural frequencies. Furthermore, it was found that the natural frequencies of nanocomposite conical shell can be decreased by increasing the porosity coefficient. Besides, the geometry and size of GPLs as well as weight fraction of GPLs have significant effects on the natural frequencies.