On the forced resonant vibration analysis of functionally graded polymer composite doubly-curved nanoshells reinforced with graphene-nanoplatelets

Abstract

The proposed work fills a gap of investigation on forced resonant vibration analysis of graphene nanoplatelets (GNPs) reinforced functionally graded polymer composite (FG-PC) doubly-curved nanoshells. For the first time, forced resonate vibration of the nanoshells including four different geometries of the shells namely spherical, elliptical, hyperbolic and cylindrical has been studied here. The Halpin–Tasi model and a rule of mixture are adopted to estimate the effective material properties due to distribution patterns of GNPs (UD, FG-O and FG-X) The governing equations are obtained through the Hamiltonian principle for general third-order shear deformation shell theory in conjunction with the nonlocal strain gradient theory, and then solved for simply-supported boundaries. Using this work, it is possible to accurately analyze the roles of weight fraction, total number of layers as well as distribution pattern of GNPs, nonlocal parameter, strain gradient parameter, type of doubly-curved nanoshell and geometrical parameters on the resonant phenomena of GNPs reinforced FG-PC nanoshells. The results indicate that resonant phenomenon will occur firstly in the hyperbolic type of the nanoshell, followed by cylindrical, elliptical and spherical ones. In addition, the resonant phenomenon will occur sooner in flat structures compared to curved ones.