In-plane and out-of-plane free vibrations of functionally graded composite arches with graphene reinforcements

This article presents in-plane and out-of-plane free vibration analyses of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) arches. The arch is composed of multiple layers reinforced with graphene nanoplatelets (GPLs) that are evenly distributed in each layer but its weight fraction varies layer-by-layer in the thickness direction. The effective material properties are calculated by Halpin-Tsai micromechanics model for Young’s modulus and the rule of mixture for both mass density and Poisson’s ratio of each GPLRC layer. Analytical solutions are obtained for the fundamental frequencies of the in-plane anti-symmetric vibration and out-of-plane vibration of both fixed and pinned FG-GPLRC arches by using Hamilton’s principle. A comprehensive parametric study is carried out to investigate the influences of distribution pattern, concentration and dimensions of GPLs as well as the geometrical parameters of the arch on the fundamental frequency of the FG-GPLRC arch. It is found that the fundamental frequency of the arch can be considerably improved by adding a lower quantity of GPLs as reinforcing nanofillers.