Simple first-order shear deformation theory for free vibration of FGP-GPLRC spherical shell segments

Abstract

This study presents a free vibration analysis of spherical shell segments using simple first-order shear deformation shell theory (S-FSDT) for the first time. The shell structure is made of functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) – one kind of porous material strengthened by graphene platelets (GPLs). Effective material properties of the FGP-GPLRC are determined by the modified Halpin-Tsai micromechanical model and the mixture rule. Four types of porosity distributions and GPL dispersions are considered fully in this study. The governing equations of the shell are derived based on the S-FSDT and classical shell theory, then solved by the well-known Rayleigh-Ritz method and the artificial spring technique. The results show that the S-FSDT can capture well the behaviors of the spherical shell segments. Besides, the best profile of novel FGP-GPLRC is not fixed; the physical parameters, geometric parameters, and material characteristics of the shells need to be investigated fully.