On the use of Chebyshev polynomials in the Rayleigh-Ritz method for vibration and buckling analyses of circular cylindrical three-dimensional graphene foam shells

Abstract

This study aims to perform free vibration and buckling analyses of circular cylindrical shells made of three-dimensional (3D) graphene foam. Three kinds of porosity distribution are considered including two kinds of symmetrical distribution and uniform distribution. The Kirchhoff-Love shell theory is utilized to establish the mathematical model of 3D graphene foam (3D-GF) shells. Natural frequencies and buckling loads of the shells under various boundary conditions are obtained via the Rayleigh-Ritz method in conjunction with Chebyshev polynomials. Results show that the mechanical characteristics of the 3D-GF shells are significantly affected by the porosity coefficient and porosity distribution. Moreover, the effect of porosity coefficient is closely related to boundary conditions of the shells. It is also shown that as the porosity coefficient increases, the porosity distribution effect on the mechanical characteristics of 3D-GF shells becomes increasingly significant.