Buckling and free vibration of axially functionally graded graphene reinforced nanocomposite beams

Abstract

This paper presents the buckling and free vibration analyses of axially functionally graded graphene reinforced nanocomposite (AFG-GPLRC) beams. Graphene platelets (GPLs) are uniformly or non-uniformly dispersed into the composite matrix as nanofillers according to five different distribution patterns (namely, UD, AFG-X, AFG-O, AFG-A, AFG-V) along the beam axial length. The effective material properties are approximated by using the improved Halpin-Tsai micromechanics model and the rule of mixture. Governing differential equations of AFG-GPLRC beams are derived based on the state-space method in the framework of Euler-Bernoulli beam theory, and then solved with the approximate laminated model (ALM) to obtain analytical solutions of critical buckling loads and natural frequencies. The present analysis is validated against the existing solutions. A comprehensive parametric study is carried out to scrutinize the effects of GPL distribution patterns, weight fraction, and geometric parameters on the buckling and free vibration behaviors of AFG-GPLRC beams.