A numerical study on free vibration analysis of detailed and homogenized models for FG-CNTRC beams

The goal of this study is to compare and investigate the free vibration characteristics of detailed and homogenized models for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams, based on the finite element method (FEM). In this study, three types of FG-CNTRC beams and boundary conditions are considered for different volume fractions of CNT: UD (uniformly distributed), FG-X, and FG-Λ beams. These beams in which single-walled carbon nanotubes (SWCNTs) are distributed with a gradient through the thickness are employed and analyzed for simply supported (SS), clamped-clamped (CC), and free-free (FF) boundary conditions. For the homogenized model, the effective material properties are determined in terms of the CNT volume fraction using the linear rule of mixture. A commercial midas NFX program is used for finite element simulations to analyze the free vibration responses of FG-CNTRC beams. The numerical results are compared with the existing analytical solutions in the literature in order to validate the developed finite element models.