Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Higher Order Refined Composite Beams Using Differential Quadrature Finite Element Method

Abstract

Present paper deals on the free vibration investigation of carbon nanotube-reinforced composite (CNTs) beams, based on refined third order shear deformation finite element beam theory. The particularity of this model is that, it can capture shear deformation effect without using of any shear correction factor by satisfying shear stress free at free edges. The carbon nanotubes are supposed to be immersed in a polymeric matrix with functionally graded pattern across the thickness direction of the beam, and their material properties are evaluated using the rule of mixture. The differential equations of motion and related boundary conditions are extracted using Lagrange’s principle and solved employing a robust numerical tool called, Differential Quadrature Finite Element Method (DQFEM) for the first time, with high convergence speed, fast calculus performance as well as a good numerical stability. The obtained results have been validated with those available in literature, in order to show the correctness of the present model. Afterwards, a deep parametric study is performed to examine the effects of various geometrical and material parameters on the vibration behavior of FG-CNTs beams.