Three-Dimensional Static and Free Vibration Analysis of Carbon Nano Tube Reinforced Composite Cylindrical Shell Using Differential Quadrature Method

Abstract

In this paper, bending and free vibration analysis of carbon nanotubes reinforced composite (CNTRC) cylindrical shell is carried out using the three-dimensional theory of elasticity. The single-walled carbon nanotubes (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction which, are specified as the cases [Formula: see text], [Formula: see text], [Formula: see text] and FG-X. Effective material properties of CNTRC cylindrical shell are estimated according to the rule of mixture as well as considering the CNT efficiency parameters. An analytical solution is performed by using Fourier series along the axial coordinate together with state space technique along the radial coordinate for the simply supported CNTRC cylindrical shell. Moreover, for CNTRC cylindrical shell with other edges boundary conditions, a semi-analytical solution is accomplished by using differential quadrature method (DQM) along the axial coordinate and state space technique along the radial coordinate. Present approach is validated by comparing the numerical results with the available published results. Furthermore, effect of types of CNT distributions in the polymer matrix, volume fraction of CNT, edges boundary conditions and radial-to-thickness ratio on the bending and free vibration behavior of FG-CNTRC cylindrical are examined.