Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method

Abstract

This work presents bending and free vibration behaviour of carbon nanotubes reinforced composite (CNTRC) plates using the three dimensional theory of elasticity. The single-walled carbon nanotubes reinforcement is either uniformly distributed or functionally graded (FG) along the thickness direction indicated with FG-V, FG-O and FG-X. In the present study the effective material properties of CNTRC plates, are estimated according to the rule of mixture along with considering the CNT efficiency parameters. For the plate with simply supported edges we used Fourier series expansion across the in plane coordinates as well as the state space technique across the thickness direction to obtain closed form solution. Since in the case of plate with non-simply supported boundary conditions it is not possible to use Fourier series along the longitudinal and width directions, therefore it should be employed numerical method along the above mentioned coordinates. In this investigation we used semi analytical technique, differential quadrature method along the in-plane coordinates and state-space technique across the thickness direction. Present approach is validated by comparing the numerical results with those published results. Furthermore, effect of types of CNT distributions in the polymer matrix, volume fraction of CNT, edges boundary conditions and width-to-thickness ratio on the bending and free vibration behaviour of FG-CNTRC plate are discussed.