Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment

Abstract

In this paper, a free vibration analysis of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), using the element-free kp-Ritz method, is presented. Different types of distributions of uniaxially aligned SWCNTs are considered. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded through the thickness direction according to several linear distributions of the volume fraction of carbon nanotubes. The governing equations are based on the first-order shear deformation plate theory and the two-dimensional displacement fields are approximated by mesh-free kernel particle functions. Convergence and comparison studies have been carried out to verify the stability and accuracy of the present method for analysis of free vibration of various types of CNTRC plates. In computational simulation, several examples are presented to analyze the effects of carbon nanotue volume fraction, plate width-to-thickness ratio, plate aspect ratio and temperature change on natural frequencies and mode shapes of various types of FG-CNTRC plates, and results for uniformly distributed (UD) CNTRC plates are also provided for comparison. The effect of boundary conditions is also examined.