Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates

Abstract

In this paper, elastodynamic problem of carbon nanotube-reinforced functionally graded (CNTR-FG) plates is studied using the element-free kp-Ritz method based on first order shear deformation theory (FSDT). The plates are reinforced by single-walled carbon nanotubes (SWCNTs) with different types of distributions, i.e. uniform and three kinds of functionally graded distributions of carbon nanotubes along thickness direction of the panels. Extended rule of mixture is employed to estimate effective material properties of the resulting nanocomposites. Two-dimensional displacement fields of the plates are approximated by a set of mesh-free kernel particle functions. The discretized governing equations are developed via the Ritz procedure, and numerical time integration is performed through the Newmark-β method. Convergence studies are carried out by considering the influence of support size and number of nodes to verify the numerical stability of the present element-free method. Numerical simulations are used to study the effect of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, boundary condition, load type and distribution type of carbon nanotubes on the dynamic responses of CNTR-FG plates.