The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method

Abstract

In this paper, axisymmetric natural frequencies of nanocomposite cylinders reinforced by straight single-walled carbon nanotubes are presented based on a mesh-free method. The straight carbon nanotubes (CNTs) are oriented, aligned or randomly or locally aggregated into some clusters. Volume fractions of the CNTs and clusters are assumed to be functionally graded along the thickness, so material properties of the carbon nanotube reinforced composite cylinders are variable and are estimated based on the Eshelby–Mori–Tanaka approach. In the mesh-free analysis, moving least squares shape functions are used for an approximation of the displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. The effects of orientation and aggregation of the functionally graded CNT are studied. It is observed that kind of distributions, aggregation or even randomly orientations of CNTs has significant effect on the effective stiffness and frequency parameter.