Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method

Abstract

In this paper, a first-known dynamic stability analysis of carbon nanotube-reinforced functionally graded (CNTR-FG) cylindrical panels under static and periodic axial force by using the mesh-free kp-Ritz method is presented. The cylindrical panels 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. Eshelby–Mori–Tanaka approach is employed to estimate effective material properties of the resulting nanocomposite panels. By applying the Ritz minimization procedure to the energy expressions, a system of Mathieu–Hill equations is formulated. Then the principal instability regions are analyzed through Bolotin’s first approximation. Detailed parametric studies have been carried out to reveal the influences of volume fraction of carbon nanotubes, edge-to-radius ratio and radius-to-thickness ratio. In addition, effects of different boundary conditions and types of distributions of carbon nanotubes are examined in detail.