Investigating nonlinear vibrations of multi-scale truncated conical shell segments with carbon nanotube/fiberglass reinforcement using a higher order conical shell theory

Abstract

This research deals with the nonlinear vibration analysis of functionally graded carbon nanotubes and fiber-reinforced composite truncated conical shell segments based upon third-order shear deformation theory. A detailed procedure for obtaining material properties of the multi-scale carbon nanotube/fiber-reinforced composite based on the three-dimensional Mori–Tanaka scheme has been provided. The truncated conical shell segments have been reinforced by distributed carbon nanotubes in the thickness direction according to uniform, linear, and nonlinear functions. The nonlinear equations have been solved via both Galerkin’s technique and Jacobi elliptic function method. Based on the numerical results, the effects of diverse carbon nanotube distribution, fiber volume, fiber orientation, and semi-vertex and open angles of the segment on vibrational frequencies of the truncated conical shell have been studied.