Stability analysis of an axially moving nanocomposite circular cylindrical shell with time-dependent velocity in thermal environments

Abstract

This article investigates the instability of an axially moving simply supported nanocomposite circular cylindrical shell reinforced by single-walled carbon nanotubes (SWCNTs) with time variant velocity in thermal environments considering the effect of viscous structure damping. The nanocomposite material properties are obtained from the extended mixture rule for uniformly distributed CNT, furthermore three different types of functionally graded distribution CNT in the matrix are represented. In addition, the Hamilton principle via the simplification assumption of the Donnell shallow-shell theory is employed to derive motion equations. At first, related displacements are obtained in terms of displacement in radius direction which is expressed in a combination of driven and companion modes from motion equations in axial and circumferential directions. The dimensionless motion equation in radius direction is discretized by the Galerkin method. The critical speed values of different types of CNT distribution reinforcement, various types of volume-fraction of CNT reinforcement and different temperatures are established using the multiple scale method. Moreover, the first order solution of the perturbation theory makes it possible to predict the unstable regions of principle parametric resonances and combination resonances. It occurs under the effect of temperature rising condition, changing the kind of SWCNTs as well as increasing the value of viscous structure damping, volume-fraction of CNT distribution, constant part of velocity function and fluctuation domain. Results show a system with the symmetric distribution of CNT reinforcement, while the outer and inner are CNT-rich, represents higher stability in axially moving nanocomposite cylindrical shells with constant and time-dependent velocity.

Communicated by Eleonora Tubaldi

Keywords:

• Nanocomposite
• cylindrical shell
• axially moving
• stability
• free vibration
• multiple-scale