Dynamic Instability Analysis of Embedded Multi-walled Carbon Nanotubes under Combined Static and Periodic Axial Loads using Floquet–Lyapunov Theory

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

Habib Ramezannejad ¹ , Hemad Keshavarzpour ² , Reza Ansari ³

1 - Department of Mechanical Engineering, Ramsar branch, Islamic Azad University, Ramsar, Iran
2 - Department of Mechanical Engineering, Rasht branch, Islamic Azad University, Rasht, Iran
3 - Associate Professor, Department of Mechanical Engineering, University of Guilan

Received: 2017-06-25 Accepted : 2017-11-16 Published : 2017-08-01

Keywords: Multi-walled Carbon Nanotubes, Dynamic instability, Mathieu-Hill model, Floquet&ndash, Lyapunov theory,

Abstract :

The dynamic instability of single-walled carbon nanotubes (SWCNT), double-walled carbon nanotubes (DWCNT) and triple-walled carbon nanotubes (TWCNT) embedded in an elastic medium under combined static and periodic axial loads are investigated using Floquet–Lyapunov theory. An elastic multiple-beam model is utilized where the nested slender nanotubes are coupled with each other through the van der Waals (vdW) interlayer interaction. Moreover, a radius-dependent vdW interaction coefficient accounting for the contribution of the vdW interactions between adjacent and non-adjacent layers is considered. The Galerkin’s approximate method on the basis of trigonometric mode shape functions is used to reduce the coupled governing partial differential equations to a system of extended Mathieu-Hill equations. Applying Floquet–Lyapunov theory, the effects of elastic medium, length, number of layers and exciting frequencies on the instability conditions of CNTs are investigated. Results show that elastic medium, length of CNTs, number of layer and exciting frequency have significant effect on instability conditions of multi-walled CNTs.

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