Transverse vibration and instability of fluid conveying triple-walled carbon nanotubes based on strain-inertia gradient theory

Abstract

A B S T R A C T In this paper, the transverse vibration of a triple -walled carbon nanotube (TWCNT) conveying fluid flow is studied based on the strain/inertia gradient theory with van der Waals interaction take n into consideration. The nanotube is modelled using Euler-Bernoulli beam model and the Galerkin's method is employed to obtain the CNT complex valued Eigen-frequencies. The effects of the fluid flow thorough the innermos t tube and the van der Waals force interaction between any two walls on th e instability of the nanotube are studied. In addition, the effects of t he nano-flow size, the characteristic lengths and the aspect ratio on the critical flow velocities are investigated. Results indicate that due to the flui d flow the nanotube natural frequencies decrease. By considering the size effec t of the fluid flow, frequencies decrease more rapidly causing reduction of the stability region. Moreover, it is shown that the length of the nanotu be can play an important role in the vibration response.