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

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 taken 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 innermost tube and the van der Waals force interaction between any two walls on the instability of the nanotube are studied. In addition, the effects of the nano-flow size, the characteristic lengths and the aspect ratio on the critical flow velocities are investigated. Results indicate that due to the fluid flow the nanotube natural frequencies decrease. By considering the size effect of the fluid flow, frequencies decrease more rapidly causing reduction of the stability region. Moreover, it is shown that the length of the nanotube can play an important role in the vibration response.