Longitudinal and transverse wave propagation analysis of stationary and axially moving carbon nanotubes conveying nano-fluid

In this study, the longitudinal and transverse wave propagation of the stationary and the axially moving carbon nanotubes (CNTs) with and without inside flowing fluid are investigated and analyzed. For this purpose, the nano-rod model for the longitudinal vibration and the Euler-Bernoulli beam model for the transverse vibration are utilized in order to modeling of the stationary CNT. Furthermore, the Rayleigh beam model is employed for modeling the axially moving CNT. In addition, for considering the nano-scale effects of the structure and fluid flowing through carbon nanotubes, the nonlocal elasticity theory and the Knudsen number are utilized, respectively, and their effects on the system wave frequency and phase velocity are investigated. Moreover, complex-valued wave dispersion relations and corresponding characteristic equations are derived according to the wave frequency, phase velocity, and the wave number. The results show that the axial velocity of the CNT has more effective role than the flowing fluid velocity for dispersed wave magnitude and intensification of the frequency, especially for the longitudinal dispersion. It is observed that the phase velocity is decreased by increasing the wave number on both longitudinal and transverse wave propagation.