Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory

This paper initiates a theoretical analysis of wave propagation of fluid-conveying single-walled carbon nanotubes based on strain gradient elasticity theory with consideration of both inertia and strain gradients, in which two small-scale parameters are accounted for. For comparison purpose, the stress gradient theory for fluid-conveying carbon nanotubes is also discussed. Both theories are formulated using either the Euler–Bernoulli or the Timoshenko beam assumptions. It is found that the results predicted by these beam models are quite different. From a continuum-based point-of-view, the combined strain/inertia gradient Timoshenko beam model and its conclusion regarding wave propagation may be more reliable. Results show that the effect of internal fluid flow on the phase velocity of upstream-travelling wave is significant when the wave number is relatively low. However, this effect may be ignored when the wave number is sufficiently high. Moreover, the two small-scale parameters related to the inertia and strain gradients are shown to significantly affect the phase velocity at higher wave numbers. The present theoretical study highlights the significance of the effects of fluid flow and small scale related to inertia gradients on wave propagation in carbon nanotubes conveying fluid.