Vibration analysis of nanotubes conveying fluid based on gradient elasticity theory

In this paper two theoretical beam models are proposed for the vibration analysis of fluid-conveying nanotubes using the theory of strain gradient elasticity combined with inertia gradients. For comparison purposes, two stress gradient elasticity beam models were also discussed. Both theories were formulated using either the Euler-Bernoulli or the Timoshenko assumptions. Unlike the stress gradient beam models, in which only one material length scale parameter is introduced, the combined strain/inertia gradient beam models include two material length scale parameters related to the inertia and strain gradients, which enable us to investigate the size effect on the dynamical behavior of nanotubes conveying fluid. Results show that the size effect predicted by stress gradient beam models is not pronounced. However, for combined strain/inertia gradient beam models, the natural frequencies obtained display size-dependent properties. For small aspect ratios, the natural frequencies predicted by the combined strain/inertia gradient beam models are much smaller than the stress gradient results. Moreover, the critical flow velocities predicted by the combined strain/inertia gradient beam models are slightly higher than those predicted by the stress gradient beam models, showing that the stability of nanotubes is enhanced due to the consideration of inertia gradients.