The effects of Knudsen-dependent flow velocity on vibrations of a nano-pipe conveying fluid

In this paper, we investigate the effect of nano-flow on vibration of nano-pipe conveying fluid using Knudsen (Kn). We use Euler-Bernoulli plug-flow beam theory. We modify no-slip condition of nano-pipe conveying fluid based on Kn. We define a Kn-dependent flow velocity. We consider effect of slip condition, for a liquid and a gas flow. We reformulate Navier-Stokes equations, with modified versions of Kn-dependent flow velocity. We observe that for passage of gas through nano-pipe with nonzero Kn, the critical flow velocities decreased considerably as opposed to those for zero Kn. This can show that ignoring Kn effect on a gas nano-flow may cause non-conservative design of nano-devices. Furthermore, a more impressive phenomenon happens in the case of clamped-pinned pipe conveying gas fluid. While we do not observe any coupled-mode flutter for a zero Kn, we can see the coupled-mode flutter, accompanying the second-mode divergence, for a nonzero Kn.