Effects of nonlocal elasticity and Knudsen number on fluid–structure interaction in carbon nanotube conveying fluid

In this paper, we investigate the effect of nano-size of both fluid flow and elastic structure simultaneously on the vibrational behavior of a pinned–pinned and a clamped–clamped nanotube conveying fluid, using both Knudsen number (Kn) and nonlocal continuum theory. Euler–Bernoulli plug flow (EBPF) theory is used for modeling fluid–structure interaction (FSI). It is observed that nonlocal parameter has more effect than Kn on the reduction of critical velocities of a liquid nano-flow. This effect has considerable impact on the reduction of critical velocities for a clamped–clamped beam in comparison with a pinned–pinned one. We concluded that the dimensionless nonlocal parameter, had more impressive effect on the dimensionless critical flow velocity of the second mode divergence and coupled mode flutter instabilities. However, in a gas nano-flow, the situation is totally different and Kn causes more reduction in critical velocities. Furthermore, it is emphasized that ignoring nano-size effects on liquid and gas nano-flow might cause non-conservative design of nano-devices.