Effects of nonlocal elasticity and slip condition on vibration of nano-plate coupled with fluid flow

Fluid–structure interaction (FSI) problem of a nano-plate under fluid flow is addressed in this article, where this nano-plate together with two rigid walls and a solid roof, is transformed to a fluid-carrying channel. We would analyze static instability (divergence) and dynamic instability for this system. To consider the effect of nano-size of the plate, the nonlocal elasticity theory and the effect of Knudsen number (Kn) in fluid boundary are used. Kn directly affects the velocity correction factor (VCF) defined as the ratio of average sliding velocity of fluid over channel wall to average no-sliding fluid velocity. Classical plate theory (CPT) and Navier–Stokesʹ continuum equation are used for modeling the FSI problem. The results show that nonlocal parameter could have a higher effect for liquid nano-flow than Kn, in reducing the divergence and flutter critical flow velocities. It is due to small range of variations of Kn for a liquid. Nonlocal parameter could have more effect on reducing the divergence critical liquid velocity of higher modes, specifically coupled-mode flutter. However, the results would be somewhat different from gas nano-flows. The range of variations of Kn for nano-gas flow would be higher and regarding the nonlocal parameter, the effect of Kn would be quite considerable for reducing critical gas velocities.