The fluid structure interaction e ect on the vibration and instability of a conveyed double-walled boron nitride nanotube

Abstract

The eff ect of Knudsen number (Kn) on the nonlinear vibration and instability of double-walled boron nitride nanotubes (DWBNNTs) conveying fluid has been investigated, based on Fluid Structure Interaction (FSI). The embedded DWBNNT is simulated as a Timoshenko Beam (TB), which includes rotary inertia and transverse shear deformation. The electro-mechanical governing equations are derived using the nonlocal piezoelectricity theory and discretized by a Di erential Quadrature Method (DQM). Regarding the types of flow regime in FSI, including continuum, slip, transition and free molecular, the value of Knudsen number as a small size parameter is designated and utilized to modify the fluid velocity. Considering the slip condition for an internal nanotube, the e ects of Knudsen number on various vibration modes, small scale, and nonlinear frequency amplitude are also taken into account for a clamped-clamped boundary condition. Results indicate that, based on the slip flow regime, the Knudsen number is an important parameter in FSI that changes the critical flow velocity and instability of nano systems and, therefore, should be considered in nanotubes conveying fluid.