Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field

Abstract

Based on the nonlocal elasticity theory, a nonlocal beam model is utilized to investigate the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive single-walled carbon nanotube (SWCNT) conveying fluid. The effect of longitudinal magnetic field is considered through the Lorentz magnetic force obtained from Maxwell's relations. Hamilton's principle is applied to the energy expressions to derive the higher-order FSI governing equation and the corresponding higher-order boundary conditions. In the solution part the differential transformation method (DTM) is used to solve the higher-order differential equations of motion. The effects of longitudinal magnetic field and nonlocal parameter on the vibration frequency and divergence instability of SWCNT conveying fluid are investigated. It can be concluded that the longitudinal magnetic field increases the critical flow velocities and the natural frequencies of the SWCNT. Numerical results from the model show that the fundamental natural frequency and critical flow velocity for the SWCNT increase as the nonlocal parameter increases, while in the presence of a strong longitudinal magnetic field the influence of internal fluid flow and nonlocal parameter on the vibrational frequencies of SWCNT can be reduced.