Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection

Based on the nonlocal continuum theory, transverse vibration of a single-walled carbon nanotube (SWCNT) conveying fluid with immovable support conditions is investigated. Unlike previous similar studies, the SWCNT is assumed to be not perfectly straight and initially includes a slight geometrical curvature as an imperfection. The SWCNT is assumed to be embedded in a Pasternak-type foundation. Hamilton’s principle is applied to drive an efficient governing equation of motion, which covers stretching, large deformation, and imperfection nonlinearities. The perturbation method of multi scales (MMS) is applied and the nonlinear flow-induced frequency ratio is analytically calculated. The obtained results reveal that the imperfection of the nanotube at high flow velocities makes the model severely nonlinear, especially when considering the nonlocal effects. A noteworthy observation is that the nonlinear flow-induced frequency ratio is decreased as the imperfection of the nanotube increases. Whereas through a parametric study, the effects of the flow velocity, nonlocal parameter, the stiffness of the elastic foundation, and the boundary conditions (BCs) on this frequency reduction are calculated and discussed widely.