Nanofluidic flow-induced longitudinal and transverse vibrations of inclined stocky single-walled carbon nanotubes

Abstract

Dynamic interaction of an inclined stocky single-walled carbon nanotube (SWCNT) and a viscous nanofluid flow in the context of nonlocal continuum theory of Eringen is of concern. The SWCNT is modeled based on the nonlocal Timoshenko and higher-order beam theories. To this end, the governing equations of an inclined SWCNT are constructed for each nonlocal beam by taking into account the applied interaction forces on the inner surface of the SWCNT. By employing a slip-flow model and using Newton’s second law, the governing equations of the viscous nanofluidic flow inside the SWCNT are obtained. Through combining the resulting governing equations of the SWCNT and those of the nanofluidic flow, the dimensionless governing equations of the SWCNT conveying nanofluid flow are established. Using Galerkin method, the discrete form of the governing equations is obtained for each nonlocal beam model. In the case of a SWCNT with simply supported and immovable ends, the resulting sets of ordinary differential equations are solved in the time domain via an efficient scheme. The effects of the slenderness ratio, small-scale parameter, speed and density of the nanofluid flow, inclination angle, and initial axial force within the SWCNT on the maximum values of dynamic longitudinal and transverse displacements as well as maximum values of nonlocal axial force and bending moment within the SWCNT are examined and discussed.