Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method

In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects, nonlocal elasticity theory is applied due to its simplicity and accuracy. The small-size effects and slip boundary conditions of nano-flow are taken into account through Knudsen number (Kn). The Y-SWCNT is surrounded by elastic medium which is simulated as nonlinear Visco-Pasternak foundation. Using energy method and Hamilton’s principle, the nonlinear governing motion equation is obtained. The governing motion equation is solved using both Galerkin procedure and Homotopy analysis method (HAM). Numerical results indicate the significant effects of the mass and velocity of the fluid flow, strength of longitudinally magnetic field, (Kn), angle between the centerline of carbon nanotube and the downstream elbows, nonlocal parameter and nonlinear Visco-Pasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nano-devices in which Y-shaped nanotubes act as basic elements.