Nonlinear vibration of fluid-conveying carbon nanotube using homotopy analysis method

Nonlinear vibration analysis of a single-walled carbon nanotube, using the Eringen nonlocal elasticity and Euler-Bernoulli beam theories, is carried out. Pasternak-type foundation and the simply-supported boundary conditions are assumed for the carbon nanotube and the governing equation of motion is developed using those theories. The Galerkin method is utilized to obtain the nonlinear ordinary differential equation of vibration of the single-walled carbon nanotube and the homotopy analysis method is employed to determine its nonlinear natural frequency. A parametric sensitivity study is then carried out. Few of the parameters were the axial tension, nonlocal parameter, fluid velocity and the foundation stiffness. The parametric study is mainly focused on the nonlinear natural frequency of single-walled carbon nanotube. Finally, a numerical simulation is carried out to determine the accuracy of the obtained results. Furthermore, an elliptical integral is utilized to verify the nonlinear natural frequency, which was obtained using the homotopy analysis method.