Nonlocal nonlinear vibration of an embedded carbon nanotube conveying viscous fluid by introducing a modified variational iteration method

In this study, the large amplitude vibration and the stability of embedded carbon nanotubes (CNTs) conveying viscous fluid are analyzed. The effects of small-scale are presented into the model based on the nonlocal elasticity theory by changes in the fluid properties. Moreover, the viscosity effect is modeled by Rayleigh's dissipation function. After separating the time part of the governing equation, a modified method based on He's variational iteration method is proposed, the time response, and the complex nonlinear frequencies are obtained. Then, the effects of the geometric parameters, the velocity and the viscosity of the flowing fluid and small-scale effects are investigated on the nonlinear vibration behavior of CNTs. Results reveal that small-scale effects reduce the critical flow velocity. The viscosity effect appears as the nonlinearity due to large vibration amplitude increases, which cause reduction in both nonlinear frequencies and critical flow velocities.