Bifurcation analysis of double-walled carbon nanotubes conveying fluid subjected to van der Waals nonlinear forces

In the recent years, double-walled carbon nanotubes (DWCNTs) have been used for different indusrial applications such as separation and purification technology. So, the main purpose of this paper is to analyze the bifurcation behavior of double-walled carbon nanotubes conveying fluid with considering van der Waals nonlinear forces. The internal flow is considered to be pulsating. In the framework of the Von Karman's theory and the Euler-Bernoulli beam model, the nonlinear governing equations of motion are developed using the Hamilton's principle. The governing partial differential equations are discretized by means of the assumed modes method and solved by the Rung-Kutta method. Then, the effects of flow velocity and pulsation frequency on the dynamic behavior of the system are investigated by the bifurcation diagrams, phase plan portrait, time series and Poincar'e maps. The results indicate that the flow velocity and pulsation frequency have significant effects on the dynamic responses of the system. Also, the results of analysis reveal a variety of nonlinear behavior such as periodic, multi-periodic and chaotic motions that can give some insight to researchers in designing and studying these systems in the future.