Mechanics of nonlinear internal flow induced vibration and stability analysis of a pre-tensioned single walled carbon nanotube using classical differential transform method with CAT and SAT after-treatment techniques

Abstract

This paper explores nonlinear internal flow induced vibration and stability of a pre-tensioned nanotube (SWCNT) that rests on elastic foundations. During the process of modeling, the impact of nonlinear Winkler foundation is considered and incorporated. For simplicity, the established nonlinear partial differential equation (PDE) for the vibrating SWCNT is converted into ordinary differential equation (ODE) via the method of Galerkin decomposition. Thereafter, the ODE is solved via classical differential transform method (DTM). The obtained analytical solution is further treated by the application of CAT and SAT after-treatment techniques to enable it captures large time domain during dynamic response. The treated solution is then validated and used for parametric studies. The parametric studies show how nonlocal elastic theory produces more accurate results than the classical equivalent and also how the foundation parameter increases the frequency of the system. It also shows how an increase in pre-tension has similar effect as that of flow velocity as they both increase the nonlinear frequency ratio. It is envisioned that this work will serve as point of reference for subsequent investigations and studies in this research area.