Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method

A nonlinear model is developed for the vibration of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory. The nanotube is assumed to be embedded in a Pasternak-type foundation with simply supported boundary conditions. The nonlinear equation of motion is solved by the energy balance method (EBM) to obtain a sufficiently accurate flow-induced frequency. It is demonstrated that the nonlinearity of the model makes a reasonable change to the frequency at high flow velocity and for the large deformations. Furthermore, the deviation of the frequency from the linear frequency will be exaggerated with an increase in the nonlocal parameter and a decrease of the Pasternak parameters. Ultimately, the results show that the nonlinearity of the model can be effectively tuned by applying axial tension to the nanotube.