Solutions of Nonlinear Free Vibration of Single-Walled Carbon Nanotubes Conveying Fluid.

Flow-induced vibration of carbon nanotubes becomes an important topic in nanotechnology. In our study, the non-linear vibrational behaviour of single-walled carbon nanotubes is presented. A singlewalled carbon nanotube is modelled as a simply supported beam embedded in the Winkler-Pasternak foundation. For the analysis, the Euler-Bernoulli beam theory is used to develop the model. This study uses a continuum approach which is widely employed for the dynamic behaviour of carbon nanotubes. The governing non-linear equation of motion is solved using the homotopy perturbation method. Elliptical functions are used to solve the exact solutions of these differential equations. The results of the exact solutions in terms of elliptic functions are compared to both the linear and nonlinear frequencies. Concerning changes in the Winkler and Pasternak parameters, axial force and flow velocity, the variation between linear and non-linear frequencies is studied. Furthermore, by adjusting these parameters, the non-linear vibrational frequency can be fine-tuned. [ABSTRACT FROM AUTHOR]