Nonlinear radial vibration of single-walled carbon nanotubes using numerical methods

This paper investigates the nonlinear radial breathing mode (RBM) vibration of single-walled carbon nanotubes (SWCNTs) based on numerical methods. A second order partial differential equation that governs the nonlinear RBM vibration for such nanotubes is derived using doublet mechanics (DM) . This nonlinear equation is reduced to ordinary differential equation using Galerkin method and then solved using Homotopy perturbation method (HPM) to obtain the nonlinear natural frequency in nonlinear RBM vibration. It is shown that tube radius and the vibration velocity play significant roles in the nonlinear RBM vibration response of SWCNTs. Increasing the vibration velocity increases the natural frequency of vibration compared to the predictions of the linear models. However, with increase in tube radius, the effect of vibration velocity on the natural frequency decreases. To show the accuracy and capability of this method, the results obtained herein are compared with the forth ordered Runge-Kuta method and good agreement is observed.

Keywords:

doublet mechanics , homotopy perturbation method , radial breathing mode vibration , single-walled carbon nanotubes , nonlinear vibration