Nonlinear radial vibration of single-walled carbon nanotubes with 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 the first time that DM is used to model the nonlinear RBM vibration of CNTs. It is shown that tube radius and the amplitude of vibration play significant role in the nonlinear RBM vibration response of SWCNTs. Increasing the vibration amplitude decreases the natural frequency of vibration compare to the predictions of the linear models. However, with increase in tube radius, the effect of vibration amplitude on the natural frequency decreases. To show the accuracy and capability of this method, the results obtained herein are compared with the numerical results and good agreement is observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.