Nonlinear free vibration analysis of a double-walled carbon nanotube

Free vibration analysis of a double-walled carbon nanotube (DWCNT) is performed where the surrounding medium has been modeled employing a Winkler model. The nonlinear differential equation of motion is derived for both layers of the nanotube by using an analytical method. In order to solve the coupled nonlinear differential equations of the system, the variational iteration method is utilized. By applying this method, analytical expressions are derived to predict the vibration characteristics of the model and the nonlinear frequencies and responses of the double-walled carbon nanotube are obtained. Results obtained for the nonlinear frequencies are also compared with the frequencies found by the numerical method. It has been shown that the results determined by these two procedures are in an excellent agreement. Finally, a parametric study is carried out and the effects of different parameters, namely, the amplitudes, boundary conditions, and the geometrical dimensions on the frequencies of the system have been examined.