Application of VIM to the Nonlinear Vibrations of Multiwalled Carbon Nanotubes

The present work deals with applying the variational iteration method to the problem of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals inter layer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled carbon nanotubes are obtained. The influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube geometrical parameters on the vibration characteristics are studied by comparing the results with those from the open literature. This comparison illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method.