Application of HPM to the nonlinear vibrations of multiwalled carbon nanotubes



This work deals with applying the homotopy perturbation 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 interlayer 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 on the vibration characteristics of multiwalled carbon nanotubes is discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of this method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010