International Journal of Differential Equations
Volume 2011 (2011), Article ID 343576, 17 pages
Research Article

Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions

1Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, Iran
2Faculty of Mechanical Engineering, Takestan Branch, Islamic Azad University, P.O. Box 3351, Takestan 58937, Iran

Received 7 May 2011; Accepted 20 June 2011

Academic Editor: S. Grace

Copyright © 2011 Hossein Aminikhah and Milad Hemmatnezhad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. 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 influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are 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 the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.