Table of Contents
Journal of Composites
Volume 2015, Article ID 750392, 11 pages
Research Article

Rayleigh-Ritz Vibrational Analysis of Multiwalled Carbon Nanotubes Based on the Nonlocal Flügge Shell Theory

1Department of Engineering Science, Faculty of Technology and Engineering (East of Guilan), University of Guilan, Vajargah, Rudsar 44891-63157, Iran
2Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

Received 1 June 2015; Accepted 3 December 2015

Academic Editor: Federico Juan Sabina

Copyright © 2015 H. Rouhi et al. 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.


A nonlocal elastic shell model considering the small scale effects is developed to study the free vibrations of multiwalled carbon nanotubes subject to different types of boundary conditions. Based on the nonlocal elasticity and the Flügge shell theory, the governing equations are derived which include the interaction of van der Waals forces between adjacent and nonadjacent layers. To analytically solve the problem, the Rayleigh-Ritz method is employed. In the present analysis, different combinations of layerwise boundary conditions are taken into account. Some new intertube resonant frequencies and the associated noncoaxial vibrational modes are identified owing to incorporating circumferential modes into the shell model.