Table of Contents
ISRN Mechanical Engineering
Volume 2012, Article ID 232498, 13 pages
Research Article

Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

1Department of Mathematics, G. C. University Faisalabad, Faisalabad 38000, Pakistan
2Department of Mathematics, Government Post Graduate College Jhang, Jhang 35200, Pakistan
3Department of Civil Engineering, Iqra National University Peshawar, Peshawar 25000, Pakistan
4Department Mathematics, The Islamia University Bahawalpur, Bahawalpur 63100, Pakistan

Received 31 May 2012; Accepted 25 July 2012

Academic Editors: C. C. Huang, M. Lefik, and A. Tounsi

Copyright © 2012 Muhmmad Nawaz Naeem 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.


The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.