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Advances in Acoustics and Vibration
Volume 2012 (2012), Article ID 507031, 11 pages
Research Article

Vibrations of Three-Layered Cylindrical Shells with FGM Middle Layer Resting on Winkler and Pasternak Foundations

1Government Post Graduate College Jhang, Jhang 35200, Punjab, Pakistan
2G. C. University Faisalabad, Faisalabad 38000, Punjab, Pakistan
3Department of Civil Engineering, Iqra National University Peshawar, Peshawar 25000, Pakistan

Received 28 April 2012; Revised 31 July 2012; Accepted 15 August 2012

Academic Editor: Marc Asselineau

Copyright © 2012 Abdul Ghafar Shah 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.


Vibrations of a cylindrical shell composed of three layers of different materials resting on elastic foundations are studied out. This configuration is formed by three layers of material in thickness direction where the inner and outer layers are of isotropic materials and the middle is of functionally graded material. Love shell dynamical equations are considered to describe the vibration problem. The expressions for moduli of the Winkler and Pasternak foundations are combined with the shell dynamical equations. The wave propagation approach is used to solve the present shell problem. A number of comparisons of numerical results are performed to check the validity and accuracy of the present approach.