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Shock and Vibration
Volume 19, Issue 3, Pages 273-285

Transverse Vibrations of Clamped and Simply-Supported Circular Plates with Two Dimensional Thickness Variation

N. Bhardwaj,1 A.P. Gupta,2 K.K. Choong,1 C.M. Wang,3 and Hiroshi Ohmori4

1School of Civil Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Seberang Perai Selatan, Pulau Pinang, Malaysia
2Department of Applied Sciences and Humanities, Huda- Sector 23-A, ITM University, Gurgaon- Haryana-122017, India
3Department of Civil Engineering, National University of Singapore, Kent Ridge, Singapore
4Department of Environmental Engineering and Architecture, School of Environmental Studies, Nagoya University, Japan

Received 20 May 2008; Revised 23 September 2010

Copyright © 2012 Hindawi Publishing Corporation. 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.


Two dimensional boundary characteristic orthonormal polynomials are used in the Ritz method for the vibration analysis of clamped and simply-supported circular plates of varying thickness. The thickness variation in the radial direction is linear whereas in the circumferential direction the thickness varies according to cos kθ, where k is an integer. In order to verify the validity, convergence and accuracy of the results, comparison studies are made against existing results for the special case of linearly tapered thickness plates. Variations in frequencies for the first six normal modes of vibration and mode shapes for various taper parameters are presented.