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Shock and Vibration
Volume 15, Issue 6, Pages 599-617
http://dx.doi.org/10.1155/2008/858025

Asymmetric Vibration of Polar Orthotropic Annular Circular Plates of Quadratically Varying Thickness with Same Boundary Conditions

N. Bhardwaj,1 A.P. Gupta,1 and K.K. Choong2

1Department of Applied Sciences and Humanities, Huda- Sector 23-A, Institute of Technology and Management, Gurgaon- Haryana-122017, India
2School of Civil Enginnering, Universiti Sains Malaysia, Engineering Campus, 14300 Nobong Tebal, Seberang Perai Selatan, P. Pinang, Malaysia

Received 2 July 2006; Revised 24 April 2007

Copyright © 2008 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.

Abstract

In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a) higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b) Lateral vibration characteristics of F-Fplates is more sensitive towards parametric changes in material orthotropy and foundation stiffness than C-C and S-Splates; (c) Effect of quadratical thickness variation on fundamental frequency is more significant in cases of C-C and S-S plates than that of F-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d) Fundamental mode of vibration of C-C and S-Splates is axisymmetrical while that of F-Fplates is asymmetrical.