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Shock and Vibration
Volume 12, Issue 5, Pages 363-376
http://dx.doi.org/10.1155/2005/128640

Vibration Analysis of Rectangular Plates with One or More Guided Edges via Bicubic B-Spline Method

W.J. Si,1 K.Y. Lam,1 and S.W. Gong2

1Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
2Institute of High Performance of Computing, 1 Science Park Road No. 01-01, the Capricorn, Science Park II, 117528, Singapore

Received 19 January 2004; Revised 17 January 2005

Copyright © 2005 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

A simple and accurate method is proposed for the vibration analysis of rectangular plates with one or more guided edges, in which bicubic B-spline interpolation in combination with a new type of basis cubic B-spline functions is used to approximate the plate deflection. This type of basis cubic B-spline functions can satisfy simply supported, clamped, free, and guided edge conditions with easy numerical manipulation. The frequency characteristic equation is formulated based on classical thin plate theory by performing Hamilton's principle. The present solutions are verified with the analytical ones. Fast convergence, high accuracy and computational efficiency have been demonstrated from the comparisons. Frequency parameters for 13 cases of rectangular plates with at least one guided edge, which are possible by approximate or numerical methods only, are presented. These results are new in literature.