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Shock and Vibration
Volume 18, Issue 3, Pages 471-484

Free In-Plane Vibration of Super-Elliptical Plates

Murat Altekin

Department of Civil Engineering, Yildiz Technical University, 34210 Esenler, Istanbul, Turkey

Received 4 March 2008; Revised 17 April 2009

Copyright © 2011 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.


Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.