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Shock and Vibration
Volume 14, Issue 6, Pages 447-457

Free Vibration Analysis of a Rectangular Plate with Kelvin Type Boundary Conditions

R. Kırışık1 and Ş. Yüksel2

1Turkish Atomic Energy Authority, Eskişehir Yolu 06530 Lodumlu, Ankara, Turkey
2Department of Mechanical Engineering, Faculty of Engineering and Architecture, Gazi University, 06570 Maltepe, Ankara, Turkey

Received 6 August 2006; Revised 16 October 2006

Copyright © 2007 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.


The transverse vibrations of a rectangular plate with the Kelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented.