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Journal of Engineering
Volume 2013, Article ID 937596, 7 pages
Research Article

Coupling between Transverse Vibrations and Instability Phenomena of Plates Subjected to In-Plane Loading

1Department of Engineering, Institute of Applied Mechanics (IMA), Universidad Nacional del Sur (UNS), Alem 1253, B8000CPB Bahía Blanca, Argentina
2Consejo Nacional de Investigaciones Científicas y Técnicas, (CONICET), Bahía Blanca, Argentina

Received 27 November 2012; Accepted 31 January 2013

Academic Editor: Gabriele Milani

Copyright © 2013 D. V. Bambill and C. A. Rossit. 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.


As it is known, the problems of free transverse vibrations and instability under in-plane loads of a plate are two different technological situations that have similarities in their approach to elastic solution. In fact, they are two eigenvalue problems in which we analyze the equilibrium situation of the plate in configurations which differ very slightly from the original, undeformed configuration. They are coupled in the event where in-plane forces are applied to the edges of the transversely vibrating plate. The presence of forces can have a significant effect on structural and mechanical performance and should be taken into account in the formulation of the dynamic problem. In this study, distributed forces of linear variation are considered and their influence on the natural frequencies and corresponding normal modes of transverse vibration is analyzed. It also analyzes their impact for the case of vibration control. The forces' magnitude is varied and the first natural frequencies of transverse vibration of rectangular thin plates with different combinations of edge conditions are obtained. The critical values of the forces which cause instability are also obtained. Due to the analytical complexity of the problem under study, the Ritz method is employed. Some numerical examples are presented.