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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 85623, 16 pages
http://dx.doi.org/10.1155/MPE/2006/85623

Mathematical model of dissipative parametric vibrations of flexible plates with nonhomogeneous boundary conditions

1Department of Automatics and Biomechanics, Technical University of Łódź, 1/15 Stefanowski Street, Łódź 90-924, Poland
2Mechanics and Mathematics Department, Saratov State University, B. Sadovaya, 96 a, fl. 77, 410054 Saratov, Russia

Received 31 August 2005; Accepted 11 September 2005

Copyright © 2006 J. Awrejcewicz et al. 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 this work, parametric vibrations of flexible squared plates with changeable boundary conditions along their contours are studied. The known T. von Kármán equations serve as a mathematical model. This continuous system is reduced to a discrete one through the method of finite approximations of O(h4) order, which is solved further by the fourth-order Runge-Kutta technique. New scenarios of transition from harmonic to chaotic vibrations are reported.