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

Awrejcewicz, J.; Krysko, V. A.; Moldenkova, T.

doi:https://doi.org/10.1155/MPE/2006/85623

Mathematical Problems in Engineering

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Volume 2006 | Article ID 085623 | https://doi.org/10.1155/MPE/2006/85623

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

J. Awrejcewicz,¹V. A. Krysko,²and T. Moldenkova²

Received31 Aug 2005

Accepted11 Sept 2005

Published22 Mar 2006

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.

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Copyright

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.

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