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Shock and Vibration
Volume 19 (2012), Issue 5, Pages 979-994
http://dx.doi.org/10.3233/SAV-2012-0705

Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading

J. Awrejcewicz,1,2 I.V. Papkova,3 E.U. Krylova,3 and V.A. Krysko3

1TU Darmstadt LOEWE-Zentrum AdRIA, Darmstadt, Germany
2TU Lodz, Department of Automation and Biomechanics, Lodz, Poland
3Department of Mathematics and Modeling, The Saratov State Technical University, Saratov, Russia

Received 25 April 2012; Accepted 25 April 2012

Copyright © 2012 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.

Abstract

We investigate non-linear dynamics of flexible rectangular plates subjected to external shear harmonic load action. We show that an application of the classical and widely used Fourier analysis does not allow to obtain real picture of the frequency vibration characteristics in each time instant. On the other hand, we show that application of the wavelets approach allows to follow frequency time evolutions. Our numerical results indicate that vibrations in different plate points occur with the same frequencies set although their power is different. Hence, the vibration characteristics can be represented by one arbitrary taken plate point. Furthermore, using wavelets scenarios of transitions from regular to chaotic dynamics are illustrated and discussed including two novel scenarios not reported so far in the existing literature.