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Shock and Vibration
Volume 11 (2004), Issue 5-6, Pages 533-546
http://dx.doi.org/10.1155/2004/486249

A Single and Double Mode Approach to Chaotic Vibrations of a Cylindrical Shell with Large Deflection

Liming Dai,1 Qiang Han,2 and Mingzhe Dong3

1Industrial Systems Engineering, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, S4S 0A2, Canada
2Department of Mechanics, College of Traffic and Communications, South China University of Technology, Guangzhou 510640, China
3Petroleum Systems Engineering, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, S4S 0A2, Canada

Received 13 October 2003; Revised 8 December 2003

Copyright © 2004 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

The chaotic vibrations of a cylindrical shell of large deflection subjected to two-dimensional exertions are studied in the present research. The dynamic nonlinear governing equations of the cylindrical shell are derived on the basis of single and double mode models established. Two different types of nonlinear dynamic equations are obtained with varying dimensions and loading parameters. The criteria for chaos are determined via Melnikov function for the single mode model. The chaotic motion of the cylindrical shell is investigated and the comparison between the single and double mode models is carried out. Results of the research show that the single mode method usually used may lead to incorrect conclusions under certain conditions. Double mode or higher order mode methods should be used in these cases.