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Mathematical Problems in Engineering
Volume 2016, Article ID 3275750, 12 pages
http://dx.doi.org/10.1155/2016/3275750
Research Article

Global Dynamics of a Compressor Blade with Resonances

1Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224051, China

Received 24 March 2016; Revised 16 June 2016; Accepted 12 July 2016

Academic Editor: Jaromir Horacek

Copyright © 2016 Xiaoxia Bian 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

The global bifurcations and chaotic dynamics of a thin-walled compressor blade for the resonant case of 2 : 1 internal resonance and primary resonance are investigated. With the aid of the normal theory, the desired form associated with a double zero and a pair of pure imaginary eigenvalues for the global perturbation method is obtained. Based on the simpler form, the method developed by Kovacic and Wiggins is used to find the existence of a Shilnikov-type homoclinic orbit. The results obtained here indicate that the orbit homoclinic to certain invariant sets for the resonance case which may lead to chaos in the sense of Smale horseshoes for the system. The chaotic motions of the rotating compressor blade are also found by using numerical simulation.