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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 802970, 19 pages
Research Article

Chaotic Patterns in Aeroelastic Signals

Laboratory of Aeroelasticity, School of Engineering of São Carlos, University of São Paulo, Avenue Trabalhador Sancarlense, 400, 13566-590 São Carlos, SP, Brazil

Received 1 December 2008; Revised 18 February 2009; Accepted 24 August 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 F. D. Marques and R. M. G. Vasconcellos. 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.


This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.