Abstract
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.
Highlights
The assessment of aeroelastic phenomena with linear models has provided a reasonable amount of tools for the analysis of most of adverse instability behavior 1, 2
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
Techniques from nonlinear time series analysis theory have been presented in this work to investigate chaotic patterns of nonlinear motion-induced aeroelastic responses
Summary
The assessment of aeroelastic phenomena with linear models has provided a reasonable amount of tools for the analysis of most of adverse instability behavior 1, 2. Nonlinear behavior is inherent to aeroelastic systems and can be associated with aerodynamic sources compressibility, separated flows, aerodynamic heating, and turbulence effects and structural sources effects of aging, loose attachments, material features, and large deformations 3–5. Aeroelastic systems can face those effects, for instance, in transonic flight, high angle of attack manoeuvres, and in all cases leading to complex models beyond linearity suppositions. Nonlinear systems typically present features like, Mathematical Problems in Engineering multiple equilibrium points, bifurcations, limit-cycle oscillations, and chaos 6, 7. The presence of such effects results in modifications to the aeroelastic dynamics, leading to more laborious prediction of instabilities. The flutter phenomenon in the presence of nonlinearities happens in a different way to that foreseen in linear models
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