Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch |
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Authors: | Zhao De-Min and Zhang Qi-Chang |
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Institution: | Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China |
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Abstract: | The dynamics character of a two degree-of-freedom
aeroelastic airfoil with combined freeplay and cubic stiffness
nonlinearities in pitch submitted to supersonic and hypersonic flow
has been gaining significant attention. The Poincaré mapping
method and Floquet theory are adopted to analyse the limit cycle
oscillation flutter and chaotic motion of this system. The result
shows that the limit cycle oscillation flutter can be accurately
predicted by the Floquet multiplier. The phase trajectories of both
the pitch and plunge motion are obtained and the results show that
the plunge motion is much more complex than the pitch motion. It is
also proved that initial conditions have important influences on the
dynamics character of the airfoil system. In a certain range of
airspeed and with the same system parameters, the stable limit cycle
oscillation, chaotic and multi-periodic motions can be detected
under different initial conditions. The figure of the Poincaré
section also approves the previous conclusion. |
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Keywords: | airfoil flutter bifurcation and chaos freeplay nonlinearity Poincaré map |
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