Applied Mathematics and Mechanics

, Volume 34, Issue 5, pp 627–636 | Cite as

Bifurcation and chaos of airfoil with multiple strong nonlinearities

  • Ming Cai (蔡铭)Email author
  • Wei-fei Liu (刘卫飞)
  • Ji-ke Liu (刘济科)


The bifurcation and chaos phenomena of two-dimensional airfoils with multiple strong nonlinearities are investigated. First, the strongly nonlinear square and cubic plunging and pitching stiffness terms are considered in the airfoil motion equations, and the fourth-order Runge-Kutta simulation method is used to obtain the numerical solutions to the equations. Then, a post-processing program is developed to calculate the physical parameters such as the amplitude and the frequency based on the discrete numerical solutions. With these parameters, the transition of the airfoil motion from balance, period, and period-doubling bifurcations to chaos is emphatically analyzed. Finally, the critical points of the period-doubling bifurcations and chaos are predicted using the Feigenbaum constant and the first two bifurcation critical values. It is shown that the numerical simulation method with post-processing and the prediction procedure are capable of simulating and predicting the bifurcation and chaos of airfoils with multiple strong nonlinearities.

Key words

airfoil motion strong nonlinearity bifurcation chaos simulation prediction 

Chinese Library Classification

O322 V215.3+

2010 Mathematics Subject Classification

37M20 65P20 65P30 


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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ming Cai (蔡铭)
    • 1
    Email author
  • Wei-fei Liu (刘卫飞)
    • 1
  • Ji-ke Liu (刘济科)
    • 1
  1. 1.School of EngineeringSun Yat-sen UniversityGuangzhouP. R. China

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