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Limit cycle flutter and chaotic motion of two-dimensional airfoil system. (Chinese. English summary) Zbl 1449.34139

Summary: Limit cycle flutter and the motion of chaos of two-dimensional airfoil with quadratic nonlinear pitching stiffness in incompressible flow on nonzero equilibrium points are investigated. The center manifold theory is used to reduce a four-dimensional system to a two-dimensional system, and the bifurcation points of the system are determined by bifurcation theory. The type and stability of bifurcation points are determined by computing focal values of system. The type of Hopf bifurcation is determined by the second Lyapunov method of bifurcation problem. The theoretical analysis presented here provides a good agreement with numerical simulations obtained by using a fourth-order Runge-Kutta method. Furthermore, the way leads to chaos in the airfoil system is found and there exits large field of the period-five motion. The results indicate that the bifurcation point is a stable weak focus, when the supercritical Hopf occurs, there exists a stable limit cycle. The motion of chaos occurs due to period-doubling bifurcation.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C23 Bifurcation theory for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C45 Invariant manifolds for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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