Abstract
In this paper, we combined analytic method with numerical method to investigate complex dynamic behavior in a three-degree-of-freedom nonlinear aeroelastic system of an airfoil with external store. Center manifold and normal form theories are performed to derive the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves. Stable and unstable Hopf bifurcations appear when the damping coefficient of the plunge and the positive parameter Q, which is associated with the flow velocity and the pitch movement, are perturbed a little at the linear critical values. Under certain conditions, quasi-periodic motions on 2-D and 3-D torus may occur. Furthermore, with the aid of Poincare map, the largest Lyapunov exponent and frequency spectra, chaotic dynamics arise when 2-D tori become unstable and are violated. These rich results contribute to show the various characteristics of structural nonlinearities and avoid aerodynamic flutter of the airfoil. In the end, the numerical solutions achieved by fourth order Runge–Kutta method agree with the analytic results.
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