Bifurcations and stability analysis for nonlinear oscillations of an airfoil

Analytic and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Stability parametric regions and multiple bifurcations for the system are investigated. The damping coefficients of the plunge and pitch are considered as perturbation parameters. With aid of center manifold and normal form theories, the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves are achieved, which can result in static bifurcation and Hopf bifurcation. Nonlinear flutter happens with a phenomenon of limit cycle oscillations (LCOs) when the damping coefficients are less than or greater than the linear critical values. Under certain conditions, quasi-periodic motions on 2T torus may occur. These complex dynamical behaviours are discussed in detail in this paper. This is useful to characterize the effects of different parameters on structural nonlinearities of the system and ensure that aerodynamic flutter of the airfoil does not take place. Finally, the numerical solutions simulated by four-order Runge-Kutta method are illustrated to tally with the analytic results.