Bifurcation analysis of airfoil in subsonic flow with coupled cubic restoring forces

The effects of coupled nonlinearities In the pitch and plunge degrees of freedom of an airfoil placed In a subsonic airflow are studied using a numerical time-marching scheme. The initial conditions are fixed, and the airfoil parameters are adopted from a previous study where primary and secondary Hopf bifurcations and modulated oscillations in a subcritical Hopf bifurcation were observed. The investigation is first carried out for fixed spring stiffness in the pitch degree of freedom while the plunge spring constant is varied. The second example fixes the plunge spring constant and varies the pitch spring stiffness. Both weak and strong restoring forces are considered. It is shown that coupled nonlinearities can generate a variety of motions and that chaotic behavior is possible in a narrow window of the bifurcation parameter.