Chaotic motions of an airfoil with non-linear stiffness in incompressible flow

Two-dimensional airfoils with cubic pitching stiffness in incompressible flow are analyzed to investigate the chaotic behaviour of self-excited dynamical system. Airfoils with different elastic axis positions will have different aerodynamic divergence speeds and hence different post-divergence angles of attack. Also there is a chaotic region for certain elastic axis positions. Several different phase plots together with their period doubling patterns have been calculated systematically by numerical integration, and boundaries of different motion types are shown in the parameter map of airspeed and elastic axis position. A two-step approximate analysis gives some interpretation of the route to chaos for the airfoil system investigated.