Codimension-two bifurcation of motions of an airfoil in incompressible flow

Codimension-two bifurcations of an airfoil with non-linear pitching stiffness in incompressible flow are investigated. The nonlinearity of the spring is regarded as cubic pitching stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations, and the analytic solutions of the critical speed and linear stiffness for codimension-two bifurcation are obtained. The stabilities of the equilibrium points and limit cycles in different regions of two parameter plane are studied. Some numerical integration results are given.