The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics

The nonlinear dynamical response of a two-degree-of-freedom aeroelastic airfoil motion with cubic restoring forces is investigated. A secondary bifurcation after the primary Hopf (flutter) bifurcation is detected for a cubic hard spring in the pitch degree-of-freedom. Furthermore, there is a hysteresis in the secondary bifurcation: starting from different initial conditions the motion may jump from one limit cycle to another at different fluid flow velocities. A high-order harmonic balance method is employed to investigate the possible bifurcation branches. Furthermore, a numerical time simulation procedure is used to confirm the stable and unstable bifurcation branches.