Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method

Periodic oscillations and bifurcations of a two-dimensional airfoil in plunge and pitching motions with cubic pitching stiffness in incompressible flow is investigated using the incremental harmonic balance (IHB) method. The bifurcations are obtained with the parametric continuation technique and the stability of the periodic motions is investigated using the Floquet theory. The autonomous non-linear system of the airfoil undergoes initial Hopf bifurcation leading to limit cycle oscillation as the airspeed parameter is increased. Further increase in the airspeed causes symmetry breaking, saddle-node and period-doubling bifurcations leading to chaos. The frequency of the limit cycle oscillation is also determined in the IHB method. (C) 1999 Academic Press.