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

Periodic oscillations and bifurcations of a two-dimensional airfoil in plun ge and pitching motions with cubic pitching stiffness in incompressible flo w is investigated using the incremental harmonic balance (IHB) method. The bifurcations are obtained with the parametric continuation technique and th e stability of the periodic motions is investigated using the Floquet theor y. The autonomous non-linear system of the airfoil undergoes initial Hopf b ifurcation leading to limit cycle oscillation as the airspeed parameter is increased. Further increase in the airspeed causes symmetry breaking, saddl e-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.