In this work limit-cycle oscillations (LCOs) caused by aerodynamic non-linearities were analysed using fluid-structure interaction (FSI) simulations of a two-degree-of-freedom airfoil system. A comparison with sinusoidal forced motion oscillation simulations at the fundamental frequency was performed. The results show that using the first harmonic component for the forced motion oscillations is a good approach to describe the limit-cycle oscillations considered in this work. Following the work of G. Dietz, G. Schewe and H. Mai (2004), Journal of Fluids and Structures, Vol. 19, an energy budget analysis of the limit-cycle oscillations was performed. Power analysis of the LCO reveals that the power of the lift and moment show non-linear behaviour with increasing amplitude. The linearised equivalent power components that would occur in case of flutter were computed. These show that the defect in the power of the lift in the non-linear case is caused by the increase of the phase of the lift with oscillation amplitude, which is the result of the unsteady shock wave motions on both upper and lower surface of the airfoil. The power of the moment also shows a defect, which is much smaller than in case of the lift. This defect is caused by variations in both the magnitude and the phase of the moment with oscillation amplitude.

Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities have been studied numerically in this PhD thesis. A frequency domain-based method called ADePK has been developed to study the bifurcation behaviour of the LCO solutions. From several extensive (structural) parameter studies, it was found that aerodynamic non-linearities, especially shock wave motions, can lead to limit-cycle oscillations that occur already below the linearly predicted flutter boundary.