Measurements revealed the contribution of multiple traveling waves to the flutter vibrations of bladed disks. Saturated flutter vibration, whether in this multi-wave or in its better-understood single-wave form, is a nonlinear phenomenon. However, it is still not understood of what physical origin the relevant nonlinearities are, and under what conditions single-wave or multi-wave flutter vibration occurs. Recent theoretical work suggests that multi-wave flutter vibration can be explained by strongly nonlinear frictional inter-blade coupling. The verity of this hypothesis is strictly limited by the simplicity of the considered model, namely a cyclic chain of seven oscillators with frictional coupling and rather unrealistic aeroelastic behavior. In the present work, it is demonstrated that nonlinear dynamical contact interactions at tip shrouds are a likely cause for the observed multi-wave flutter vibration. To this end, a more realistic structural turbine blade row model with a more realistic aeroelastic behavior is considered. Some insight into its intriguing dynamics, dependence of limit states on initial conditions and eigenvalue placement is provided. For instance, it is shown that there is an intimate relation between internal combination resonance conditions of certain traveling wave modes and the spectral content of single- and multi-wave flutter oscillations.