The mode split on disc like structures rotating in a dense fluid leads to a deviation of eigenfrequencies at high rotational speeds compared to their values in still water. Predicting eigenfrequencies correctly is essential to avoid fatigue cracks on prototype turbine runners. Analytical models for simple geometric configurations and complex numerical models using fully coupled fluid structure interaction to predict the mode split on arbitrary geometries exist. We are presenting a complementary approach of intermediate complexity applicable to arbitrary geometries. Mode shapes and modal parameters are computed by finite element analysis in still water. These mode shapes are imposed with a harmonic variation in time during an unsteady computational fluid dynamics computation. From the interaction between the flow and the modal motion, the modal force and the modal work can be computed. These can be converted into added modal mass and hydrodynamic damping and further into the shift of the eigenfrequency under rotation due to the fluid for a given mode. The tendencies of the frequencies with rotation compare reasonably well with experimental data. The numerical method can be applied to disc rotation speeds far beyond the range of experimental data revealing interesting tendencies and a phenomenological interpretation of the cause of the mode split.