Two new vibration modes of the disk-shell shaped big medium gears placedon the three separate medium shafts of a turboprop engine have been found. They have the same nodal diameters as the conventional ones but their frequencies are higher. The tooth ring vibrates both radially and axially and has greater deflection than the gear hub. The resonance of these two new nodal diameter modes is much more dangerous than that of the conventional nodal diameter modes. Moreover they occur just nearly at the upper and lower bounds of the gear operating speed range. A special detuning method is developed for removing the resonance of these two new modes out of the upper and lower bounds respectively and the effectiveness of the damping rings in this case has been researched. The vibration responses measured on the reductor casing have been then reduced to a quite low level after the damping rings were applied to the three big medium gears.