A torsional vibration damper is integrated into a rotating electrical machine. A rotatable assembly of the electrical machine includes a rotor core pack having a first end and a second end. The integrated torsional vibration damper consists of a torsional elastic coupling and a torsional elastic damper and provides mechanical damping. The integrated torsional vibration damper is mounted to the rotatable shaft of the electrical machine by a flange. The rotor core pack is mounted at the first end to the integrated torsional vibration damper by suitable structure members such as a mounting flange and is not fixedly mounted directly to the rotatable shaft. In the case where the rotor core pack is cooled by circulating coolant fluid (e.g. MIDEL) then the integrated torsional vibration damper may be a viscous damper that uses the coolant fluid as a viscous working fluid.