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It is the purpose of this paper to make clear the effect of typical torsional viscous-friction damper on the reduction of the axial, torsional and two directions of lateral vibrations from the analytical and experimental points of view. At first, a typical type of the torsional viscous-friction damper is fitted to a high-speed diesel engine and the axial, torsional and two directions of lateral vibration displacements at the pulley end are measured in order to investigate the effect of the damper on the reduction of these vibrations in the three dimensional space of the engine shaftings from the experimental point of view. Next, the characteristics of the axial, torsional and two directions of lateral vibrations of the engine shaftings are investigated by three dimensional analysis of forced vibration by the transfer matrix method, which has been developed by the authors.