@article{oai:nagoya.repo.nii.ac.jp:00030910,
 author = {Yamamoto, Toshio and Ishida, Yukio},
 issue = {1},
 journal = {Memoirs of the Faculty of Engineering, Nagoya University},
 month = {Nov},
 note = {When single-row deep groove ball bearings with small angular clearance are used in a rotating shaft system, there appear nonlinear spring characteristics in a restoring force of a shaft. With reference to nonlinear forced oscillations, almost all the researches reported till now is on the topic of rectilinear systems. Nonlinear forced oscillations in a rotating shaft system with gyroscopic moments have unique characteristics. In the first place, we discuss a particular vibration phenomena at the major critical speed when rotating spring characteristics and rotating difference in shaft stiffness exist. In such a case, resonance curves at the major critical speed vary extremely with the change of the angular position of the unbalance and the unstable region appear. Next we consider nonlinear forced oscillations in a shaft system with static nonlinearity. We obtained experimentally various kinds of subharmonic and summed-and-differential harmonic oscillations. It is clarified that the occurrence of these oscillations depends on the assembling condition of the shaft system. Nonlinear forced oscillations are also discussed theoretically. The representation of nonlinear characteristics in polar coordinates gives a clear description of the phenomena and aids in the prediction of the occurrence. It is showed that the experimental results may clearly explained in the light of this theoretical results.},
 pages = {59--109},
 title = {On the vibrations of a shaft with nonlinear spring characteristics},
 volume = {30},
 year = {1978}
}