Abstract
Various kinds of nonlinear forced oscillations may appear, when the restoring force of a rotating shaft has nonlinear spring characteristics. A rotating shaft system with gyroscopic moments acting does not experience rectilinear lateral vibrations of the shaft but a whirling type of motion. The nonlinear spring characteristics of the shaft are assumed to be distributed two-dimensionally and polar coordinates are used for their representation. Nonlinear spring characteristics expressed in polar coordinates may be characterized by a component with a constant value and other components whose magnitudes vary 1, 2, 3, 4, ... times, during a single whirl of the shaft around its equilibrium position. This type of representation gives a clear description of the phenomena of nonlinear forced oscillations and aids in the prediction of their occurrences. The present discussion centers on the subharmonic oscillation of order 1/3 of forward precession as a representative case. Other kinds of nonlinear oscillations are discussed briefly. Experimental results of previous reports may clearly be explained in the light of the results of this paper.
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