Forced Oscillations of Rotating Shaft With Nonlinear Spring Characteristics and Internal Damping: Subharmonic Oscillation of Order 1/3 and Entrainment

An elastic rotating shaft supported by ball bearings may have nonlinear spring characteristics due to clearance and internal damping due to friction between the shaft and the bearings. In such a system, self-excited oscillations appear in the post critical region and nonlinear forced oscillations appear at various resonance points. In this paper, a phenomenon in the neighborhood of the critical speed of the subharmonic oscillation of order 1/3 of a forward whirling mode is discussed. It is clarified that, similar to the case of the subharmonic oscillation of order 1/2 of a forward whirling mode, an entrainment phenomenon appears due to the interplay between self-excited oscillations and forced oscillations.