Nonlinear forced oscillations of an unsymmetrical shaft and an unsymmetrical rotor with quartic nonliearity. 2nd report. Variations of resonance curves of summed-and-differential harmonic and super-summed-and-differential harmonic oscillations and the occurrence of unstable vibrations.

Abstract

This paper deals with the summed-and differential harmonic and super-summed-and-differential harmonic oscillations in an unsymmetrical shaft system and an unsymmetrical rotor system with nonlinear spring characteristics, involving quartic nonlinear terms in addition to quadratic and cubic terms. The former system is constituted by an unsymmetrical shaft and a symmetrical rotor, and the latter by a round shaft and an unsymmetrical rotor. We theoretically investigated the effects of the directional difference of shaft stiffness or rotor inertia on these oscillations, paying attention to the nonlinear components represented by the polar coordinates. Resonance curves for each oscillation are obtained by numerical calculation. As the results, it is clarified that the shapes of resonance curves vary due to the unsymmetry of the shaft or the rotor, and that an unstable vibration occurs in a particular type of oscillation. In experiments, the probability of occurrence of this unstable vibration was investigated.