Nonlinear Forced Oscillations of an Unsymmetrical Shaft and an Unsymmetrical Rotor with Quartic Nonlinearity : Variations of Resonance Curves of Subharmonic and Ultra-Subharmonic Oscillations and the Occurrence of Unstable Vibrations

Abstract

This paper deals with the subharmonic oscillations of order 1/4 and the ultra-subharmonic oscillations of orders 3/2 and 2/3 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 analyzed the effects of nonuniformity of the shaft stiffness or the rotor inertia on these oscillations, paying attention to the nonlinear components represented by the polar coordinates. By numerical calculations, resonance curves of each oscillation are presented. As a result, it is clarified that unstable vibrations occur in particular types of oscillations. In experiments, we observed these unstable vibrations in the unsymmetrical shaft system and the unsymmetrical rotor system, where the shafts were supported by cylindrical roller bearings.