Forced Oscillations of a Continuous Rotor with Strong Geometric Nonlinearity. Separation of Resonance Point by Effect of Gravity and Axial Force.

Abstract

When both ends of the rotor are supported by self-aligning double-row ball bearings, the geometric nonlinearity appears due to the stiffening effect in elongation of the shaft if the movements of the bearings in the longitudinal direction are restricted. As the rotor becomes more slender, this nonlinearity becomes stronger. In this paper, we study unique nonlinear phenomena due to the strong nonlinear spring characteristics. When the shaft is supported horizontally, the difference in support stiffnesses and the asymmetrical nonlinearity appear due to the shift of the equilibrium position. By the influences of the internal resonance and the axial force, the nonlinear resonance phenomena become very complex. For example, a peak of resonance curves split into two peaks, these two peaks leave each other and then become a hard and a soft spring types, respectively, and almost periodic motions and chaotic vibration appear. We clarified these phenomena theoretically and experimentally.