Vibrations of an Asymmetrical Shaft with Gravity and Nonlinear Spring Characteristics : Effect of Internal Resonance

Abstract

When an asymmetrical shaft is supported horizontally by single row deep groove ball bearings, a difference in shaft stiffnesses, that of support stiffnesses, and nonlinear spring characteristics coexist, and various kinds of nonlinear forced oscillations and nonlinear parametric oscillations occur. In this paper, internal resonance phenomena in the neighborhood of the secondary critical speed and the major critical speed are investigated. The following are clarified in both cases : (1) two peaks of a superharmonic resonance with both a forward and a backward components appear. (2) almost periodic motion due to Hopf bifurcation and one verified from a super combination resonance occur.