Vibrations of a rotating shaft with nonlinear spring characteristics and unsymmetry

Rotating machines with nonlinear spring characteristics and the unsymmetry of shaft stiffness or rotor inertia have been often used in industries. Since vibrations due to the coexistence of nonlinearity and unsymmetry are complicated in theoretical treatments, there have been few studies on these vibrations. This paper mainly deals with the nonlinear forced oscillations at the major critical and other subcritical speeds in a rotating shaft system having both nonlinearity and unsymmetry. Such systems have unique vibratory characteristics different from those of a symmetrical system with nonlinearity. For example, at the major critical speed various types of resonance curves are obtained depending on the angular position of rotor unbalance. The unstable vibrations of subharmonic and summed-and-differential harmonic oscillations appear although only stable oscillations occur in the symmetrical system. And, stable and unstable vibrations of super-summed-and-differential harmonic oscillations occur only in the system with both nonlinearity and unsymmetry. In addition, we investigated the sub-combination tones in a symmetrical system with nonlinearity and the unstable vibrations of an unsymmetrical shaft with linear spring characteristics at the secondary critical speed.