| The non-linear dynamic behavior of symmetric rotors is investigated using methods from dynamical systems and bifurcation theories. Rotordynamic instabilities and resonances caused by internal hysteresis, fluid film bearing forces and mass unbalance are analyzed. Two types of models have been proposed to study these effects on rotordynamics: a slender, flexible shaft made of a viscoelastic material and rotating at a constant rate about its longitudinal axis is used to study the effects of internal hysteresis and mass unbalance on rotordynamics, and an unbalanced disk mounted midway between two supporting fluid film journal bearings on a rigid shaft is used to examine the effects of fluid bearing forces and mass unbalance.; For the perfectly balanced flexible shaft model it is well known that internal damping can cause an instability at a certain critical speed. The instabilities are predicted using the linearized shaft model and the post-critical behaviors are determined by applying the center manifold theory to the full non-linear equations of motion. It is determined that synchronous whirl, non-synchronous whirl, and competing-mode types of behaviors are possible for various ranges of the parameter values.; The first vibrational mode of the shaft is then used to determine the effect of unbalance on system behavior. Special attention is paid to the interaction between the primary resonance caused by mass unbalance and the destabilizing influence of internal damping. The results show that the shaft responses include synchronous constant amplitude motions and amplitude modulated solutions.; For the second model the non-linear oscillations of a rotor supported in fluid film journal bearings is analyzed. With the introduction of periodic forcing due to rotor unbalance, the results show that the limit cycle arising from the whirl instability (a Hopf bifurcation) in the neighborhood of the threshold speed is perturbed and a rich variety of response types is observed when certain resonant conditions occur. These include harmonic, subharmonic, as well as amplitude modulated responses. |
