Computation of Stationary Deterministic Behavior of Nonlinear Dynamic Systems with Applications to Rotor-Bearing Structures

摘要

A numerical method for determining the solutions and stability of nonlinear ordinary differential equations used to model nonlinear dynamic systems is outlined. The method is based on a discrete time presentation. The combination of this method with an arc continuation method forms a flexible tool for investigating dynamic behavior as a function of various design variables. A typical nonlinear model resulted from the study of a rotor rubbing against its housing. The dynamic behavior of the model is reported. Models of plain cylindrical bearings were used to investigate the dynamic behavior of a model, with two degrees of freedom, representing a rotor-bearing structure. The effects of various design variables on the linear stability threshold were analyzed. The periodic motions that bifurcate at the linear stability threshold were determined to show the influence of nonlinear characteristics of the bearing models. For a harmonically excited rotor, their influence on motion and stability behavior was examined.