Mode-Locking, Quasi-Period and Chaos ofRotors Mounted on Nonlinear Bearings

This study is to investigate the dynamics of a rotor, with a single degree of freedom (SDOF), mounted on nonlinear bearings. This system has piecewise-linear stiffness and is subjected to a forcing excitation due to residual mass imbalance as well as a parametric one due to an axial periodic thrust. The frequencies for each individual parametric and forcing excitations are not equivalent, neither do they have a ratio of two simple integers. By using the fourthorder Runge–Kutta method a J-integral model, this strongly nonlinear system can be estimated for various parameters. The J-integral bifurcation can be analyzed by using the Poincare maps, the frequency spectra, the response waveforms, and the Lyapunov exponents in order to illustrate the jump phenomenon, the frequency-locking, and the routes to chaos. Furthermore, the intra-systematic relationship can be determined by the frequencies of spontaneous sidebanding clusters.