Remarks on multiparameter mappings: Controlled-parameter and threshold maps

Abstract

A rotor system in rubbing is shown to exhibit complex phenomena including higher subharmonic oscillation, period-doubling bifurcation and chaotic motions due to its strongly nonlinear dynamic characteristics. This study introduces an alternative Poincaré section method to analyze the dynamic behavior of a rotor in rubbing. This response integration for analyzing high-order harmonic and chaotic responses is used to integrate the distance between state trajectory and the origin in the phase plane during a specific period. This integration process is based on the fact that the integration value would be constant if the integration interval is equal to the response period. It provides a quantitative characterization of system responses and can assist the role of the traditional stroboscopic technique (Poincaré section method) to observe bifurcations and chaos of the nonlinear oscillators. For a rubbing rotor the response composes of multiple high-order harmonic motions or chaos with extreme contamination, which cannot be easily to be distinguished either from orbit plot or from Poincaré map. Combining the capability of precisely identifying period and constructing bifurcation diagrams, the advantages of the proposed method are shown by simulations.