Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model

We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived.

► We consider a non-smooth model of a Jeffcott rotor with a bearing clearance. ► Path-following is applied for bifurcation analysis of the periodic motion. ► Fold, flip, grazing, torus and cusp bifurcations of cycles are detected and studied. ► We derive an analytical expression predicting grazing incidences. ► Unstable periodic motion embedded within a chaotic attractor is found numerically.