Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator

The chaotic vibration analysis of a rotating flexible continuous shaft-disk system with rub-impact is studied. The system is modeled as a continuous shaft with a rigid disk in its mid-section with Coriolis and centrifugal effects included. The governing partial differential equations of motion are extracted based on the Euler–Bernoulli beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. Time series, phase plane portrait, power spectra, Poincaré map, bifurcation diagrams, and Lyapunov exponents are used to analyze the vibration behavior of the system. Initially, the case is investigated in which no Coriolis or centrifugal effects are considered. Then, another case is studied in which these effects are considered. The results confirm the claim that the rub-impact occurs at lower speed ratios due to the Coriolis and centrifugal forcing effects, and that the dynamic behaviors of the system for the two cases are much different as a result of the rub-impact in the second case. Periodic, quasi-periodic, sub-harmonic, and chaotic states can be observed while the appearance or disappearance of the chaos is different. The centrifugal forcing effect plays a greater role than that of the Coriolis force on the incidence of the rub-impact. These results can be useful in identifying the undesirable behaviors in these types of rotating systems.