Chaotic torsional vibration of imbalanced shaft driven by a limited power supply

In this paper, torsional vibrations of imbalanced shaft driven by a limited power supply are studied. It is shown that mutual interaction of shaft and power supply may in particular result in chaotic self-oscillations that correspond to the strange attractors in the phase space of the coupled dynamical system “shaft–power supply”. In this particular model, strange attractors represent classical Lorenz and Feigenbaum attractors. Rotation characteristic of the power supply and resonance characteristic of the shaft rotational motion in one of the resonance zones are studied. It is shown that at certain intervals, these characteristics may be non-unique, which corresponds to the case of chaotic dynamics. Such non-trivial properties of the coupled system “shaft–power supply” could be used for a better understanding of complex vibrational phenomena in real applied systems such as problems related to the damping of the torsional vibrations.

► The results on chaotic dynamics are obtained analytically and are linked to the classical Lorentz system.
► The mutual interaction of shaft and power supply may result in chaotic self-oscillations.
► Strange attractors represent classical Lorenz and Feigenbaum attractors.
► Rotation and resonance characteristics are studied.
► At intervals corresponding to the chaotic dynamics rotation and resonance characteristics scatter.