Near-critical behaviour of a rotating shaft actively stabilised by piezoelectric elements

The paper is concerned with dynamical phenomena that occur in rotating shafts near critical threshold, i.e. close to the critical rotation speed at which such systems are known to exhibit self-excited vibration. The critical rotation speed can be changed by application of an active control system based on piezoelectric elements attached to rotating shaft. Use of piezoelectric sensors and actuators can shift the critical speed towards higher values; it is expected however to affect near-critical behaviour of the shaft. Vertically rotating shafts always undergo supercritical self-excitation when dispossessed of any stabilising system. The paper discloses that application of a piezoelectric stabilisation system gives, apart from advantageous growth of the critical speed, a disadvantageous change of character of the self-excited vibration. It has been observed that the supercritical soft evolution of the vibration amplitude can assume a rapid nature typical for subcritical bifurcation when the shaft is stabilised and greater gain factors in the control system are applied.