Resonant Oscillations of a Vertical Unbalanced Gyroscopic Rotor with Nonlinear Characteristics

Below is a presentation of resonant oscillations of a vertical rigid gyroscopic rotor with soft nonlinear elastic characteristics, viscous nonlinear resistance and a skewed disk with imbalanced mass. Particular attention is paid to the influence of the skewed disk and the imbalanced mass, as well as nonlinear resistance, on rotor dynamics. The first is determined by the behavior of external exciting torques and influences on the amplitude and phase of the oscillation, and the second is determined by the rheological properties of the environment and the rotation rate of the rotor shaft, influence not only the amplitude- and phase-frequency characteristics but also the stability of movement. These research results could be important for the development of optimal control technology of resonant vibration in order to determine optimal design parameters, the range of operating speeds and rotor balancing techniques during pre-work.