Stability of an internally damped non-ideal flexible spinning shaft

The stability domain of an internally damped flexible spinning shaft, which is driven by a non-ideal source, is studied in this paper. It is found that the higher transverse modes may become unstable before the lower ones under certain conditions. In particular, we find the entrainment of the shaft spinning speed at specific values corresponding to the lowest stability threshold among all transverse modes. Moreover, the steady state amplitude of the transverse vibrations when the shaft spinning speed is stuck at the stability threshold is determined analytically. The analytical results thus obtained are validated with numerical simulations.