Stability Analysis of Symmetrical Rotor-Bearing Systems With Internal Damping Using Finite Element Method

This paper deals with the stability analysis of self-excited bending vibrations of linear symmetrical rotor-bearing systems caused by internal damping using the finite element method. The rotor system consists of uniform circular Rayleigh shafts with internal viscous damping, symmetrical rigid disks, and discrete undamped isotropic bearings. By combining the sensitivity method and the matrix representation of the rotor dynamic equations in complex form to assess stability, it is proved theoretically that the stability threshold speed and the corresponding whirling speed coincide with the first forward critical speed regardless of the magnitude of the internal damping.