A finite element model for stability analysis of symmetrical rotor systems with internal damping (Q2714413)

The finite element method is used to investigate the stability of self-excited bending vibrations of linear symmetrical rotor-bearing systems with internal damping. It is well known that the stability of rotors is strongly influenced by internal damping. The internal damping destabilizes the whirling motion of the rotor at speed above the first critical speed. But there are many investigations in which the effects of rotatory inertia, gyroscopic moments, and both internal viscous and hysteretic damping are taken into consideration. In particularly, by using the numerical examples of a uniform circular shaft with viscous material damping, supported at its ends by two identical undamped isotropic bearings, it was found that the first and second forward precessional modes become unstable at the first and second critical speeds, respectively. The author of the article firstly generalized the above-mentioned results for symmetric rotor systems with viscous internal damping, supported by isotropic undamped bearings. By applying the sensitivity analysis and the eigenvalue problem of the rotor dynamics equation in complex form, it has been proved that the stability threshold speed, at which the rotor loses its stability, coincides with the first forward critical speed regardless of the magnitude of internal viscous damping coefficients. The main purpose of the article is to demonstrate that the finite element simulation and the sensitive analysis are adequate methods to study the combined effect of internal damping and isotropic bearing damping on the stability of complex symmetrical rotor system. Two numerical examples are presented to confirm the validity of the aforementioned theoretical results.