A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems

This study develops a modified transfer matrix method for analyzing the coupling lateral and torsional vibrations of the symmetric rotor-bearing system with an external torque. Eulerʹs angles are used to describe the orientations of the shaft element and disk. Additionally, to enhance accuracy, the symmetric rotating shaft is modeled by the Timoshenko beam and considered using a continuous-system concept rather than the conventional “lumped system” concept. Moreover, the harmonic balance method is adopted in this approach to determine the steady-state responses comprising the synchronous and superharmonic whirls. According to our analysis, when the unbalance force and the torque with n × frequency of the rotating speed excite the system simultaneously, the ( n + 1 ) × and ( n - 1 ) × whirls appear along with the synchronous whirl. Finally, several numerical examples are presented to demonstrate the applicability of this approach.