Applied Mathematics and Mechanics

, Volume 33, Issue 4, pp 499–510

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

  • Zhong-gang Li (李忠刚)
  • Yu-shu Chen (陈予恕)

DOI: 10.1007/s10483-012-1566-7

Cite this article as:
Li, Z. & Chen, Y. Appl. Math. Mech.-Engl. Ed. (2012) 33: 499. doi:10.1007/s10483-012-1566-7


The 1:2 subharmonic resonance of the labyrinth seals-rotor system is investigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics (CFD). Based on the multiple scale method, the 1:2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.

Key words

rotor-seal1:2 subharmonic resonanceflow field computationgas flow exciting forcesingularity

Chinese Library Classification


2010 Mathematics Subject Classification


Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhong-gang Li (李忠刚)
    • 1
  • Yu-shu Chen (陈予恕)
    • 1
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinP. R. China