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Order Reduction of a Two-Span Rotor-Bearing System Via the Predictor-Corrector Galerkin Method

  • Deng-Qing Cao
  • Jin-Lin Wang
  • Wen-Hu Huang
Conference paper

Abstract

The predictor-corrector Galerkin method (PCGM) is employed to obtain a lower order system for a two-span rotor-bearing system. First of all, a 32-DOF nonlinear dynamic model is established for the system. Then, the predictor-corrector algorithm based on the Galerkin method is employed to deal with the problem of order reduction for such a complicated system. The first six modes are chosen to be the master subsystem and the following six modes are taken to be the slave subsystem. Finally, the dynamical responses are numerically worked out for the master and slave subsystems using the PCGM, and the results obtained are used to compare with those obtained by using the SGM. It is shown that the PCGM provides a considerable increase in accuracy for a little computational cost in comparison with the SGM in which the first six modes are reserved.

Keywords

Order Reduction Jump Phenomenon Component Mode Synthesis Order Reduction Method Reduce Order System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This research was supported by National Natural Science Foundation of China (10772056, 10632040) and the Natural Science Foundation of Hei-Long-Jiang Province, China (ZJG0704).

References

  1. 1.
    Ding J, Krodkiewski JM (1993) Inclusion of static indetermination in the mathematical model for non-linear dynamic analyses of multi-bearing rotor systems. J Sound Vib 164(2):267–280MATHCrossRefGoogle Scholar
  2. 2.
    Krodkiewski JM, Ding J, Zhang N (1994) Identification of unbalance change using a non-linear mathematical model for multi-bearing rotor systems. J Sound Vib 169(5):685–698CrossRefGoogle Scholar
  3. 3.
    Ding J (1997) Computation of multi-plane imbalance for a multi-bearing rotor system. J Sound Vib 205(3):364–371CrossRefGoogle Scholar
  4. 4.
    Hu W, Miah H, Feng NS, et al (2000) A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings. Tribol Int 33:197–204CrossRefGoogle Scholar
  5. 5.
    Ding Q, Leung AYT (2005) Numerical and experimental investigations on flexible multi-bearing rotor dynamics. J Vib Acoust 127:408–415CrossRefGoogle Scholar
  6. 6.
    Guyan RJ (1965) Reduction of stiffness and mass matrices. AAIA J 3(2):380CrossRefGoogle Scholar
  7. 7.
    Sundararajan P, Noah ST (1998) An algorithm for response and stability of large order non-linear systems-application to rotor systems. J Sound Vib 214(4):695–723CrossRefGoogle Scholar
  8. 8.
    Devulder C, Marion M (1992) A class of numerical algorithms for large time integration: the nonlinear Galerkin method. SIAM J Numer Anal 29(2):462–483MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Foias C, Manley O, Temam R (1993) Iterated approximate inertial manifolds for Navier–Stokes equations in 2-D. J Math Anal Appl 178:567–583MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Sthindl A, Troger H (2001) Methods for dimension reduction and their application in nonlinear dynamics. Int J Solids Struct 38:2131–2147CrossRefGoogle Scholar
  11. 11.
    Titi ES (1990) On approximate inertial manifolds to the Navier–Stokes equations. J Math Anal Appl 149:540–570MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Garcia-Archilla B, Novo J, Titi ES (1998) Postprocessing the Galerkin method: a novel approach, to approximate inertial manifolds. SIAM J Numer Anal 35:941–972MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Sansour C, Wriggers P, Sansour J (2003) A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids: applications to shells. Comput Mech 32:104–114MATHCrossRefGoogle Scholar
  14. 14.
    Garcia-Archilla B, Novo J, Titi ES (1999) An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier–Stokes equations. Math Comput 68:893–911MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Rega G, Troger H (2005) Dimension reduction of dynamical systems: methods, models, applications. Nonlinear Dyn 41:1–15MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Matthies HG, Meyer M (2003) Nonlinear Galerkin methods for the model reduction of nonlinear dynamical systems. Comput Struct 81:1277–1286CrossRefGoogle Scholar
  17. 17.
    Cao DQ, Wang JL, Huang WH (2010) The predictor-corrector Galerkin method and its application in a large-scale rotor-bearing system. J Vib Shock 29(2):100–105Google Scholar
  18. 18.
    Adiletta G, Guido AR, Rossi C (1996) Chaotic motions of a rigid rotor in short journal bearings. Nonlinear Dyn 10:251–269CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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