A frequency-domain approach for direct parametric analysis of limit points (LPs) of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of LPs is performed. The whole numerical procedure is based on the harmonic balance method (HBM) and can be decomposed in three distinct steps. First, a response curve is calculated by HBM combined with a continuation technique until an LP is detected. Then this starting LP is used to initialize the direct tracking of LPs which is based on the combination of a so-called extended system and a continuation technique. With only one computation, a complete branch of LPs is obtained, which provides the stability boundary with respect to system parameters such as nonlinearity or excitation level. Several numerical examples demonstrate the capabilities and the performance of the proposed method.
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April 2016
Research-Article
Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
Lihan Xie,
Lihan Xie
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France;
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France;
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Sébastien Baguet,
Sébastien Baguet
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France
e-mail: sebastien.baguet@insa-lyon.fr
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France
e-mail: sebastien.baguet@insa-lyon.fr
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Benoit Prabel,
Benoit Prabel
CEA-Saclay, DEN, DANS, DM2S, SEMT, DYN
Gif sur Yvette F-91191, France;
Gif sur Yvette F-91191, France;
IMSIA,
UMR9219, CNRS-EDF-CEA-ENSTA,
Université Paris Saclay,
Palaiseau F-91762, France
e-mail: benoit.prabel@cea.fr
UMR9219, CNRS-EDF-CEA-ENSTA,
Université Paris Saclay,
Palaiseau F-91762, France
e-mail: benoit.prabel@cea.fr
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Régis Dufour
Régis Dufour
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259
Villeurbanne F-69621, France
e-mail: regis.dufour@insa-lyon.fr
CNRS,
INSA-Lyon,
LaMCoS, UMR5259
Villeurbanne F-69621, France
e-mail: regis.dufour@insa-lyon.fr
Search for other works by this author on:
Lihan Xie
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France;
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France;
Sébastien Baguet
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France
e-mail: sebastien.baguet@insa-lyon.fr
CNRS,
INSA-Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France
e-mail: sebastien.baguet@insa-lyon.fr
Benoit Prabel
CEA-Saclay, DEN, DANS, DM2S, SEMT, DYN
Gif sur Yvette F-91191, France;
Gif sur Yvette F-91191, France;
IMSIA,
UMR9219, CNRS-EDF-CEA-ENSTA,
Université Paris Saclay,
Palaiseau F-91762, France
e-mail: benoit.prabel@cea.fr
UMR9219, CNRS-EDF-CEA-ENSTA,
Université Paris Saclay,
Palaiseau F-91762, France
e-mail: benoit.prabel@cea.fr
Régis Dufour
Université de Lyon,
CNRS,
INSA-Lyon,
LaMCoS, UMR5259
Villeurbanne F-69621, France
e-mail: regis.dufour@insa-lyon.fr
CNRS,
INSA-Lyon,
LaMCoS, UMR5259
Villeurbanne F-69621, France
e-mail: regis.dufour@insa-lyon.fr
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 10, 2015; final manuscript received November 13, 2015; published online January 20, 2016. Assoc. Editor: Izhak Bucher.
J. Vib. Acoust. Apr 2016, 138(2): 021007 (9 pages)
Published Online: January 20, 2016
Article history
Received:
June 10, 2015
Revised:
November 13, 2015
Citation
Xie, L., Baguet, S., Prabel, B., and Dufour, R. (January 20, 2016). "Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics." ASME. J. Vib. Acoust. April 2016; 138(2): 021007. https://doi.org/10.1115/1.4032182
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