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.
Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
Villeurbanne F-69621, France;
Gif sur Yvette F-91191, France
Gif sur Yvette F-91191, France;
Université Paris Saclay,
Palaiseau F-91762, France
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.
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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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