Research Papers

Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics

[+] Author and Article Information
Lihan Xie

Université de Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France;
Gif sur Yvette F-91191, France
e-mail: lihan.xie@insa-lyon.fr

Sébastien Baguet

Université de Lyon,
LaMCoS, UMR5259,
Villeurbanne F-69621, France
e-mail: sebastien.baguet@insa-lyon.fr

Benoit Prabel

Gif sur Yvette F-91191, France;
Université Paris Saclay,
Palaiseau F-91762, France
e-mail: benoit.prabel@cea.fr

Régis Dufour

Université de 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 138(2), 021007 (Jan 20, 2016) (9 pages) Paper No: VIB-15-1210; doi: 10.1115/1.4032182 History: Received June 10, 2015; Revised November 13, 2015

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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Fig. 1

Frequency response of the Duffing system for α = 0.02

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Fig. 2

Frequency response of the Duffing system for α = 10

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Fig. 3

LPs tracking for α ∈ [0 10]

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Fig. 4

Zoom of LPs tracking

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Fig. 5

Projections of LPs tracking

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Fig. 6

Forced response of the Jeffcott rotor for μ = 0

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Fig. 7

Forced response of the Jeffcott rotor for μ = 0.11

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Fig. 8

Forced response of the Jeffcott rotor for μ = 0.2

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Fig. 9

Forced response of the Jeffcott rotor for μ = 0.11, comparison with time integration for increasing and decreasing frequency sweeps

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Fig. 10

LPs tracking of the Jeffcott rotor with varying friction coefficient μ

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Fig. 11

Multi-DOFs FE rotor [23]

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Fig. 12

FE rotor: forced response at node 6 for μ = 0

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Fig. 13

FE rotor: forced response at node 6 for μ = 0.03

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Fig. 14

FE rotor: forced response at node 6 for μ = 0.03, comparison with time integration for increasing sweep

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Fig. 15

FE rotor: LPs tracking with varying friction coefficientμ



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