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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

[+] Author and Article Information
E. Capiez-Lernout

C. Soize

Laboratory of Engineering Mechanics, University of Marne-La-Vallée, 5, Bd Descartes, 77454 Marne-La Vallée Cedex 02, France

J. Eng. Gas Turbines Power 126(3), 610-618 (Aug 11, 2004) (9 pages) doi:10.1115/1.1760527 History: Received June 01, 2002; Revised December 01, 2003; Online August 11, 2004
Copyright © 2004 by ASME
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References

Figures

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Finite element mesh of the bladed disk. Input force localization (symbol •).
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Graph of the eigenfrequencies values (in Hz) of the tuned bladed disk versus the circumferential wave number m
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(1) Displacement forced response (m) of the tuned system with respect to the excitation frequency (Hz): ν↦‖u_j(ν)‖ (thick dashed line). (2) Graph of one realization θ1 of the random displacement forced response (m) with respect to the excitation frequency (Hz): ν↦maxj∊{0,[[ellipsis]],N−1}‖Uj(ν,θ1)‖ (thick line), ν↦‖Uj(ν,θ1)‖,j∊{0,[[ellipsis]],N−1} (thin lines).
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Spatial localization: graph of one realization θ1 of magnification factor j↦Bj(ν,θ1) for all the blades
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Convergence analysis: graph of functions ns↦Conv(ns,Ng,ñ) for several values of the couple (Ng,ñ)
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Comparison of the nonparametric and the parametric models: probability density functions of random magnification factors B(ω0) and Bpara0para) in a logarithmic scale: b↦pB(ω0)(b,ω0) (thick line), b↦pBpara0para)(b,ω0para) (thin line)
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Comparison of the nonparametric and the parametric models: graphs of the probability density functions b↦pB(b) (thick line) and b↦pBpara(b) (thin line) for δK=0.01
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Comparison of the nonparametric and the parametric models: graphs of the probability density functions b↦pB(b) (thick line) and b↦pBpara(b) (thin line) for δK=0.02
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Comparison of the nonparametric and the parametric models: graphs of the probability density functions b↦pB(b) (thick line) and b↦pBpara(b) (thin line) for δK=0.04
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Comparison of the nonparametric and the parametric models: graphs of b↦P(B>b) (thick line), b↦P(Bpara>b) (thin line) in a logarithmic scale for δK=0.01
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Comparison of the nonparametric and the parametric models: graphs of b↦P(B>b) (thick line), b↦P(Bpara>b) (thin line) in a logarithmic scale for δK=0.02
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Comparison of the nonparametric and the parametric models: graphs of b↦P(B>b) (thick line), b↦P(Bpara>b) (thin line) in a logarithmic scale for δK=0.04
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Influence of the mistuning rate: graph of δK↦bpK) such that P(B≤bp)=p. The thick (or thin) lines are related to the nonparametric (or parametric) model (the lower, middle and upper curves correspond respectively to p=0.05,p=0.5 and p=0.95).
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Influence of the mean loss factor for a mistuning rate δK=0.02; graphs of η↦E{B} (thick line), η↦E{Bpara} (thin line)
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Influence of the mean loss factor for a mistuning rate δK=0.02: graphs of η↦σB (thick line), η↦σBpara (thin line)

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