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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

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Ohayon, R., and Soize, C., 1998, Structural Acoustics and Vibration, Academic Press, San Diego, CA.
Whitehead,  D. S., 1966, “Effects of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes,” J. Mech. Eng. Sci., 8(1), pp. 15–21.
Ewins,  D. J., 1969, “The Effects of Detuning Upon the Forced Vibrations of Bladed Disks,” J. Sound Vib., 9(1), pp. 65–69.
Wei,  S. T., and Pierre,  C., 1988, “Localization Phenomena in Mistuned Assemblies for Cyclic Symmetry—Part II: Forced Vibrations,” ASME J. Vib., Acoust., Stress, Reliab. Des., 110(4), pp. 439–449.
Lin,  C. C., and Mignolet,  M. P., 1996, “Effects of Damping and Damping Mistuning on the Forced Vibration Response of Bladed Disks,” J. Sound Vib., 193(2), pp. 525–543.
Lin,  C. C., and Mignolet,  M. P., 1997, “An Adaptative Perturbation Scheme for the Analysis of Mistuned Bladed Disks,” ASME J. Eng. Gas Turbines Power, 119, pp. 153–160.
Griffin,  J. H., and Hoosac,  T. M., 1984, “Model Development and Statistical Investigation of Turbine Blade Mistuning,” ASME J. Vib., Acoust., Stress, Reliab. Des., 106, pp. 204–210.
Mignolet,  M. P., and Lin,  C. C., 1993, “The Combined Closed Form–Perturbation Approach to the Analysis of Mistuned Bladed Disks,” ASME J. Turbomach., 115, pp. 771–780.
Yang,  M.-T., and Griffin,  J. H., 2001, “A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes,” ASME J. Eng. Gas Turbines Power, 123, pp. 893–900.
Bladh,  R., Castanier,  M. P., and Pierre,  C., 2001, “Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models,” ASME J. Eng. Gas Turbines Power, 123, pp. 89–99.
Seinturier, E., Dupont, C., Berthillier, M., and Dumas, M., 2002, “A New Aeroelastic Model for Mistuned Bladed Disks,” AIAA Paper No. 2002-1533.
Mignolet,  M. P., Rivas-Guerra,  A. J., and Delor,  J. P., 2001, “Identification of Mistuning Characteristics of Bladed Disks From Free Response Data (Part I),” ASME J. Eng. Gas Turbines Power, 123, pp. 395–403.
Rivas-Guerra,  A. J., Mignolet,  M. P., and Delor,  J. P., 2001, “Identification of Mistuning Characteristics of Bladed Disks From Free Response Data (Part II),” ASME J. Eng. Gas Turbines Power, 123, pp. 404–411.
Soize,  C., 2000, “A Nonparametric Model of Random Uncertainties for Reduced Matrix Models in Structural Dynamics,” Probab. Eng. Mech.,15(3), pp. 277–294.
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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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