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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

[+] Author and Article Information
R. Bladh, M. P. Castanier, C. Pierre

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125

J. Eng. Gas Turbines Power 123(1), 100-108 (Apr 02, 2000) (9 pages) doi:10.1115/1.1338948 History: Received January 14, 2000; Revised April 02, 2000
Copyright © 2001 by ASME
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References

Srinivasan,  A. V., 1997, “Flutter and Resonant Vibration Characteristics of Engine Blades,” ASME J. Eng. Gas Turbines Power, 119, pp. 742–775.
Irretier, H., 1983, “Spectral Analysis of Mistuned Bladed Disk Assemblies by Component Mode Synthesis,” Vibrations of Bladed Disk Assemblies, ASME, New York, pp. 115–125.
Zheng, Z.-C., and Wang, F.-R., 1985, “Dynamic Analysis of Blade Groups Using Component Mode Synthesis,” Vibrations of Blades and Bladed Disk Assemblies, ASME, New York, pp. 97–103.
Kruse, M. J., and Pierre, C., 1996, “Forced Response of Mistuned Bladed Disks Using Reduced-Order Modeling,” Proc. 37th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Vol. 4, AIAA, New York, pp. 1938–1950.
Kruse, M. J., and Pierre, C., 1996, “Dynamic Response of an Industrial Turbomachinery Rotor,” Proc. 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA, New York.
Castanier,  M. P., Óttarsson,  G., and Pierre,  C., 1997, “A Reduced-Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 439–447.
Yang,  M.-T., and Griffin,  J. H., 1997, “A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies,” ASME J. Eng. Gas Turbines Power, 119, pp. 161–167.
Yang, M.-T., and Griffin, J. H., 1999, “A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes,” Proc. 44th ASME Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, ASME, New York.
Bladh,  R., Castanier,  M. P., and Pierre,  C., 1999, “Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies with Shrouds,” ASME J. Eng. Gas Turbines Power, 121, pp. 515–522.
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.
Craig,  R. R., and Bampton,  M. C. C., 1968, “Coupling of Substructures for Dynamics Analyses,” AIAA J., 6, pp. 1313–1319.
Bladh, R., Castanier, M. P., and Pierre, C., 1998, “Reduced Order Modeling and Efficient Forced Response Statistics Prediction for Mistuned Bladed Disks,” Proc. 3rd National Turbine Engine High Cycle Fatigue Conference, San Antonio, TX.
Allemang, R. J., and Brown, D. L., 1982, “A Correlation Coefficient for Modal Vector Analysis,” Proc. 1st International Modal Analysis Conference, Union College, Schenectady, NY, pp. 110–116.
Óttarsson, G., and Pierre, C., 1995, “On the Effects of Interblade Coupling on the Statistics of Maximum Forced Response Amplitudes in Mistuned Bladed Disks,” Proc. 36th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, AIAA, New York, Vol. 5, pp. 3070–3078. Also, J. Sound Vib. (in print).

Figures

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Finite element meshes for the “small” example blisk: (a) the full model; (b) the fundamental sector
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Finite element meshes for the “large” example blisk: (a) the full model; (b) the fundamental sector
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Natural frequencies versus nodal diameters for the small example finite element model. The circles show the natural frequency values, while the connecting lines are drawn to aid in visualization of the mode families and the frequency veerings. The character of each family of blade-dominated modes is indicated on the right, where F=Flex, T=Torsion, and A=Axial (edgewise) bending.
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Modal convergence trends in the region surrounding veering 1 for the small example model
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Reduced order model representations of mistuned mode shape number 37 for the small example model
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Reduced order model representations of mistuned mode shape number 38 for the small example model
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Sensitivity of modal assurance criterion (MAC) values (mistuned mode shape number 38)
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Method efficiency with respect to mistuned natural frequencies for δf≤0.1 percent for the small example model
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Method efficiency with respect to mistuned natural frequencies for δf≤1.0 percent for the small example model
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Method efficiency with respect to mistuned mode shapes for δmac≤0.1 percent for the small example model
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Method efficiency with respect to mistuned mode shapes for δmac≤1.0 percent for the small example model
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Forced response frequency sweep through veering 1 for engine order one (1E) excitation of the tuned small example model
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Forced response frequency sweep through veering 1 for engine order one (1E) excitation of the mistuned small example model (tuned FEM solution included for reference)
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Forced response frequency sweep through veering 2 for engine order three (3E) excltation of the mistuned small example model (tuned FEM solution included for reference)
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Maximum response amplitudes for all blades from forced response frequency sweep through veering 1 for engine order one (1E) excitation of the mistuned small example model
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Natural frequencies versus nodal diameters for the large example model. The character of each family of blade-dominated modes is indicated on the right, where F=Flex,T=Torsion, and A=Axial (edgewise) bending.
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Reduced order model representations of mistuned mode shape number 64 for the large example model
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Reduced order model representations of mistuned mode shape number 135 for the large example model
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Forced response frequency sweep through veering 1 for engine order two (2E) excltation of the tuned large example model
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Forced response frequency sweep through veering 1 for engine order two (2E) excitation of the mistuned large example model (tuned FEM solution included for reference)
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Forced response frequency sweep through veering 2 for engine order three (3E) excitation of the mistuned large example model (tuned FEM solution included for reference)

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