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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

[+] Author and Article Information
J. Judge, C. Pierre

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

O. Mehmed

NASA Glenn Research Center, Cleveland, OH 44135

J. Eng. Gas Turbines Power 123(4), 940-950 (Oct 01, 2000) (11 pages) doi:10.1115/1.1377872 History: Received October 01, 1999; Revised October 01, 2000
Copyright © 2001 by ASME
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References

Tobias,  S. A., and Arnold,  R. N., 1957, “The Influence of Dynamical Imperfection on the Vibration of Rotating Disks,” Proc. Inst. Mech. Eng., 171, pp. 669–690.
Whitehead,  D. S., 1966, “Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes,” J. Mech. Eng. Sci., 8, No. 1, pp. 15–21.
Dye,  R. C. F., and Henry,  T. A., 1969, “Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies,” ASME J. Eng. Power, 91, pp. 182–188.
Ewins,  D. J., 1969, “The Effects of Detuning Upon the Forced Vibrations of Bladed Disks,” J. Sound Vib., 9, No. 1, pp. 65–79.
Ewins,  D. J., 1973, “Vibration Characteristics of Bladed Disc Assemblies,” J. Mech. Eng. Sci., 15, No. 3, pp. 165–186.
Ewins,  D. J., 1976, “Vibration Modes of Mistuned Bladed Disks,” ASME J. Eng. Power, 98, pp. 349–355.
Fabunmi,  J., 1980, “Forced Vibration of a Single Stage Axial Compressor Rotor,” ASME J. Eng. Power, 102, pp. 322–329.
Irretier, H., 1983, “Spectral Analysis of Mistuned Bladed Disk Assemblies by Component Mode Synthesis,” Vibrations of Bladed Disk Assemblies, Proceedings of the ASME 9th Biennial Conference on Mechanical Vibration and Noise, Dearborn, MI, ASME, New York, pp. 115–125.
Wei,  S. T., and Pierre,  C., 1988, “Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry, Part I: Free Vibrations,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 110, No. 4, pp. 429–438.
Wei,  S. T., and Pierre,  C., 1988, “Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry, Part II: Forced Vibrations,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 110, pp. 439–449.
Stange,  W. A., and MacBain,  J. C., 1983, “An Investigation of Dual Mode Phenomena in a Mistuned Bladed Disk,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 105, pp. 402–407.
Jay,  R. L., MacBain,  J. C., and Burns,  D. W., 1984, “Structural Response Due to Blade Vane Interaction,” ASME J. Eng. Gas Turbines Power, 106, pp. 50–56.
Jay,  R. L., and Burns,  D. W., 1986, “Characteristics of the Diametral Resonant Response of a Shrouded Fan Under Prescribed Distortion,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 108, pp. 125–131.
MacBain,  J. C., and Whaley,  P. W., 1984, “Maximum Resonant Response of Mistuned Bladed Disks,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 106, pp. 218–223.
Wei,  S. T., and Pierre,  C., 1990, “Statistical Analysis of the Forced Response of Mistuned Cyclic Assemblies,” ASME Journal, 28, pp. 861–868.
Ottarsson, G. S., and Pierre, C., 1995, “On the Effects of Interblade Coupling on the Statistics of Maximum Forced Response Amplitudes in Mistuned Bladed Disks,” Proceedings of the 36th AIAA/ASME Structures, Structural Dynamics, and Materials Conference, Vol. 5, AIAA, New York, pp. 3070–3078.
Kruse, M. J., and Pierre, C., 1996, “Forced Response of Mistuned Bladed Disks Using Reduced-Order Modeling,” Proceedings of the 37th AIAA/ASME 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,” Proceedings of the 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Lake Buena Vista, FL.
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Ewins, D. J., 1980, “Further Studies of Bladed Disc Vibration: Effects of Packeting,” Vibrations in Rotating Machinery, Mechanical Engineering Publications Ltd., London, pp. 97–102.
Griffin,  J. H., and Hoosac,  T. M., 1984, “Model Development and Statistical Investigation of Turbine Blade Mistuning,” ASME J. Vibr., Acoust., Stress, Reliab. Des. 106, pp. 204–210.
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Castanier, M. P., and Pierre, C., 1997, “Consideration on the Benefits of Intentional Blade Mistuning for the Forced Response of Turbomachinery Rotors,” Proceedings of The 1997 International Mechanical Engineering Congress and Exposition, The Winter Annual Meeting of the ASME, Vol. AD-55, pp. 419–425.
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Kruse, M. J., and Pierre, C., 1997a, “An Experimental Investigation of Vibration Localization in Bladed Disks, Part I: Free Response,” Proceedings of the 42nd ASME Gas Turbine & Aeroengine Congress, User’s Symposium & Exposition, Orlando, FL.
Kruse, M. J., and Pierre, C., 1997b, “An Experimental Investigation of Vibration Localization in Bladed Disks, Part II: Forced Response,” Proceedings of the 42nd ASME Gas Turbine & Aeroengine Congress, User’s Symposium & Exposition, Orlando, FL.

Figures

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Closeup of a blade, showing proximity probe above blade tip, piezoelectric actuator at blade root, and added mass at blade tip
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Natural frequencies versus number of nodal diameters for the tuned blisk
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2-nodal-diameter “free” response shapes: (a) and (b) show schematics of the blisk indicating the location of the nodal diameters, (c) and (d) compare response amplitudes to the sinusoids the data would fall on if the modes were perfectly harmonic (negative amplitudes indicate vibration 180 deg out of phase from excitation, positive amplitudes are in phase with excitation)
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Experimental frequency response of “tuned” blisk to engine order 4 excitation: (a) full frequency spectrum, blade 1 response, (b) response of all blades in the 4-nodal-diameter modes
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Engine order 2 forced response shapes of “tuned” system (compare with Fig. 4)
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Predicted amplitude increase (largest blade tip resonant response, scaled by tuned resonant response) versus mistuning, as obtained from Monte Carlo simulations of the reduced order model
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Comparison of resonant response pattern predictions based on stiffness and mass mistuning, for engine order 6 excitation
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Finite element prediction of engine order 3 frequency response of all blades for mistuned case (observe strong response for modes 6 and 7)
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Engine order 3 response shapes for mistuned case (finite element method predictions are normalized by maximum tuned amplitude)
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Finite element prediction of engine order 5 frequency response of all blades for mistuned disk (observe strong response in modes 10, 11, and 12)
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Engine order 5 response shapes for mistuned blisk (finite element method predictions are normalized by maximum tuned amplitude)
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Nodal diameter composition of experimental mistuned modes remaining spatially extended
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Nodal diameter composition of experimental mistuned modes which exhibit localization
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Engine order 6 response amplitudes of mistuned peaks 11 and 12 and tuned peak 12: (a) finite element, and (b) experimental
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Engine order 6 frequency response of blades with highest amplitude: (a) finite element, and (b) experimental

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