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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment

[+] Author and Article Information
B.-K. Choi

School of Mechanical and Aerospace Engineering, The Institute of Marine Industry, Gyeongsang National University, Tongyoung, Kyongnam 650-160, Korea

J. Lentz

Honeywell Engines and Systems, Department 93-31/301-125, P.O. BOX 52181, Phoenix, AZ 85072-2181

A. J. Rivas-Guerra, M. P. Mignolet

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

J. Eng. Gas Turbines Power 125(1), 131-140 (Dec 27, 2002) (10 pages) doi:10.1115/1.1498270 History: Received December 01, 2000; Revised March 01, 2001; Online December 27, 2002
Copyright © 2003 by ASME
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References

Ewins,  D. J., 1969, “The Effects of Detuning Upon the Forced Vibrations of Bladed Disks,” J. Sound Vib., 9, pp. 65–79.
Whitehead,  D. S., 1966, “Effect of Mistuning on the Vibration of Turbomachines Blades Induced by Wakes,” J. Mech. Eng. Sci., 8, pp. 15–21.
Kaza,  K. R. V., and Kielb,  R. E., 1984, “Flutter of Turbofan Rotors With Mistuned Blades,” AIAA J., 22(11), pp. 1618–1625.
Kaza,  K. R. V., and Kielb,  R. E., 1985, “Vibration and Flutter of Mistuned Bladed-Disk Assemblies,” J. Propul., 1(5), pp. 336–344.
Basu,  P., and Griffin,  J. H., 1986, “The effect of Limiting Aerodynamic and Structural Coupling in Models of Mistuned Bladed Disk Vibration,” ASME J. Vib., Acoust., Stress, Reliab. Des., 108, pp. 132–139.
Wei,  S. T., and Pierre,  C., 1988, “Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry—Part I: Free Vibrations,” ASME J. Vib., Acoust., Stress, Reliab. Des., 110(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. Vib., Acoust., Stress, Reliab. Des., 110, pp. 439–449.
Sinha,  A., and Chen,  S., 1989, “A Higher Order Technique to Compute the Statistics of Forced Response of a Mistuned Bladed Disk,” J. Sound Vib., 130, pp. 207–221.
Wei,  S.-T., and Pierre,  C., 1990, “Statistical Analysis of the Forced Response of Mistuned Cyclic Assemblies,” AIAA J., 28(5), pp. 861–868.
Lin,  C. C., and Mignolet,  M. P., 1997, “An Adaptive Perturbation Scheme for the Analysis of Mistuned Bladed Disks,” ASME J. Eng. Gas Turbines Power, 119, pp. 153–160.
Mignolet,  M. P., Hu,  W., and Jadic,  I., 2000, “On the Forced Response of Harmonically and Partially Mistuned Bladed Disks. Part I: Harmonic Mistuning,” Int. J. Rotating Mach., 6(1), pp. 29–41.
Mignolet,  M. P., Hu,  W., and Jadic,  I., 2000, “On the Forced Response of Harmonically and Partially Mistuned Bladed Disks. Part II: Partial Mistuning and Applications,” Int. J. Rotating Mach., 6(1), pp. 43–56.
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(4), pp. 893–900.
Petrov, E., Sanliturk, K., Ewins, D. J., and Elliott, R., 2000, “Quantitative Prediction of the Effects of Mistuning Arrangement on Resonant Response of a Practical Turbine Bladed Disc,” 5th National Turbine Engine High Cycle Fatigue (HCF) Conference, Chandler, AZ, Mar. 7–9.
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 ASME Aerospace Division, AD-Vol. 55 , pp. 419–425.
Castanier, M. P., and Pierre, C., 1998, “Investigation of the Combined Effects of Intentional and Random Mistuning on the Forced Response of Bladed Disks,” AIAA Paper No. AIAA-98-3720.
Kenyon, J. A., and Griffin, J. H., 2000, “Intentional Harmonic Mistuning for Robust Forced Response of Bladed Disks,” 5th National Turbine Engine High Cycle Fatigue (HCF) Conference, Chandler, AZ, Mar. 7–9.
Ottarsson, G., 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 Structures, Structural Dynamics, and Materials Conference and Adaptive Structures Forum, New Orleans, LA, Apr. 10–13, 5 , pp. 3070–3078.
Kruse, M. J., and Pierre, C., 1996, “Forced Response of Mistuned Bladed Disks Using Reduce-Order Modeling,” Proceedings of the 37th Structures, Structural Dynamics, and Materials Conference, Salt Lake City, UT, Apr. 15–17, pp. 1938–1950.
Mehmed, O., and Murthy, D. V., 1988, “Experimental Investigation of Propfan Aeroelastic Response in Off-Axis Flow With Mistuning,” Proceedings of the 24th AIAA/SAE/ASEE Joint Propulsion Conference, Boston, MA.
Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization & Machine Leaning, Addision-Wesley, Reading, MA.
Gen, M., and Cheng, R., 1997, Genetic Algorithms & Engineering Design, John Wiley and Sons, New York.
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.
Castanier,  M. P., Ottarsson,  G., and Pierre,  C., 1997, “A Reduced-Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 439–447.
Bladh, R., Castanier, M. P., and Pierre, C., 2002, “Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks, Part I: Theoretical Models,” ASME J. Eng. Gas Turbines Power, to appear.
Castanier,  M. P., and Pierre,  C., 1993, “Individual and Interactive Mechanisms for Localization and Dissipation in a Mono-Coupled Nearly Periodic Structure,” J. Sound Vib., 168(3), pp. 479–505.
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LaBorde, B. H., 1999, “Assessment of Predictive Capabilities of Mistuning Effects on the Resonant Response of Bladed Disks,” M. S. thesis, Arizona State University, Tempe, AZ, Dec.
Rivas-Guerra, A. J., and Mignolet, M. P., 2003, “Local/Global Effects of Mistuning on the Forced Response of Bladed Disks,” ASME J. Eng. Gas Turbines Power, to appear.

Figures

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Graphical description of the single-point crossover technique
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Single-degree-of-freedom per blade disk model
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Convergence plot of the simple genetic algorithm, single-degree-of-freedom model, kC=8,606 N/m
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Amplification factor of the forced response with respect to the tuned disk as a function of the level of unintentional mistuning, single-degree-of-freedom model, kC=45,430 N/m. Blades C are tuned, A and B have natural frequencies 5% lower and higher, respectively, than tuned. The notation 3A3B refers to disks formed of two groupings AAABBB or (AAABBB)2 and similarly 2B1A represents (BBA)4.
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Amplification factor of the forced response with respect to the tuned disk as a function of the level of unintentional mistuning, single-degree-of-freedom model, kC=8,606 N/m. Blades C are tuned, A and B have natural frequencies 5% lower and higher, respectively, than tuned. The notation 2A2B refers to disks formed of three groupings AABB or (AABB)3 and similarly 2B1A represents (BBA)4.
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Typical APU load compressor with inlet guide vanes
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Single sector structural model of the 17-blade centrifugal compressor rotor
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Natural frequencies versus number of nodal diameters for the tuned rotor in Fig. 7 by finite element and ROM
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Complex mode shape of the compressor disk for a nodal diameter 3 mode
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Amplitude magnification for the nominal and intentionally mistuned rotors
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Typical convergence plot of the combination of subproblem approximation and steepest descent algorithms
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Sensitivity of the tuned and optimized intentionally mistuned disks to unintentional random mistuning
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Sensitivity of the optimized and some harmonically intentionally mistuned disks to unintentional random mistuning
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Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of 2B1A and 2B2A disks, kC=8606 N/m, no random mistuning
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Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of ten randomly mistuned 2B1A disks, kC=8606 N/m
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Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of ten randomly mistuned 2B2A disks, kC=8606 N/m
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Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of 2B1A and 7A5B disks, kC=45,430 N/m, no random mistuning

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