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TECHNICAL PAPERS

Local/Global Effects of Mistuning on the Forced Response of Bladed Disks

[+] Author and Article Information
A. J. Rivas-Guerra, M. P. Mignolet

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106e-mail: marc. mignolet@asu.edu

J. Eng. Gas Turbines Power 126(1), 131-141 (Mar 02, 2004) (11 pages) doi:10.1115/1.1581898 History: Received December 01, 2000; Revised March 01, 2001; Online March 02, 2004
Copyright © 2004 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.
Kielb,  R. E., and Kaza,  K. R. V., 1984, “Effects of Structural Coupling on Mistuned Cascade Flutter and Response,” ASME J. Eng. Gas Turbines Power 106, pp. 17–24.
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 (4), 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.
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.
Wei,  S.-T., and Pierre,  C., 1990, “Statistical Analysis of the Forced Response of Mistuned Cyclic Assemblies,” AIAA J. 28(5), pp. 861–868.
Mignolet,  M. P., Hu,  W., and Jadic,  I., 2000, “On the Forced Response of Harmonically and Partially Mistuned Bladed Blisks. Part I: Harmonic Mistuning,” International Journal of Rotating Machinery 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,” International Journal of Rotating Machinery 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, E., 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.
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.
Ibrahim, R. A., 1985, Parametric Random Vibration, Research Studies Press, John Wiley and Sons, New York.
Whitehead,  D. S., 1998, “The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning,” ASME J. Eng. Gas Turbines Power 120, pp. 115–119.
Castanier,  M. P., Ottarson,  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., 2001, “Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application,” ASME J. Eng. Gas Turbines Power 123(1), pp. 100–108.
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.
Castanier,  M. P., and Pierre,  C., 1997, “Predicting Localization via Lyapunov Exponent Statistics,” J. Sound Vib. 203 (1), pp. 151–157.
Cha,  P. D., and Morganti,  C. R., 1994, “Numerical Statistical Investigation on the Dynamics of Finitely Long, Nearly Periodic Chains,” AIAA J. 32(11), pp. 2269–2275.
LaBorde, B. H., 1999, “Assessment of Predictive Capabilities of Mistuning Effects on the Resonant Response of Bladed Disks,” M.S. thesis, Arizona State University, AZ, Dec.
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 3070–3078.
Sinha, A., 1997, “Computation of the Maximum Amplitude of a Mistuned Bladed Disk Assembly via Infinity Norm,” Proceedings of the 1997 ASME International Mechanical Engineering Congress and Exposition ASME, New York, Vol. AD-55, pp. 427–432.
Rivas-Guerra, A. J., and Mignolet, M. P., 2003, “Maximum Amplification of Blade Response due to Mistuning: Localization and Mode Shapes Aspects of the Worst Disks,” ASME J. Turbomach 125(3), pp. 442-454.
Rivas-Guerra, A. J., Mignolet, M. P., and LeBorde, B. H, 2000, “On the Value of Tuned-Like Systems for Mistuned Forced Response Analyses,” 5th National Turbine Engine High Cycle Fatigue (HCF) Conference, Chandler, AZ, Mar. 7–9.
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Figures

Grahic Jump Location
Maximum response prediction error with partial mistuning versus mistuning level, blisk on lower third EO mode 0.125% damping
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of five randomly mistuned disks, blisk on lower third EO mode. 0.025% damping, 0.5% mistuning.
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of five randomly mistuned disks, blisk in veering 2 (third EO modes). 0.125% damping, 4% mistuning.
Grahic Jump Location
Single degree-of-freedom per blade disk model
Grahic Jump Location
Blisk example: (a) blisk view, (b) blade sector finite element mesh, and (c) natural frequency versus nodal diameter plot
Grahic Jump Location
Mean value of the response of blade 1 (typical blade) by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=6 (Xpa(5,6))
Grahic Jump Location
Standard deviation of the response of blade 1 (typical blade) by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=6 (Xpa(5,6))
Grahic Jump Location
Mean value of the maximum response on the disk by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=2 (Xpa(5,2))
Grahic Jump Location
Standard deviation of the maximum response on the disk by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=2 (Xpa(5,2))
Grahic Jump Location
Mean value of the maximum response on the disk in a sweep by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=2 (Xpa(5,2))
Grahic Jump Location
Standard deviation of the maximum response on the disk in a sweep by Monte Carlo simulation (Xm), three-blade and five-blade partial mistuning models (Xp(3) and Xp(5)), adaptive perturbation method with two and six modes (Xa(2) and Xa(6)) and local+global approximation with s=5 and d=2 (Xpa(5,2))
Grahic Jump Location
Maximum response on the population of disks by Monte Carlo simulation (Xm), five-blade partial mistuning model (Xp(5)), and by optimization of three and seven-blade mistuning models (Opti-3bl and Opti-7bl)
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of five randomly mistuned disks, kC=45,430 N/m
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of five randomly mistuned disks, kC=20,000 N/m
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 10% on the amplitude of response of the blades of five randomly mistuned disks, kC=5,000 N/m
Grahic Jump Location
Scatter plot of the width of partial mistuning required to achieve an accuracy of 3% on the amplitude of response of the blades of five randomly mistuned disks, kC=20,000 N/m

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