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Research Papers

A Novel Perturbation-Based Approach for the Prediction of the Forced Response of Damped Mistuned Bladed Disks

[+] Author and Article Information
Yun Han

Stress Engineering Services, Inc.,
13610 Westland East Boulevard,
Houston, TX 77041-1205
e-mail: yun.han@stress.com

Marc P. Mignolet

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

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 22, 2013; final manuscript received February 24, 2015; published online March 23, 2015. Assoc. Editor: Jiong Tang.

J. Vib. Acoust 137(4), 041008 (Aug 01, 2015) (7 pages) Paper No: VIB-13-1252; doi: 10.1115/1.4029946 History: Received July 22, 2013; Revised February 24, 2015; Online March 23, 2015

This paper focuses on the formulation and validation of a novel perturbation method for the prediction of the forced response of mistuned bladed disks. At the contrary of most previous methods, this approach leads to a convergent series representation over the entire range of blade–disk coupling levels for small mistuning. The dominant parameter affecting the magnitude of the largest mistuning for which convergence occurs is shown to be the system damping with a weaker effect of the blade–disk coupling. Examples of application on a single degree-of-freedom per blade model and the reduced order model of a blisk demonstrate the potential of this novel approach. Finally, the applicability of this technique for the optimization of intentional mistuning pattern is shown.

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References

Whitehead, D. S., 1966, “Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes,” J. Mech. Eng. Sci., 8(1), pp. 15–21. [CrossRef]
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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. [CrossRef]
Wei, S. T., and Pierre, C., 1988, “Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry—Part II: Forced Vibrations,” ASME J. Vib. Acoust., 110(4), pp. 439–449. [CrossRef]
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(2), pp. 207–221. [CrossRef]
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(1), pp. 153–160. [CrossRef]
Happawana, G. S., Bajaj, A. K., and Nwokah, O. D. I., 1991, “A Singular Perturbation Perspective on Mode Localization,” J. Sound Vib., 147(2), pp. 361–365. [CrossRef]
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(4), pp. 771–780. [CrossRef]
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. [CrossRef]
Lalanne, B., 2005, “Perturbations Methods in Structural Dynamics and Applications to Cyclic Symmetric Domains,” ASME J. Eng. Gas Turbines Power, 127(3), pp. 654–662. [CrossRef]
Castanier, M. P., Ottarson, G., and Pierre, C., 1997, “A Reduced Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vib. Acoust., 119(3), pp. 439–447. [CrossRef]
Yang, M. T., and Griffin, J. H., 1997, “A Reduced Order Approach for the Vibration of Mistuned Bladed Disks Assemblies,” ASME J. Eng. Gas Turbines Power, 119(1), pp. 161–167. [CrossRef]
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. [CrossRef]
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(1), pp. 89–99. [CrossRef]
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. [CrossRef]
Petrov, E. P., Sanliturk, K. Y., and Ewins, D. J., 2002, “A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on Exact Relationship Between Tuned and Mistuned Systems,” ASME J. Eng. Gas Turbines Power, 124(3), pp. 586–597. [CrossRef]
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Choi, B.-K., Lentz, J., Rivas-Guera, A. J., and Mignolet, M. P., 2003, “Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning,” ASME J. Eng. Gas Turbines Power, 125(1), pp. 131–140. [CrossRef]
Han, Y., Murthy, R., and Mignolet, M. P., 2014, “Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning,” ASME J. Eng. Gas Turbines Power, 136(6), p. 062505. [CrossRef]

Figures

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Fig. 1

Single degree-of-freedom per blade bladed disk model (all mj are equal)

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Fig. 2

Blisk example: (a) blisk view, (b) blade sector finite element mesh, and (c) natural frequency versus nodal diameter plot

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Fig. 3

Largest magnitude of the eigenvalues of (D+ΔH-1)-1ND for a two-blade system, single degree-of-freedom per blade model

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Fig. 4

Mean amplification factor versus coupling stiffness, two-blade disk, single degree-of-freedom per blade model, for perturbation orders 1–4

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Fig. 5

Standard deviation of the amplification factor versus coupling stiffness, two-blade disk, single degree-of-freedom per blade model, for perturbation orders 1–4

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Fig. 6

Mean amplification factor versus coupling stiffness, six-blade disk, single degree-of-freedom per blade model, for perturbation orders 1–4

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Fig. 10

Probability density function of the amplification factor, 24-blade blisk, case 1

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Fig. 11

Probability density function of the amplification factor, 24-blade blisk, case 2

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Fig. 12

Probability density function of the amplification factor, 24-blade blisk, case 3

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Fig. 13

Probability density function of the amplification factor, 24-blade blisk, case 4

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Fig. 7

Standard deviation of the amplification factor versus coupling stiffness, six-blade disk, single degree-of-freedom per blade model, for perturbation orders 1–4

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Fig. 8

Mean amplification factor in sweep versus coupling stiffness, 24-blade disk, third engine order excitation, single degree-of-freedom per blade model

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Fig. 9

Standard deviation of the amplification factor in sweep versus coupling stiffness, 24-blade disk, third engine order excitation, single degree-of-freedom per blade model

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