This paper explores the effects of random blade mistuning on the dynamics of an advanced industrial compressor rotor, using a component-mode-based reduced-order model formulation for tuned and mistuned bladed disks. The technique uses modal data obtained from finite element models to create computationally inexpensive models of mistuned bladed disks in a systematic manner. Both free and forced responses of the rotor are considered, and the obtained results are compared with “benchmark” finite element solutions. A brief statistical study is presented, in which Weibull distributions are shown to yield reliable estimates of forced response statistics. Moreover, a simple method is presented for computing natural frequencies of noninteger harmonics, using conventional cyclic symmetry finite element analysis. This procedure enables quantification of frequency veering data relevant to the assessment of mistuning sensitivity (e.g., veering curvatures), and it may provide a tool for quantifying structural interblade coupling in finite element rotor models of arbitrary complexity and size. The mistuned forced response amplitudes and stresses are found to vary considerably with mistuning strength and the degree of structural coupling between the blades. In general, this work demonstrates how reduced order modeling and Weibull estimates of the forced response statistics combine to facilitate thorough investigations of the mistuning sensitivity of industrial turbomachinery rotors.

1.
Ewins
,
D. J.
,
1969
, “
The Effects of Detuning Upon the Forced Vibrations of Bladed Disks
,”
J. Sound Vib.
,
9
, pp.
65
79
.
2.
Ewins
,
D. J.
,
1973
, “
Vibration Characteristics of Bladed Disc Assemblies
,”
J. Mech. Eng. Sci.
,
15
, pp.
165
186
.
3.
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.
4.
Castanier
,
M. P.
,
O´ttarsson
,
G.
, and
Pierre
,
C.
,
1997
, “
A Reduced-Order Modeling Technique for Mistuned Bladed Disks
,”
ASME J. Vibr. Acoust.
,
119
, pp.
439
447
.
5.
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.
6.
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
.
7.
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
.
8.
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
.
9.
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
, pp.
100
108
.
10.
Moyroud, F., Jacquet-Richardet, G., and Fransson, T., 2000, “A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed-Disks,” Proc. 45th ASME Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, ASME, New York.
11.
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.
12.
Gumbel, E. J., 1958, Statistics of Extremes, Columbia University Press, New York.
13.
O´ttarsson, G. S., 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, Vol. 5, AIAA, New York, pp. 3070–3078, also, Journal of Sound and Vibration (in print).
14.
Pierre
,
C.
,
1988
, “
Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures
,”
J. Sound Vib.
,
126
, pp.
485
502
.
15.
Mignolet
,
M. P.
, and
Lin
,
C.-C.
,
1997
, “
Identification of Structural Parameters in Mistuned Bladed Disks
,”
ASME J. Vibr. Acoust.
,
119
, pp.
428
438
.
16.
Wei
,
S. T.
, and
Pierre
,
C.
,
1988
, “
Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry, Part I: Free Vibrations; Part II: Forced Vibrations
,”
ASME J. Vibr. Acoust., Stress, Reliab. Des.
,
110
, pp.
429
449
.
17.
Castanier, M. P., and Pierre, C., 1997, “Consideration on the Benefits of International Blade Mistuning for the Forced Response of Turbomachinery Rotors,” Proc. ASME International Mechanical Engineering Congress and Exposition, Vol. 55, ASME, New York, pp. 419–425.
18.
Castanier, M. P., and Pierre, C., 1998, “Investigation of the Combined Effects of Intentional and Random Mistuning on the Forced Response of Bladed Disks,” Proc. 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA, New York.
19.
Castillo, E., 1988, Extreme Value Theory in Engineering, Academic Press, San Diego, CA.
20.
Whitehead
,
D. S.
,
1966
, “
Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes
,”
J. Mech. Eng. Sci.
,
8
, pp.
15
21
.
21.
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
.
22.
Mead
,
D. J.
,
1975
, “
Wave Propagation and Natural Modes in Periodic Systems, I: Mono-Coupled Systems
,”
J. Sound Vib.
,
40
, pp.
1
18
.
23.
Davis, P. J., 1979, Circulant Matrices, John Wiley and Sons, New York.
24.
Thomas
,
D. L.
,
1979
, “
Dynamics of Rotationally Periodic Structures
,”
Int. J. Numer. Methods Eng.
,
14
, pp.
81
102
.
25.
Strang, G., 1988, Linear Algebra and Its Applications, 3rd Ed., Saunders, Philadelphia, PA.
You do not currently have access to this content.