It is well known that the vibrational behavior of a mistuned bladed disk differs strongly from that of a tuned bladed disk. A large number of publications dealing with the dynamics of mistuned bladed disks are available in the literature. The vibrational phenomena analyzed in these publications are either forced vibrations or self-excited flutter vibrations. Nearly, all published literature on the forced vibrations of mistuned blades disks considers harmonic, i.e., steady-state, vibrations, whereas the self-excited flutter vibrations are analyzed by the evaluation of the margin against instabilities by means of a modal, or rather than eigenvalue, analysis. The transient forced response of mistuned bladed disk is not analyzed in detail so far. In this paper, a computationally efficient mechanical model of a mistuned bladed disk to compute the transient forced response is presented. This model is based on the well-known fundamental model of mistuning (FMM). With this model, the statistics of the transient forced response of a mistuned bladed disk is analyzed and compared to the results of harmonic forced response analysis.

References

References
1.
Thomas
,
D. L.
,
1979
, “
Dynamics of Rotationally Periodic Structures
,”
Int. J. Numer. Methods Eng.
,
14
(
1
), pp.
81
102
.
2.
Srinivasan
,
A. V.
,
1997
, “
Flutter and Resonant Vibration Characteristics of Engine Blades
,”
ASME J. Eng. Gas Turbines Power
,
119
(
4
), pp.
742
775
.
3.
Castanier
,
M. P.
, and
Pierre
,
C.
,
2006
, “
Modeling and Analysis of Mistuned Bladed Disk Vibration: Status and Emerging Directions
,”
J. Propul. Power
,
22
(
2
), pp.
384
396
.
4.
Kellenberger
,
W.
,
1984
, “
Double-Frequency Forced Vibration of Turbine Blades due to an Elliptical Orbit of the Rotor
,”
3rd IMechE International Conference on Vibrations in Rotating Machinery
, Heslington, UK, Sept. 11–13, Paper No. C293/84.
5.
Elchuri
,
V.
,
Smith
,
G. C. C.
, and
Gallo
,
A. M.
,
1984
, “
NASTRAN Forced Vibration Analysis of Rotating Cyclic Structures
,”
ASME J. Vib. Acoust., Stress Reliab. Des.
,
106
(
2
), pp.
224
234
.
6.
Sinha
,
A.
,
2005
, “
Statistics of the Peak Maximum Amplitude of the Forced Response of a Mistuned Bladed Disk
,”
ASME
Paper No. GT2005-69070.
7.
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
(
1
), pp.
115
119
.
8.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2001
, “
Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies
,”
ASME
Paper No. 2001-GT-0292.
9.
Chan
,
Y. J.
, and
Ewins
,
D. J.
,
2009
, “
A Comprehensive Set of Procedures to Estimate the Probability of Extreme Vibration Levels due to Mistuning
,”
ASME
Paper No. GT2009-59088.
10.
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
.
11.
Laxalde
,
D.
,
Thouverez
,
F.
,
Sinou
,
J. J.
,
Baumhauer
,
S.
, and
Lombard
,
J. P.
,
2006
, “
Mistuning Identification and Model Updating of an Industrial Blisk
,”
ASME
Paper No. GT2006-90569.
12.
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
(
1
), pp.
161
167
.
13.
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
.
14.
Hohl
,
A.
,
Siewert
,
C.
,
Panning
,
L.
, and
Wallaschek
,
J.
,
2009
, “
A Substructure Based Reduced Order Model for Mistuned Bladed Disks
,”
ASME
Paper No. DETC2009-87459.
15.
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
.
16.
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2002
, “
A Fundamental Model of Mistuning for a Single Family of Modes
,”
ASME
Paper No. GT-2002-30425.
17.
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2004
, “
Mistuning Identification of Bladed Disks Using a Fundamental Mistuning Model—Part I: Theory
,”
ASME J. Turbomach.
,
126
(
1
), pp.
150
158
.
18.
Martel
,
C.
, and
Corral
,
R.
,
2008
, “
Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response
,”
ASME
Paper No. GT2008-50822.
19.
Siewert
,
C.
, and
Stüer
,
H.
,
2010
, “
Forced Response Analysis of Mistuned Turbine Bladings
,”
ASME
Paper No. GT2010-23782.
20.
Lim
,
S. H.
,
Bladh
,
R.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2003
, “
A Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration
,”
AIAA
Paper No. 2003-1545.
21.
Ganine
,
V.
,
Legrand
,
M.
,
Pierre
,
C.
, and
Michalska
,
H.
,
2008
, “
A Reduction Technique for Mistuned Bladed Disks With Superposition of Large Geometric Mistuning and Small Model Uncertainties
,”
12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, Feb. 17–22.
22.
Vargiu
,
P.
,
Firrone
,
C. M.
,
Zucca
,
S.
, and
Gola
,
M. M.
,
2011
, “
A Reduced Order Model Based on Sector Mistuning for the Dynamic Analysis of Mistuned Bladed Disks
,”
Int. J. Mech. Sci.
,
8
, pp.
639
646
.
23.
Miyakozawa
,
T.
,
Kielb
,
R. E.
, and
Hall
,
K. C.
,
2008
, “
The Effects of Aerodynamic Asymmetric Perturbations on Forced Response of Bladed Disks
,”
ASME
Paper No. GT2008-50719.
24.
Petrov
,
E. P.
,
2009
, “
A Method for Forced Response Analysis of Mistuned Bladed Discs With Aerodynamic Effects Included
,”
ASME
Paper No. GT2009-59634.
25.
Vyas
,
N. S.
, and
Rao
,
J. S.
,
1994
, “
Fatigue Life Estimation Procedure for a Turbine Blade Under Transient Loads
,”
ASME J. Eng. Gas Turbines Power
,
116
(
1
), pp.
198
206
.
26.
Hartung
,
A.
,
2010
, “
A Numerical Approach for the Resonance Passage Computation
,”
ASME
Paper No. GT2010-22051.
27.
Fricker
,
A. J.
, and
Potter
,
S.
,
1981
, “
Transient Forced Vibration of Rotationally Periodic Structures
,”
Int. J. Numer. Methods Eng.
,
17
(
7
), pp.
957
974
.
28.
Omprakash
,
V.
, and
Ramamurti
,
V.
,
1990
, “
Spectral Analysis of the Transient Characteristics of a Bladed Disk During Run-Up
,”
Comput. Struct.
,
37
(
6
), pp.
983
992
.
29.
Ayers
,
J. P.
,
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2006
, “
A Reduced-Order Model for Transient Analysis of Bladed Disk Forced Response
,”
ASME J. Turbomach.
,
128
(
3
), pp.
466
473
.
30.
Kaneko
,
Y.
,
2013
, “
Study on Transient Vibration of Mistuned Bladed Disk Passing Through Resonance
,”
ASME
Paper No. GT2013-94052.
31.
Newland
,
D. E.
,
2006
,
Mechanical Vibration—Analysis and Computation
,
1st ed.
,
Dover Publications
,
Mineola, NY
.
32.
Craig
,
R. R.
, and
Kurdila
,
A. D.
,
2006
,
Fundamentals of Structural Dynamics
,
2nd ed.
,
Wiley
,
New York
.
33.
Gasch
,
R.
, and
Knothe
,
K.
,
1989
,
Strukturdynamik Bd. 2—Kontinua und ihre Diskretisierung
,
1st ed.
,
Springer
,
Berlin
.
34.
Bendat
,
J. S.
, and
Piersol
,
A. G.
,
1986
,
Random Data
,
1st ed.
,
Wiley
,
New York
.
35.
Ayers
,
J. P.
,
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2005
, “
Reducing Mistuning Effects by Optimally Switching Blades
,”
10th National Turbine Engine High Cycle Fatigue (HCF) Conference
, New Orleans, LA, Mar. 8–11.
You do not currently have access to this content.