It is well-known that flutter vibrations of bladed disks can be saturated by dry friction. Previous theoretical investigations indicated that the steady-state, friction-damped flutter vibrations of tuned bladed disks are always dominated by a single traveling wave component, even if multiple traveling wave forms are unstable. This contrasts recent experimental investigations where multiple traveling wave forms were found to participate at steady state. In this paper, we demonstrate that this phenomenon can be explained by nonlinear frictional interblade coupling. To this end, we consider a simple phenomenological model of a bladed disk with frictional intersector coupling and two unstable traveling waves forms. Vibrations occur not only in the form of limit cycle oscillations (periodic) but also in the form of limit torus oscillations (quasi-periodic). It is shown how the limit state depends on the initial conditions, and that the occurrence of multiwave flutter depends on the proximity of the complex eigenvalues of the associated unstable waves. Finally, by computing the limit torus oscillation with a frequency-domain method, we lay the cornerstone for the systematic prediction of friction-saturated flutter vibrations of state-of-the-art bladed disk models.

References

References
1.
Srinivasan
,
A. V.
,
1997
, “
Flutter and Resonant Vibration Characteristics of Engine Blades
,”
ASME J. Eng. Gas Turbines Power
,
119
(
4
), pp.
742
775
.
2.
Marshall
,
J. G.
, and
Imregun
,
M.
,
1996
, “
A Review of Aeroelasticity Methods With Emphasis on Turbomachinery Applications
,”
J. Fluids Struct.
,
10
(
3
), pp.
237
267
.
3.
Sinha
,
A.
, and
Griffin
,
J. H.
,
1983
, “
Friction Damping of Flutter in Gas Turbine Engine Airfoils
,”
AIAA J. Aircr.
,
20
(
4
), pp.
372
376
.
4.
Sinha
,
A.
, and
Griffin
,
J. H.
,
1985
, “
Stability of Limit Cycles in Frictionally Damped and Aerodynamically Unstable Rotor Stages
,”
J. Sound Vib.
,
103
(
3
), pp.
341
356
.
5.
Corral
,
R.
, and
Gallardo
,
J. M.
,
2008
, “
Verification of the Vibration Amplitude Prediction of Self-Excited LPT Rotor Blades Using a Fully Coupled Time-Domain Non-Linear Method and Experimental Data
,”
ASME
Paper No. GT2008-51416.
6.
Petrov
,
E. P.
,
2012
, “
Analysis of Flutter-Induced Limit Cycle Oscillations in Gas-Turbine Structures With Friction, Gap, and Other Nonlinear Contact Interfaces
,”
ASME J. Turbomach.
,
134
(
6
), p.
061018
.
7.
Martel
,
C.
, and
Corral
,
R.
,
2013
, “
Flutter Amplitude Saturation by Nonlinear Friction Forces: An Asymptotic Approach
,”
ASME
Paper No. GT2013-94068.
8.
Martel
,
C.
,
Corral
,
R.
, and
Ivaturi
,
R.
,
2014
, “
Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Verification
,”
ASME J. Turbomach.
,
137
(
4
), p.
041004
.
9.
Corral
,
R.
, and
Gallardo
,
J. M.
,
2014
, “
Nonlinear Dynamics of Bladed Disks With Multiple Unstable Modes
,”
AIAA J.
,
52
(
6
), pp.
1124
1132
.
10.
Schoenenborn
,
H.
, and
Breuer
,
T.
,
2012
, “
Aeroelasticity at Reversed Flow Conditions—Part II: Application to Compressor Surge
,”
ASME J. Turbomach.
,
134
(
6
), p.
061031
.
11.
Olson
,
B. J.
,
Shaw
,
S. W.
,
Shi
,
C.
,
Pierre
,
C.
, and
Parker
,
R. G.
,
2014
, “
Circulant Matrices and Their Application to Vibration Analysis
,”
ASME Appl. Mech. Rev.
,
66
(
4
), p.
040803
.
12.
Corral
,
R.
, and
Vega
,
A.
,
2015
, “
The Low Reduced Frequency Limit of Vibrating Airfoils—Part I: Theoretical Analysis
,”
ASME J. Turbomach.
,
138
(
2
), p.
021004
.
13.
Vega
,
A.
, and
Corral
,
R.
,
2015
, “
The Low Reduced Frequency Limit of Vibrating Airfoils—Part II: Numerical Experiments
,”
ASME J. Turbomach.
,
138
(
2
), p.
021005
.
14.
Laxalde
,
D.
, and
Thouverez
,
F.
,
2009
, “
Complex Non-Linear Modal Analysis for Mechanical Systems Application to Turbomachinery Bladings With Friction Interfaces
,”
J. Sound Vib.
,
322
(
4–5
), pp.
1009
1025
.
15.
Schilder
,
F.
,
Vogt
,
W.
,
Schreiber
,
S.
, and
Osinga
,
H. M.
,
2006
, “
Fourier Methods for Quasi-Periodic Oscillations
,”
Int. J. Numer. Methods Eng.
,
67
(
5
), pp.
629
671
.
16.
Kim
,
Y. B.
,
Noah
,
S. T.
, and
Choi
,
Y. S.
,
1991
, “
Periodic Response of Multi-Disk Rotors With Bearing Clearances
,”
J. Sound Vib.
,
144
(
3
), pp.
381
395
.
17.
Berthillier
,
M.
,
Dupont
,
C.
,
Mondal
,
R.
, and
Barrau
,
J. J.
,
1998
, “
Blades Forced Response Analysis With Friction Dampers
,”
ASME J. Vib. Acoust.
,
120
(
2
), pp.
468
474
.
18.
Nacivet
,
S.
,
Pierre
,
C.
,
Thouverez
,
F.
, and
Jezequel
,
L.
,
2003
, “
A Dynamic Lagrangian Frequency-Time Method for the Vibration of Dry-Friction-Damped Systems
,”
J. Sound Vib.
,
265
(
1
), pp.
201
219
.
19.
Laxalde
,
D.
,
Thouverez
,
F.
, and
Lombard
,
J. P.
,
2007
, “
Vibration Control for Integrally Bladed Disks Using Friction Ring Dampers
,”
ASME
Paper No. GT2007-27087.
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