This paper deals with the dynamics of a cyclic system, representative of a bladed disk subjected to dry friction forces, and exhibits structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response and suggests that further statistical investigations could be of great interest for the design of bladed-disks, in terms of vibration mitigation and robustness.

References

References
1.
Petrov
,
E.
, and
Ewins
,
D.
,
2006
, “
Effects of Damping and Varying Contact Area at Bladed-Disk Joints in Forced Responses Analysis of Bladed Disk Assemblies
,”
ASME J Turbomach.
,
128
(
2
), pp.
403
410
.
2.
Laxalde
,
D.
,
Thouverez
,
F.
,
Sinou
,
J.-J.
, and
Lombard
,
J.-P.
,
2007
, “
Qualitative Analysis of Forced Response of Blisks With Friction Ring Dampers
,”
Eur. J. Mech.-A/Solids
,
26
(
4
), pp.
676
687
.
3.
Salles
,
L.
,
Blanc
,
L.
,
Thouverez
,
F.
, and
Gouskov
,
A.
,
2011
, “
Dynamic Analysis of Fretting-Wear in Friction Contact Interfaces
,”
Int. J. Solids Struct.
,
48
(
10
), pp.
1513
1524
.
4.
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
.
5.
Charleux
,
D.
,
Gibert
,
C.
,
Thouverez
,
F.
, and
Dupeux
,
J.
,
2006
, “
Numerical and Experimental Study of Friction Damping in Blade Attachments of Rotating Bladed Disks
,”
Int. J. Rotating Mach.
,
2006
, p.
71302
.
6.
Berruti
,
T.
,
Firrone
,
C.
, and
Gola
,
M.
,
2011
, “
A Test Rig for Noncontact Traveling Wave Excitation of a Bladed Disk With Underplatform Dampers
,”
ASME J. Eng. Gas Turbines Power
,
133
(
3
), p.
032502
.
7.
Zucca
,
S.
,
Maio
,
D. D.
, and
Ewins
,
D.
,
2012
, “
Measuring the Performance of Underplatform Dampers for Turbine Blades by Rotating Laser Doppler Vibrometer
,”
Mech. Syst. Signal Process.
,
32
, pp.
269
281
.
8.
Schwingshackl
,
C.
,
Petrov
,
E.
, and
Ewins
,
D.
,
2012
, “
Measured and Estimated Friction Interface Parameters in a Nonlinear Dynamic Analysis
,”
Mech. Syst. Signal Process.
,
28
, pp.
574
584
.
9.
Schwingshackl
,
C.
,
Joannin
,
C.
,
Pesaresi
,
L.
,
Green
,
J.
, and
Hoffmann
,
N.
,
2014
, “
Test Method Development for Nonlinear Damping Extraction of Dovetail Joints
,”
Dynamics of Coupled Structures
, Vol. 1, Springer, Cham, Switzerland, pp.
229
237
.
10.
Pierre
,
C.
, and
Dowell
,
E.
,
1987
, “
Localization of Vibrations by Structural Irregularity
,”
J. Sound Vib.
,
114
(
3
), pp.
549
564
.
11.
Castanier
,
M. P.
, and
Pierre
,
C.
,
2002
, “
Using Intentional Mistuning in the Design of Turbomachinery Rotors
,”
AIAA J.
,
40
(
10
), pp.
2077
2086
.
12.
Mbaye
,
M.
,
Soize
,
C.
,
Ousty
,
J.-P.
, and
Capiez-Lernout
,
E.
,
2013
, “
Robust Analysis of Design in Vibration of Turbomachines
,”
ASME J. Turbomach.
,
135
, p.
021008
.
13.
Pichot
,
F.
,
Laxalde
,
D.
,
Sinou
,
J.-J.
,
Thouverez
,
F.
, and
Lombard
,
J.-P.
,
2006
, “
Mistuning Identification for Industrial Blisks Based on the Best Achievable Eigenvector
,”
Comput. Struct.
,
84
(
29–30
), pp.
2033
2049
.
14.
Vargiu
,
P.
,
Firrone
,
C.
,
Zucca
,
S.
, and
Gola
,
M.
,
2011
, “
A Reduced Order Model Based on Sector Mistuning for the Dynamic Analysis of Mistuned Bladed Disks
,”
Int. J. Mech. Sci.
,
53
(
8
), pp.
639
646
.
15.
Ewins
,
D.
,
2000
,
Modal Testing: Theory Practice and Application
, 2nd ed.,
Research Study Press
,
Baldock, UK
.
16.
Rosenberg
,
R.
,
1962
, “
The Normal Modes of Nonlinear n-Degrees-of-Freedom Systems
,”
ASME J. Appl. Mech.
,
29
(
1
), pp.
1
74
.
17.
Kerschen
,
G.
,
Peeters
,
M.
,
Golinval
,
J.
, and
Vakakis
,
A.
,
2009
, “
Nonlinear Normal Modes—Part I: A Useful Framework for the Structural Dynamicist
,”
Mech. Syst. Signal Process.
,
23
(
1
), pp.
170
194
.
18.
Shaw
,
S.
, and
Pierre
,
C.
,
1993
, “
Normal Modes for Non-Linear Vibratory Systems
,”
J. Sound Vib.
,
164
(
1
), pp.
85
124
.
19.
Vakakis
,
A. F.
,
1992
, “
Dynamics of a Nonlinear Periodic Structure With Cyclic Symmetry
,”
Acta Mech.
,
95
(
1–4
), pp.
197
226
.
20.
Vakakis
,
A. F.
, and
Cetinkaya
,
C.
,
1993
, “
Mode Localization in a Class of Multidegree-of-Freedom Nonlinear Systems With Cyclic Symmetry
,”
SIAM J. Appl. Math.
,
53
(
1
), pp.
265
282
.
21.
Vakakis
,
A.
,
Nayfeh
,
T.
, and
King
,
M.
,
1993
, “
A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System
,”
ASME J. Appl. Mech.
,
60
(
2
), pp.
388
397
.
22.
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
.
23.
Krack
,
M.
,
von Scheidt
,
L. P.
, and
Wallaschek
,
J.
,
2013
, “
A Method for Nonlinear Modal Analysis and Synthesis: Application to Harmonically Forced and Self-Excited Mechanical Systems
,”
J. Sound Vib.
,
332
(
25
), pp.
6798
6814
.
24.
Wei
,
S.-T.
, and
Pierre
,
C.
,
1989
, “
Effects of Dry Friction Damping on the Occurrence of Localized Forced Vibrations in Nearly Cyclic Structures
,”
J. Sound Vib.
,
129
(
3
), pp.
397
416
.
25.
Grolet
,
A.
, and
Thouverez
,
F.
,
2012
, “
Free and Forced Vibration Analysis of a Nonlinear System With Cyclic Symmetry: Application to a Simplified Model
,”
J. Sound Vib.
,
331
(
12
), pp.
2911
2928
.
26.
Cameron
,
T. M.
, and
Griffin
,
J. H.
,
1989
, “
An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems
,”
ASME J. Appl. Mech.
,
56
(
1
), pp.
149
154
.
27.
Nayfeh
,
A.
, and
Balachandran
,
B.
,
1995
,
Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods
,
Wiley-VCH Verlag
,
Weinheim, Germany
.
28.
Petrov
,
E.
, and
Ewins
,
D.
,
2003
, “
Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks
,”
ASME J. Turbomach.
,
125
(
2
), pp.
364
371
.
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