Abstract

It is well-known that nonlinear dry friction damping has the potential to bound the otherwise unboundedly growing vibrations of self-excited structures. An important technical example are the flutter-induced friction-damped limit cycle oscillations of turbomachinery blade rows. Due to symmetries, natural frequencies are inevitably closely spaced, and they can generally be multiples of each other. Not much is known on the nonlinear dynamics of self-excited friction-damped systems in the presence of such internal resonances. In this work, we analyze this situation numerically by regarding a two degrees-of-freedom system. We demonstrate that in the case of closely-spaced natural frequencies, the self-excitation of the lower-frequency mode gives rise to non-periodic oscillations, and the occurrence of unbounded behavior well before reaching the maximum friction damping value. If the system is close to a 1:3 internal resonance, limit cycles associated with much higher frictional damping appear, however, most of these are unstable. If more than one mode is subjected to self-excitation, the maximum resistance against self-excitation is at least given by the damping capacity of the most weakly friction-damped mode. These results are of high technical relevance, as the prevailing practice is to analyze only periodic limit states and argue the stability solely by the slope of the damping-amplitude curve. Our results demonstrate that this practice leads to considerable mis- and overestimation of the resistance against self-excitation, and a more rigorous stability analysis is required.

References

References
1.
Edwards
,
J. W.
, and
Malone
,
J. B.
,
1992
, “
Current Status of Computational Methods for Transonic Unsteady Aerodynamics and Aeroelastic Applications
,”
Comput. Syst. Eng.
,
3
(
5
), pp.
545
569
. 10.1016/0956-0521(92)90025-E
2.
Srinivasan
,
A. V.
,
1997
, “
Flutter and Resonant Vibration Characteristics of Engine Blades
,”
ASME J. Eng. Gas. Turbines. Power.
,
119
(
4
), pp.
742
775
. 10.1115/1.2817053
3.
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
. 10.1006/jfls.1996.0015
4.
Kinkaid
,
N. M.
,
O’Reilly
,
O. M.
, and
Papadopoulos
,
P.
,
2003
, “
Automotive Disc Brake Squeal
,”
J. Sound. Vib.
,
267
(
1
), pp.
105
166
. 10.1016/S0022-460X(02)01573-0
5.
Quintana
,
G.
, and
Ciurana
,
J.
,
2011
, “
Chatter in Machining Processes: A Review
,”
Int. J. Mach. Tools. Manuf.
,
51
(
5
), pp.
363
376
. 10.1016/j.ijmachtools.2011.01.001
6.
Siddhpura
,
M.
, and
Paurobally
,
R.
,
2012
, “
A Review of Chatter Vibration Research in Turning
,”
Int. J. Mach. Tools. Manuf.
,
61
, pp.
27
47
. 10.1016/j.ijmachtools.2012.05.007
7.
Waite
,
J. J.
, and
Kielb
,
R. E.
,
2016
, “
Shock Structure, Mode Shape, and Geometric Considerations for Low-Pressure Turbine Flutter Suppression
,”
Structures and Dynamics
,
Seoul, South Korea
, American Society of Mechanical Engineers.
8.
Krack
,
M.
,
Salles
,
L.
, and
Thouverez
,
F.
,
2017
, “
Vibration Prediction of Bladed Disks Coupled by Friction Joints
,”
Arch. Comput. Methods Eng.
,
24
(
3
), pp.
589
636
. 10.1007/s11831-016-9183-2
9.
Sinha
,
A.
, and
Griffin
,
J. H.
,
1983
, “
Friction Damping of Flutter in Gas Turbine Engine Airfoils
,”
J. Aircraft
,
20
(
4
), pp.
372
376
. 10.2514/3.44878
10.
Sinha
,
A.
, and
Griffin
,
J. H.
,
1985
, “
Effects of Friction Dampers on Aerodynamically Unstable Rotor Stages
,”
AIAA J.
,
23
(
2
), pp.
262
270
. 10.2514/3.8904
11.
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
. 10.1016/0022-460X(85)90427-4
12.
Krack
,
M.
,
Panning-von Scheidt
,
L.
, and
Wallaschek
,
J.
,
2017
, “
On the Interaction of Multiple Traveling Wave Modes in the Flutter Vibrations of Friction-Damped Tuned Bladed Disks
,”
ASME J. Eng. Gas. Turbines. Power.
,
139
(
4
), p.
742
. 10.1115/1.4034650
13.
Gross
,
J.
, and
Krack
,
M.
,
2020
, “
Multi-Wave Vibration Caused by Flutter Instability and Nonlinear Tip Shroud Friction
,”
ASME J. Eng. Gas. Turbines. Power.
,
142
(
2
), p.
021013
. https://doi.org/10.1115/1.4044884
14.
Krack
,
M.
, and
Gross
,
J.
,
2019
,
Harmonic Balance for Nonlinear Vibration Problems
,
Springer International Publishing
,
Cham
.
15.
Nlvib – a matlab tool for nonlinear vibration problems
,
available via
: https://www.ila.uni-stuttgart.de/nlvib
16.
Thompson
,
J. M. T.
, and
Stewart
,
H. B.
,
2002
,
Nonlinear Dynamics and Chaos
, 2nd edn.
Wiley
,
Chichester
.
17.
Rand
,
R. H.
, and
Holmes
,
P. J.
,
1980
, “
Bifurcation of Periodic Motions in Two Weakly Coupled van der pol Oscillators
,”
Int. J. Non-Linear Mech.
,
15
(
4–5
), pp.
387
399
. 10.1016/0020-7462(80)90024-4
18.
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
. 10.1016/j.jsv.2008.11.044
19.
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
. 10.1115/1.4006292
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