Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

1.
Broch, T. J., 1975, On the Measurement of Frequency Response Functions, B&K Tech. Rev. No. 4.
2.
Burtekin
 
M.
,
Cowley
 
A.
, and
Back
 
N.
,
1978
, “
An Elastic Mechanism for the Micro-sliding Characteristics Between Contacting Machined Surfaces
,”
Journal of Mechanical Engineering Science
, Vol.
20
, No.
3
, pp.
121
127
.
3.
Chen
 
S.
, and
Sinha
 
A.
,
1990
, “
Probabilistic Method to Compute the Optimal Slip Load for a Mistuned Bladed Disc Assembly With Friction Dampers
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
112
, pp.
214
221
.
4.
Den Hartog
 
J. P.
,
1931
, “
Forced Vibrations with Combined Coulomb and Viscous Friction
,”
Transactions of ASME
, Vol.
53
, pp.
107
115
.
5.
Ferri
 
A. A.
, and
Bindemann
 
A. C.
,
1992
, “
Damping and Vibration of Beams With Various Types of Frictional Support Conditions
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, pp.
289
296
.
6.
Gibson, J. E., 1963, Non-linear Automatic Control, McGraw-Hill Book Comp.
7.
Goodman, L. E., and Brown, C. B., 1962, “Energy Dissipation in Contact Friction: Constant Normal and Cyclic Tangential Loading,” ASME Journal of Applied Mechanics, pp. 17–22, March.
8.
Griffln
 
J. H.
,
1980
, “
Friction Damping of Resonant Stresses in Gas Turbines Airfoils
,”
ASME Journal of Engineering for Power
, Vol.
102
, No.
2
, pp.
329
333
.
9.
Menq
 
C-H.
,
Bielak
 
J.
, and
Griffln
 
J. H.
,
1986
a, “
The Influence of Microslip on Vibratory Response, Part II; Comparison with Experimental Results
,”
Journal of Sound and Vibration
,
107
(
2
), pp.
295
307
.
10.
Menq
 
C-H.
,
Griffin
 
J. H.
, and
Bielak
 
J.
,
1986
b, “
The Forced Vibration of Shrouded Fan Stages
,”
ASME JOURNAL OF VIBRATION ACOUSTICS, STRESS AND RELIABILITY IN DESIGN
, Vol.
108
, pp.
50
55
.
11.
Menq
 
C-H.
, and
Griffin
 
J. H.
,
1985
, “
A Comparison of Transient and Steady State Finite Element Analyses of the Forced Response of a Frictional Damped Beam
,”
ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS AND RELIABILITY IN DESIGN
, Vol.
107
, pp.
19
25
.
12.
Mickens
 
R. E.
,
1984
, “
Comments on the Method of Harmonic Balance
,”
Journal of Sound and Vibration
, Vol.
94
, No.
3
, pp.
456
460
.
13.
Muszynska
 
A.
, and
Jones
 
D. I. G.
,
1983
, “
On Tuned Bladed Disk Dynamics; Some Aspects of Friction Related Mistuning
,”
Journal of Sound and Vibration
, Vol.
86
, No.
l
, pp.
107
128
.
14.
Pfeiffer
 
F.
, and
Hajek
 
M.
,
1992
, “
Stick-Slip Motion of Turbine Blade Dampers
,”
Philosophical Transactions of the Royal Society of London
, Series A, Vol.
338
, No.
1651
, pp.
503
517
.
15.
Rogers, P. F., and Boothroyd, G., 1975, “Damping at Metallic Interfaces Subjected to Oscillating Tangential Loads,” ASME Journal of Engineering for Industry, pp. 1087–1093.
16.
Sanliturk, K. Y., Stanbridge, A. B., and Ewins, D. J., 1995, “Friction Dampers; Measurement, Modelling and Application to Blade Vibration Control,” ASME 15th Biennial Conference on Vibration and Noise, Boston USA, 17–21, September, DE-Vol. 84-2, pp. 1377–1382.
17.
Shoukry, S. N., 1985, “A Mathematical Model for the Stiffness of Fixed Joints Between Machine Parts,” Proc. Int. NUMETA Conf., Swansea, U.K., pp. 851–858.
18.
Siljak, D., 1969, Non-linear Systems: A Parameter Analysis and Design, John Wiley and Sons.
19.
Sinha
 
A.
, and
Griffin
 
J. H.
,
1984
, “
Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades
,”
ASME Journal of Engineering for Gas Turbines and Power
, Vol.
106
, pp.
65
69
.
20.
Thomas
 
R. M.
, and
Gladwell
 
I.
,
1988
, “
Variable-Order, Variable-Step Algorithms for Second-Order Systems. Part 1; The Methods, Part 2; The Codes
,”
International Journal for Numerical Methods in Engineering
, Vol.
26
, pp.
55
80
.
21.
Wang, J. H., and Chen, W. K., 1992, “Investigation of the Vibration of a Blade with Friction Damper by HBM,” ASME, 92-GT-8, Presented at the International Gas Turbine and Aeroengine Congress and Exposition, Cologne, Germany, June 1–4.
This content is only available via PDF.
You do not currently have access to this content.