This paper investigates the instability of the transverse vibration of a disk excited by two corotating sliders on either side of the disk. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. There are friction forces acting in the plane of the disk at the contact interfaces between the disk and each of the two sliders. The equation of motion of the disk is established by taking into account the bending couple acting in the circumferential direction produced by the different friction forces on the two sides of the disk. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability. Regions of instability for parameters of interest are obtained by the method of state space. It is found that the moving loads produced by the sliders are a mechanism for generating unstable parametric resonances in the subcritical speed range. The existence of stable regions in the parameter space of the simulated example suggests that the disk vibration can be suppressed by suitable assignment of the parameter values of the sliders.

1.
Mote
,
C. D.
,
1970
, “
Stability of Circular Plates Subjected to Moving Loads
,”
J. Franklin Inst.
,
290
, pp.
329
344
.
2.
Iwan
,
W. D.
, and
Moeller
,
T. L.
,
1976
, “
The Stability of a Spinning Elastic Disc With a Transverse Load System
,”
ASME J. Appl. Mech.
,
43
, pp.
485
496
.
3.
Yu
,
R. L.
, and
Mote
,
C. D.
,
1987
, “
Vibration and Parametric Excitation in Asymmetric Plates Under Moving Loads
,”
J. Sound Vib.
,
119
, pp.
409
427
.
4.
Jiang
,
Z. W.
,
Chonan
,
S.
, and
Abe
,
H.
,
1990
, “
Dynamic Response of a Read/Write Head Floppy Disc System Subjected to Axial Excitation
,”
ASME J. Vibr. Acoust.
,
112
, pp.
53
58
.
5.
Shen
,
Y.
, and
Mote
,
C. D.
,
1991
, “
On the Mechanism of Instability of a Circular Plate Under a Rotating Spring-Mass-Dashpot System
,”
J. Sound Vib.
,
148
, pp.
307
318
.
6.
Shen
,
I. Y.
,
1993
, “
Response of a Stationary Damped Circular Plate Under a Rotating Slider Bearing System
,”
ASME J. Vibr. Acoust.
,
115
, pp.
65
69
.
7.
Huang
,
F. Y.
, and
Mote
,
C. D.
,
1996
, “
Mathematical Analysis of Stability of a Spinning Disc Under Rotating, Arbitrary Large Damping Force
,”
ASME J. Vibr. Acoust.
,
118
, pp.
657
662
.
8.
Ono
,
K.
,
Chen
,
J. S.
, and
Bogy
,
D. B.
,
1991
, “
Stability Analysis of the Head-Disk Interface in a Flexible Disc Drive
,”
ASME J. Appl. Mech.
,
58
, pp.
1005
1014
.
9.
North, N. R., 1972, “Disc Brake Squeal—A Theoretical Model,” M.I.R.A. Research Report, No. 1972/5.
10.
Lee
,
D.
, and
Waas
,
A. M.
,
1997
, “
Stability Analysis of a Rotating Multi-Layer Annular Plate With a Stationary Frictional Follower Load
,”
Int. J. Mech. Sci.
,
39
(
10
), pp.
1117
1138
.
11.
Chan
,
S. N.
,
Mottershead
,
J. E.
, and
Cartmell
,
M. P.
,
1994
, “
Parametric Resonances at Subcritical Speeds in Discs With Rotating Frictional Loads
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
208
, pp.
417
25
.
12.
Mottershead
,
J. E.
,
Ouyang
,
H.
,
Cartmell
,
M. P.
, and
Friswell
,
M. I.
,
1997
, “
Parametric Resonances in an Annular Disc, With a Rotating System of Distributed Mass and Elasticity; and the Effects of Friction and Damping
,”
Proc. R. Soc. London, Ser. A
,
453
(
1
), pp.
1
19
.
13.
Ouyang
,
H.
,
Mottershead
,
J. E.
,
Cartmell
,
M. P.
, and
Friswell
,
M. I.
,
1998
, “
Friction-Induced Parametric Resonances in Discs: Effect of a Negative Friction-Velocity Relationship
,”
J. Sound Vib.
,
209
(
2
), pp.
251
264
.
14.
Tseng
,
J.-G.
, and
Wickert
,
J. A.
,
1998
, “
Nonconservative Stability of a Friction Loaded Disc
,”
ASME J. Vibr. Acoust.
,
120
, pp.
922
929
.
15.
Ouyang
,
H.
,
Mottershead
,
J. E.
,
Cartmell
,
M. P.
, and
Brookfield
,
D. J.
,
1999
, “
Friction-Induced Vibration of an Elastic Slider on a Vibrating Disc
,”
Int. J. Mech. Sci.
,
41
, pp.
325
336
.
16.
Ouyang
,
H.
,
Mottershead
,
J. E.
,
Brookfield
,
D. J.
,
James
,
S.
, and
Cartmell
,
M. P.
,
2000
, “
A Methodology for the Determination of Dynamic Instabilities in a Car Disc Brake
,”
Int. J. Veh. Des.
,
23
, pp.
241
262
.
17.
Ouyang
,
H.
, and
Mottershead
,
J. E.
,
2001
, “
Optimal Suppression of Parametric Vibration in Discs Under Rotating Frictional Loads
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
215
(
1
), pp.
65
75
.
18.
Tian
,
J.
, and
Hutton
,
S. G.
,
1999
, “
Self-Excited Vibration in Flexible Rotating Disks Subjected to Various Transverse Interactive Forces: A General Approach
,”
ASME J. Appl. Mech.
,
66
(
3
), pp.
800
805
.
19.
Mottershead
,
J. E.
,
1998
, “
Vibration and Friction-Induced Instability in Discs
,”
Shock Vib. Dig.
,
30
(
1
), pp.
14
31
.
20.
North
,
N. R.
,
1976
, “
Disc Brake Squeal
,”
Proc. Inst. Mech. Eng.
,
C38/76
, pp.
169
176
.
21.
Hulten
,
J.
, and
Flint
,
J.
,
2002
, “
Lining-Deformation-Induced Modal Coupling as Squeal Generator in a Distributed Parameter Disc Brake Model
,”
J. Sound Vib.
,
254
(
1
), pp.
1
21
.
22.
Fryba, L., 1972, Vibration of Solids and Structures Under Moving Loads, Noordhoff, Groningen.
23.
Oden
,
J. T.
, and
Martins
,
J. A. C.
,
1985
, “
Models and Computational Methods for Dynamic Friction Phenomena
,”
Comput. Methods Appl. Mech. Eng.
,
52
, pp.
527
643
.
24.
Ibrahim
,
R. A.
,
1994
, “
Friction-Induced Vibration, Chatter, Squeal, and Chaos. Part 1: Mechanics of Friction; Part 2: Dynamics of Modeling
,”
Appl. Mech. Rev.
,
47
, pp.
209
253
.
25.
Hulten, J. O., 1995, “Some Drum Brake Squeal Mechanisms,” Proc. of the 1995 Noise and Vibration Conference, Traverse City, Michigan, Vol. 1, pp. 377–388.
26.
Popp, K., and Rudolph, M., 2001, “Brake Squeal,” In Detection, Utilization and Avoidance of Nonlinear Dynamical Effects in Engineering Applications, K. Popp (ed.) Aachen: Shaker Verlag, pp. 197–225.
27.
Iwan
,
W. D.
, and
Stahl
,
K. J.
,
1973
, “
The Response of an Elastic Disc With a Moving Mass System
,”
ASME J. Appl. Mech.
,
40
, pp.
445
451
.
28.
Nayfeh, H., and Mook, D. T., 1979, Nonlinear Oscillation, Wiley, New York.
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