This paper is devoted to the theoretical and experimental investigation of a sample automotive belt-pulley system subjected to tension fluctuations. The equation of motion for transverse vibrations leads to a Duffing oscillator parametrically excited. The analysis is performed via the multiple scales approach for predicting the nonlinear response, considering longitudinal viscous damping. An experimental setup gives rise to nonlinear parametric instabilities and also exhibits more complex phenomena. The experimental investigation validates the assumptions made and the proposed model.

1.
Beikmann
,
R. S.
,
Perkins
,
N. C.
, and
Ulsoy
,
A. G.
, 1997, “
Design and Analysis of Automotive Belt Drive Systems for Steady State Performance
,”
ASME J. Mech. Des.
1050-0472,
119
, pp.
162
168
.
2.
Zhang
,
L.
, and
Zu
,
J. W.
, 1999, “
One-to-One Auto-Parametric Resonance in Serpentine Belt Drive Systems
,”
J. Sound Vib.
0022-460X,
232
, pp.
783
806
.
3.
Bechtel
,
S. E.
,
Vohra
,
S.
,
Jacob
,
K. I.
, and
Carlson
,
C. D.
, 2000, “
The Stretching and Slipping of Belts and Fibers on Pulleys
,”
ASME J. Appl. Mech.
0021-8936,
67
, pp.
197
206
.
4.
Gerbert
,
G.
and
Sorge
,
F.
, 2002, “
Full Sliding Adhesive-Like Contact of V-Belts
,”
ASME J. Mech. Des.
1050-0472,
124
, pp.
706
712
.
5.
Kong
,
L.
, and
Parker
,
R. G.
, 2005, “
Steady Mechanics of Belt-Pulley Systems
,”
ASME J. Appl. Mech.
0021-8936,
72
, pp.
25
34
.
6.
Leamy
,
M. J.
, and
Perkins
,
N. C.
, 1998, “
Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners
,”
ASME J. Vibr. Acoust.
0739-3717,
120
, pp.
909
916
.
7.
Michon
,
G.
,
Manin
,
L.
, and
Dufour
,
R.
, 2005, “
Hysteretic Behavior of a Belt Tensioner, Modeling and Experimental Investigation
,”
J. Vib. Control
1077-5463,
11
(
9
), pp.
1147
1158
.
8.
Parker
,
R. G.
, and
Lin
,
Y.
, 2004, “
Parametric Instability of Axially Moving Media Subjected to Multifrequency Tension and Speed Fluctuation
,”
ASME J. Appl. Mech.
0021-8936,
68
, pp.
49
57
.
9.
Pellicano
,
F.
,
Catellani
,
G.
, and
Fregolent
,
A.
, 2004, “
Parametric Instability of Belts, Theory and Experiments
,”
Comput. Struct.
0045-7949,
82
, pp.
81
91
.
10.
Mockensturm
,
E.
,
Perkins
,
N.
, and
Ulsoy
,
A.
, 1996, “
Stability and Limit Cycles of Parametrically Excited, Axially Moving Strings
,”
ASME J. Vibr. Acoust.
0739-3717,
118
, pp.
346
351
.
11.
Mockensturm
,
E.
, and
Guo
,
J.
, 2005, “
Nonlinear Vibration of Parametrically Excited Viscoelastic Axially Moving Media
,”
ASME J. Appl. Mech.
0021-8936,
72
, pp.
374
380
.
12.
Berlioz
,
A.
, and
Lamarque
,
C. H.
, 2005, “
A Non-Linear Model for the Dynamic of an Inclined Cable
,”
J. Sound Vib.
0022-460X,
279
, pp.
619
639
.
13.
Perkins
,
N. C.
, 1992, “
Modal Interactions in the Nonlinear Response of Elastic Cables Under Parametric/External Excitation
,”
Int. J. Non-Linear Mech.
0020-7462,
27
(
2
), pp.
233
250
.
14.
Rega
,
G.
, and
Benedettini
,
F.
, 1989, “
Planar Non-Linear Oscillations of Elastic Cables Under Subharmonic Resonance Conditions
,”
J. Sound Vib.
0022-460X,
132
(
3
), pp.
367
381
.
15.
Berlioz
,
A.
,
Der Hagopian
,
J.
,
Dufour
,
R.
, and
Draoui
,
E.
, 1996, “
Dynamic Behavior of a Drill-String. Experimental Investigation of Lateral Instabilities
,”
ASME J. Vibr. Acoust.
0739-3717,
118
, pp.
292
298
.
16.
Dufour
,
R.
, and
Berlioz
,
A.
, 1998, “
Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions
,”
ASME J. Vibr. Acoust.
0739-3717,
120
, pp.
461
467
.
17.
Thurman
,
A. L.
, and
Mote
, Jr.,
C. D.
, 1969, “
Free, Periodic, Non-Linear Oscillation of an Axially Moving String
,”
ASME J. Appl. Mech.
0021-8936,
36
, pp.
83
91
.
18.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
, 1979,
Nonlinear Oscillations
,
Wiley
,
New York
.
19.
Orloske
,
K.
,
Leamy
,
M. J.
, and
Parker
,
R. G.
, 2006, “
Flexural-Torsion Buckling of Misaligned Axially Moving Beam. I. Three-Dimensional Modeling, Equilibria, and Bifurcations
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
4297
4322
.
20.
Orloske
,
K.
, and
Parker
,
R. G.
, 2006, “
Flexural-Torsion Buckling of Misaligned Axially Moving Beam. II. Vibration and Stability Analysis
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
4323
4341
.
You do not currently have access to this content.