The goal of this experimental and theoretical study is to highlight the nonlinear dynamic behavior of an inclined cable consisting of a steel wire surrounded by copper wire. Measurements around the first frequency of vibration of the cable in and out of plane and around the second harmonic of this frequency were also carried out. These experimental results are in good agreement with the numerical results obtained via the multiple scale method applied to finite (1- and 2- degree-of-freedom (DOF) models). In order to prepare further investigations related to more complicated behavior, a 4-DOF model is added.

1.
Irvine
,
H. M.
, and
Caughey
,
T. K.
, 1974, “
The Linear Theory of Free Vibrations of a Suspended Cable
,”
Proc. R. Soc. London, Ser. A
1364-5021
341
, pp.
299
315
.
2.
Irvine
,
H. M.
, 1981,
Cable Structures
,
MIT Press
, Cambridge, MA.
3.
Meirovitch
,
L.
, 1975,
Elements of Vibration Analysis
,
McGraw-Hill
, NY.
4.
West
,
H. H.
,
Geschwindner
,
L. F.
, and
Suhoski
.
J. E.
, 1975, “
Natural Vibrations of Suspension Cables
,”
J. Struct. Div. ASCE
0044-8001
ST11
, pp.
2277
2291
.
5.
Henghold
,
W. M.
, and
Russell
,
J. J.
, 1976, “
Equilibrium and Natural Frequencies of Cable Structures (A Nonlinear Finite Element Approach)
,”
Comput. Struct.
0045-7949
6
, pp.
267
271
.
6.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
, 1979,
Nonlinear Oscillations
,
Wiley
, NY.
7.
Takahashi
,
K.
, and
Konishi
,
Y.
, 1987, “
Nonlinear Vibrations of Cables in Three Dimensions, Part I: Nonlinear Free Vibrations
,”
J. Sound Vib.
0022-460X
118
(
1
), pp.
69
84
.
8.
Takahashi
,
K.
, and
Konishi
,
Y.
, 1987, “
Nonlinear Vibrations of Cables in Three Dimensions, Part II: Out of Plane Vibrations Under In-Plane Sinusoidally Time-Varying Load
,”
J. Sound Vib.
0022-460X
118
(
1
), pp.
85
97
.
9.
Benedettini
,
F.
,
Rega
,
G.
, and
Alaggio
,
R.
, 1995, “
Nonlinear Oscillations of a Four-Degree-of-Freedom Model of a Suspended Cable Under Multiple Internal Resonance Conditions
,”
J. Sound Vib.
0022-460X
182
(
5
), pp.
775
798
.
10.
El-Attar
,
M.
,
Ghobarah
,
A.
, and
Aziz
,
T. S.
, 2000, “
Nonlinear Cable Response to Multiple Support Periodic Excitation
,”
Eng. Struct.
0141-0296
22
, pp.
1301
1312
.
11.
Luongo
,
A.
,
Rega
G.
, and
Vestroni
,
F.
, 1984, “
Planar Nonlinear Free Vibrations of Elastic Cable
,”
Int. J. Non-Linear Mech.
0020-7462
19
(
1
), pp.
39
52
.
12.
Rega
,
G.
,
Lacarbonara
,
W.
,
Nayfeh
,
A. H.
, and
Char-Ming
,
Chin
, 1997, “
Multimodal Resonances in Suspended Cables Via a Direct Perturbation Approach
,”
Proc. of ASME DETC1997
, VIB-4101, Sacramento, Sept. 14–17,
ASME
, New York.
13.
Lilien
,
J. L.
, and
Pinto da Costa
,
A.
, 1994, “
Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structure
,”
J. Sound Vib.
0022-460X
174
(
1
), pp.
69
90
.
14.
Fujino
,
Y.
,
Warnitchai
,
P.
, and
Pacheco
,
B. M.
, 1992, “
An Experimental and Analytical Study of Autoparametric Resonance in a 3 DOF Model of Cable-Stayed-Beam
,”
Nonlinear Dyn.
0924-090X
4
, pp.
111
138
.
15.
Khadraoui
,
I.
, 1999, “
Contribution à la Modélisation et à L’Analyse Dynamique des Structures à Câbles
,” Thèse de Doctorat, Université d’Evry,
262
p, (in French).
16.
Berlioz
,
A.
,
Lamarque
,
C. H.
, and
Malasoma
,
J. M.
, 2001, “
Nonlinear Behavior of an Inclined Cable: Experimental and Analytical Investigations
,”
Proc. of ASME DETC2001
, VIB-21557, Pittsburgh, Sept. 9–12,
ASME
, New York.
17.
Zhao
,
Y. Y.
,
Wang
,
L. H.
,
Chen
,
D. L.
, and
Jiang
,
L. Z.
, 2002, “
Nonlinear Dynamics Analysis of the Two-Dimensional Simplified Model of an Elastic Cable
,”
J. Sound Vib.
0022-460X,
255
(
1
), pp.
43
59
.
18.
Triantafyllou
,
M. S.
, and
Grinfogel
,
L.
, 1986, “
Natural Frequencies and Modes of Inclined Cables
,”
J. Struct. Eng.
0733-9445
112
, pp.
139
148
.
19.
Berlioz
,
A.
, and
Lamarque
,
C. H.
, 2004, “
A Nonlinear Model for the Dynamics of an Inclined Cable
,”
J. Sound Vib.
0022-460X,
279
(
3–5
), pp.
619
639
.
20.
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
.
You do not currently have access to this content.