This paper reviews models of helical cable behavior with an emphasis on recent models that study internal cable damping. Cable models are categorized into three major classes consisting of thin rod models, semicontinuous models, and beam models. Research on cable vibration damping resulting from internal factors is investigated and related, with conclusions supported by multiple bodies of work highlighted and inconsistencies that may require further study noted. Internal damping mechanisms due to interwire friction, variable bending stiffness, and internal and viscoelastic dissipation are explored with specific damping terms presented for the various models. Damping through inclusion of friction forces, viscoelastic shear effects, or bending stiffness as a function of cable curvature and wire properties must be included to produce a realistic cable model.

References

1.
Triantafyllou
,
M. S.
,
1984
, “
Linear Dynamics of Cables and Chains
,”
Shock Vib. Dig.
,
16
(
3
), pp.
9
17
.10.1177/058310248401600305
2.
Starossek
,
U.
,
1994
, “
Cable Dynamics—A Review
,”
Struct. Eng. Int.
,
3
, pp.
171
176
.10.2749/101686694780601908
3.
Rega
,
G.
,
2004
, “
Nonlinear Vibrations of Suspended Cables—Part I: Modeling and Analysis
,”
ASME Appl. Mech. Rev.
,
57
(
6
), pp.
443
478
.10.1115/1.1777224
4.
Rega
,
G.
,
2004
, “
Nonlinear Vibrations of Suspended Cables—Part II: Deterministic Phenomena
,”
ASME Appl. Mech. Rev.
,
57
(
6
), pp.
479
514
.10.1115/1.1777225
5.
Raj
,
T. M.
, and
Parthasarathy
,
N. S.
,
2007
, “
A Complete Review on Friction Models of Composite Cables
,”
Int. J. Mech. Compos. Mater. Constr., Russ. Acad. Appl. Mech. Sci.
,
13
(
3
), pp.
356
384
.
6.
Feyrer
,
K.
,
2007
,
Wire Rope: Tension, Endurance, Reliability
,
Springer
,
New York
.
7.
Chiang
,
Y. J.
,
1996
, “
Characterizing Simple-Stranded Wire Cables Under Axial Loading
,”
Finite Elem. Anal. Des.
,
24
, pp.
49
66
.10.1016/S0168-874X(97)80001-E
8.
Costello
,
G. A.
,
1990
,
Theory of Wire Rope
,
Springer
,
New York
.
9.
Rawlins
,
C. B.
,
2009
, “
Flexural Self-Damping in Overhead Electrical Transmission Conductors
,”
J. Sound Vib.
,
323
, pp.
232
256
.10.1016/j.jsv.2008.12.022
10.
Triantafyllou
,
M. S.
,
1987
, “
Dynamics of Cables and Chains
,”
Shock Vib. Dig.
,
19
(
12
), pp.
3
5
.10.1177/058310248701901202
11.
Irvine
,
H. M.
, and
Caughey
,
T. K.
,
1974
, “
The Linear Theory of Free Vibrations of a Suspended Cable
,”
Proc. R. Soc. London
,
341
, pp.
299
315
.10.1098/rspa.1974.0189
12.
Benedettini
,
F.
, and
Rega
,
G.
,
1986
, “
Non-Linear Dynamics of an Elastic Cable Under Planar Excitation
,”
Int. J. Nonlinear Mech.
,
22
(
6
), pp.
497
509
.10.1016/0020-7462(87)90039-4
13.
Hagedorn
,
P.
, and
Schafer
,
B.
,
1980
, “
On Non-Linear Free Vibrations of an Elastic Cable
,”
Int. J. Nonlinear Mech.
,
15
, pp.
333
340
.10.1016/0020-7462(80)90018-9
14.
Koh
,
C. G.
, and
Zhang
,
Y.
,
1999
, “
Low-Tension Cable Dynamics: Numerical and Experimental Studies
,”
J. Eng. Mech.
,
125
(
3
), pp.
347
354
.10.1061/(ASCE)0733-9399(1999)125:3(347)
15.
Luongo
,
A.
,
Rega
,
G.
, and
Vestroni
,
F.
,
1984
, “
Planar Non-Linear Free Vibrations Elastic Cable
,”
Int. J. Nonlinear Mech.
,
19
(
1
), pp.
39
52
.10.1016/0020-7462(84)90017-9
16.
Starossek
,
U.
,
1991
, “
Dynamic Stiffness Matrix of Sagging Cable
,”
J. Eng. Mech.
,
117
(
12
), pp.
2815
2829
.10.1061/(ASCE)0733-9399(1991)117:12(2815)
17.
Utting
,
W. S.
, and
Jones
,
N.
,
1987
, “
The Response of Wire Rope Strands to Axial Tensile Loads—Part 1. Experimental Results and Theoretical Predictions
,”
Int. J. Mech. Sci.
,
29
(
9
), pp.
605
619
.10.1016/0020-7403(87)90033-6
18.
Erdonmez
,
C.
, and
Imrak
,
C. E.
,
2011
, “
A Finite Element Model for Independent Wire Rope Core With Double Helical Geometry Subjected to Axial Loads
,”
Sadhana
,
36
(
6
), pp.
995
1008
.10.1007/s12046-011-0053-1
19.
Velinsky
,
S. A.
,
1985
, “
General Nonlinear Theory for Complex Wire Ropes
,”
Int. J. Mech. Sci.
,
27
, pp.
497
507
.10.1016/0020-7403(85)90040-2
20.
Velinsky
,
S. A.
,
1989
, “
On the Design of Wire Rope
,”
ASME J. Mech. Trans.
,
111
(
3
), pp.
382
388
.10.1115/1.3259010
21.
Sathikh
,
S.
,
Moorthy
,
M. B. K.
, and
Krishnan
,
M.
,
1996
, “
A Symmetric Linear Elastic Model for Helical Wire Strands Under Axisymmetric Loads
,”
J. Strain Anal.
,
31
(
5
), pp.
389
399
.10.1243/03093247V315389
22.
Huang
,
N. C.
,
1978
, “
Finite Extension of an Elastic Strand With a Central Core
,”
ASME J. Appl. Mech.
,
45
(4)
, pp.
852
858
.10.1115/1.3424431
23.
Raoof
,
M.
, and
Hobbs
,
R. E.
,
1988
, “
Analysis of Multilayered Structural Strands
,”
J. Eng. Mech.
,
114
(
7
), pp.
1166
1182
.10.1061/(ASCE)0733-9399(1988)114:7(1166)
24.
Jolicoeur
,
C.
, and
Cardou
,
A.
,
1996
, “
Semicontinuous Mathematical Model for Bending of Multilayered Wire Strands
,”
J. Eng. Mech.
,
122
(
7
), pp.
643
650
.10.1061/(ASCE)0733-9399(1996)122:7(643)
25.
Jolicoeur
,
C.
,
1997
, “
Comparative Study of Two Semicontinuous Models for Wire Strand Analysis
,”
J. Eng. Mech.
,
123
(
8
), pp.
792
799
.10.1061/(ASCE)0733-9399(1997)123:8(792)
26.
Raoof
,
M.
, and
Kraincanic
,
I.
,
1994
, “
Critical Examination of Various Approached Used for Analysing Helical Cables
,”
J. Strain Anal. Eng. Des.
,
29
(
1
), pp.
43
55
.10.1243/03093247V291043
27.
Dreyer
,
T. P.
, and
Van Vuuren
,
J. H.
,
1999
, “
A Comparison Between Continuous and Discrete Modeling of Cables With Bending Stiffness
,”
Appl. Mech. Model.
,
23
, pp.
527
541
.10.1016/S0307-904X(98)10097-5
28.
Hover
,
F. S.
, and
Triantafyllou
,
M. S.
,
1999
, “
Linear Dynamics of Curved Tensioned Elastic Beams
,”
J. Sound Vib.
,
228
(
4
), pp.
923
930
.10.1006/jsvi.1999.2497
29.
Ashkenazi
,
R.
,
Weiss
,
M. P.
, and
Elata
,
D.
,
2004
, “
Torsion and Bending Stresses in Wires of Non-Rotating Tower Crane Ropes
,”
OIPECC Bull.
,
87
, pp. 1157–1172.
30.
Elata
,
D.
,
Eshkenazy
,
R.
, and
Weiss
,
M. P.
,
2004
, “
The Mechanical Behavior of a Wire Rope With an Independent Wire Rope Core
,”
Int. J. Solids Struct.
,
41
, pp.
1157
1172
.10.1016/j.ijsolstr.2003.11.021
31.
Usabiaga
,
H.
, and
Pagalday
,
J. M.
,
2008
, “
Analytical Procedure for Modeling Recursively and Wire by Wire Stranded Ropes Subjected to Traction and Torsion Loads
,”
Int. J. Solids Struct.
,
45
, pp.
5503
5520
.10.1016/j.ijsolstr.2008.04.009
32.
Huang
,
C.
, and
Knapp
,
R. H.
,
2006
, “
Parametric Modeling of Double and Triple Helical Strands
,”
Proceedings of the 16th International Offshore and Polar Engineering Conference
,
San Francisco, CA
, pp.
139
144
.
33.
Koh
,
C. G.
, and
Rong
,
Y.
,
2004
, “
Dynamic Analysis of Large Displacement Cable Motion With Experimental Verification
,”
J. Sound Vib.
,
272
(
1–2
), pp.
187
206
.10.1016/S0022-460X(03)00326-2
34.
Srinil
,
N.
,
Rega
,
G.
, and
Chucheepsakul
,
S.
,
2004
, “
Three-Dimensional Non-Linear Coupling and Dynamic Tension in the Large-Amplitude Free Vibrations of Arbitrarily Sagged Cables
,”
J. Sound Vib.
,
269
, pp.
823
852
.10.1016/S0022-460X(03)00137-8
35.
Sun
,
J. F.
,
Wang
,
G. L.
, and
Zhang
,
H. O.
,
2008
, “
FE Analysis of Frictional Contact Effect for Laying Wire Rope
,”
J. Mater. Process. Technol.
,
202
, pp.
170
178
.10.1016/j.jmatprotec.2007.08.064
36.
Giglio
,
M.
, and
Manes
,
A.
,
2005
, “
Life Prediction of a Wire Rope Subjected to Axial and Bending Loads
,”
Eng. Failure Anal.
,
12
, pp.
549
568
.10.1016/j.engfailanal.2004.09.002
37.
Lacarbonara
,
W.
,
Paolone
,
A.
, and
Vestroni
,
F.
,
2007
, “
Non-Linear Modal Properties of Non-Shallow Cables
,”
Int. J. Nonlinear Mech.
,
42
(
3
), pp.
542
554
.10.1016/j.ijnonlinmec.2007.02.013
38.
Sauter
,
D.
,
2003
, “
Modeling the Dynamic Characteristics of Slack Wire Cables in Stockbridge Dampers
,” Ph.D. thesis, Technische Universität Darmstadt, Darmstadt, Germany.
39.
Zhong
,
M.
,
2003
, “
Dynamic Analysis of Cables With Variable Flexural Rigidity
,” M.S. thesis, University of Hawaii, Hilo, HI.
40.
Liu
,
X.
,
2004
, “
Cable Vibration Considering Internal Friction
,” M.S. thesis, University of Hawaii, Hilo, HI.
41.
Knapp
,
R. H.
, and
Liu
,
X.
,
2005
, “
Cable Vibration Considering Interlayer Coulomb Friction
,”
Int. J. Offshore Polar Eng.
,
15
(
3
), pp.
229
234
.
42.
Crossley
,
J. A.
,
Spencer
,
A. J. M.
, and
England
,
A. H.
,
2003
, “
Analytical Solutions for Bending and Flexure of Helically Reinforced Cylinders
,”
Int. J. Solids Struct.
,
40
, pp.
777
806
.10.1016/S0020-7683(02)00625-X
43.
Ghoreishi
,
S. R.
,
Messager
,
T.
,
Cartraud
,
P.
, and
Davies
,
P.
,
2007
, “
Validity and Limitations of Linear Analytical Models for Steel Wire Strands Under Axial Loading, Using a 3D FE Model
,”
Int. J. Mech. Sci.
,
49
, pp.
1251
1261
.10.1016/j.ijmecsci.2007.03.014
44.
Inagaki
,
K.
,
Ekh
,
J.
, and
Zahrai
,
S.
,
2007
, “
Mechanical Analysis of Second Order Helical Structure in Electrical Cable
,”
Int. J. Solids Struct.
,
44
, pp.
1657
1679
.10.1016/j.ijsolstr.2006.06.045
45.
Lacarbonara
,
W.
, and
Pacitti
,
A.
,
2008
, “
Nonlinear Modeling of Cables With Flexural Stiffness
,”
Math. Probl. Eng.
,
2008
, pp.
1
22
.10.1155/2008/370767
46.
Jiang
,
W.
,
Warby
,
M. K.
, and
Henshall
,
J. L.
,
2008
, “
Statically Indeterminate Contacts in Axially Loaded Wire Strand
,”
Eur. J. Mech. Solids
,
27
, pp.
69
78
.10.1016/j.euromechsol.2007.02.003
47.
Jiang
,
W.-G.
,
2012
, “
A Concise Finite Element Model for Pure Bending Analysis of Simple Wire Strand
,”
Int. J. Mech. Sci.
,
54
(
1
), pp.
69
73
.10.1016/j.ijmecsci.2011.09.008
48.
Papailiou
,
K. O.
,
1997
, “
On the Bending Stiffness of Transmission Line Conductors
,”
IEEE Trans. Power Delivery
,
12
(
4
), pp.
1576
1588
.10.1109/61.634178
49.
Shibu
,
G.
,
Mohankumar
,
K. V.
, and
Devendiran
,
S.
,
2011
, “
Analysis of a Three Layered Straight Wire Rope Strand Using Finite Element Method
,”
Proceedings of the World Congress on Engineering
, London, UK, Vol. 3.
50.
Argatov
,
I.
,
2011
, “
Response of a Wire Rope Strand to Axial and Torsional Loads, Asymptotic Modeling of the Effect of Interwire Contact Deformations
,”
Int. J. Solids Struct.
,
48
(
10
), pp.
1413
1423
.10.1016/j.ijsolstr.2011.01.021
51.
Castello
,
D. A.
, and
Matt
,
C. F. T.
,
2011
, “
A Validation Metrics Based Model Calibration Applied on Stranded Cables
,”
J. Braz. Soc. Mech. Sci. Eng.
,
33
(
4
), pp.
417
427
.10.1590/S1678-58782011000400005
52.
Goodding
,
J. C.
,
Ardelean
,
E. V.
,
Babuska
,
V.
,
Robertson
,
L. M.
, and
Lane
,
S. A.
,
2011
, “
Experimental Techniques and Structural Parameter Estimation Studies of Spacecraft Cables
,”
J. Spacecr. Rockets
,
48
(
6
), pp.
942
957
.10.2514/1.49346
53.
Johnson
,
E. A.
,
Christenson
,
R. E.
, and
Spencer
,
B. F.
,
2003
, “
Semiactive Damping of Cables With Sag
,”
Comput. Aided Civ. Infrastruct. Eng.
,
18
, pp.
132
146
.10.1111/1467-8667.00305
54.
Boston
,
C.
,
Weber
,
F.
, and
Guzzella
,
L.
,
2011
, “
Optimal Semiactive Damping of Cables With Bending Stiffness
,”
Smart Mater. Struct.
,
20
, p.
055005
.10.1088/0964-1726/20/5/055005
55.
Yu
,
A.
,
1949
, “
Vibration Damping of Stranded Cable
,” Ph.D. thesis, Lehigh University, Bethlehem, PA.
56.
Diana
,
G.
,
Falco
,
M.
,
Cigada
,
A.
, and
Manenti
,
A.
,
2000
, “
On the Measurement of Overhead Transmission Lines Conductor Self-Damping
,”
IEEE Trans. Power Delivery
,
15
(
1
), pp.
285
292
.10.1109/61.847264
57.
Otrin
,
M.
, and
Boltežar
,
M.
,
2007
, “
Damped Lateral Vibrations of Straight and Curved Cables With No Axial Pre-Load
,”
J. Sound Vib.
,
300
(
3–5
), pp.
676
694
.10.1016/j.jsv.2006.08.032
58.
Urchegui
,
M. A.
,
Tato
,
W.
, and
Gomez
,
X.
,
2008
, “
Wear Evolution in a Stranded Rope Subjected to Cyclic Bending
,”
J. Mater. Eng. Perform.
,
17
(
4
), pp.
550
560
.10.1007/s11665-007-9165-5
59.
Ramsey
,
H.
,
1990
, “
Analysis of Interwire Friction in Multilayered Cables Under Uniform Extension and Twisting
,”
Int. J. Mech. Sci.
,
32
(
8
), pp.
709
716
.10.1016/0020-7403(90)90011-7
60.
Raoof
,
M.
, and
Huang
,
Y. P.
,
1992
, “
Upper Bound Prediction of Cable Damping Under Cyclic Bending
,”
J. Eng. Mech.
,
117
(
12
), pp.
2729
2747
.10.1061/(ASCE)0733-9399(1991)117:12(2729)
61.
Raoof
,
M.
, and
Huang
,
Y. P.
,
1992
, “
Free Bending Characteristics of Axially Preloaded Spiral Strands
,”
Proc. Inst. Civ. Eng., Struct. Build.
,
94
, pp.
469
484
.10.1680/istbu.1992.21508
62.
Kumar
,
K.
, and
Botsis
,
J.
,
2001
, “
Contact Stresses in Multilayered Strands Under Tension and Torsion
,”
ASME J. Appl. Mech.
,
68
(3)
, pp.
432
440
.10.1115/1.1355777
63.
Labrosse
,
M.
,
Nawrocki
,
A.
, and
Conway
,
T.
,
2000
, “
Frictional Dissipation in Axially Loaded Simple Straight Strands
,”
J. Eng. Mech.
,
126
(
6
), pp.
641
646
.10.1061/(ASCE)0733-9399(2000)126:6(641)
64.
Zhu
,
Z. H.
, and
Meguid
,
S. A.
,
2007
, “
Nonlinear FE-Based Investigation of Flexural Damping of Slacking Wire Cables
,”
Int. J. Solids Struct.
,
44
, pp.
5122
5132
.10.1016/j.ijsolstr.2006.12.024
65.
Cutchins
,
M. A.
,
Cochran
,
J. E.
,
Kumar
,
K.
,
Fitz-Coy
,
N. G.
, and
Tinker
,
M. L.
,
1987
, “
Initial Investigations Into the Damping Characteristics of Wire Rope Vibration Isolators
,”
Tech. Report
,
Auburn University
,
Alabama
.
66.
Goodding
,
J. C.
,
2008
, “
Spacecraft Electrical Cable Harness Structural Test and Analysis Methods
,”
IMAC: Conference and Exposition on Structural Dynamics
, pp.
437
443
.
67.
Raoof
,
M.
, and
Huang
,
Y. P.
,
1992
, “
Axial and Free-Bending Analysis of Spiral Strands Made Simple
,”
J. Eng. Mech.
,
118
(
12
), pp.
2335
2351
.10.1061/(ASCE)0733-9399(1992)118:12(2335)
68.
Raoof
,
M.
, and
Davies
,
T. J.
,
2006
, “
Simple Determination of the Maximum Axial and Torsional Energy Dissipation in Large Diameter Spiral Strands
,”
Comput. Struct.
,
84
, pp.
676
689
.10.1016/j.compstruc.2005.11.005
69.
Gnanavel
,
B. K.
, and
Parthasarathy
,
N. S.
,
2011
, “
Effect of Interfacial Contact Forces in Radial Contact Wire Strand
,”
Arch. Appl. Mech.
,
81
, pp.
303
317
.10.1007/s00419-010-0406-y
70.
Gnanavel
,
B. K.
, and
Parthasarathy
,
N. S.
,
2012
, “
Effect of Interfacial Contact Forces in Single Layer Cable Assemblies
,”
Int. J. Mech. Mater. Des.
,
8
, pp.
183
195
.10.1007/s10999-012-9185-7
71.
Dastous
,
J.-B.
,
2005
, “
Nonlinear Finite-Element Analysis of Stranded Conductors With Variable Bending Stiffness Using the Tangent Stiffness Method
,”
IEEE Trans. Power Delivery
,
20
(
1
), pp.
328
338
.10.1109/TPWRD.2004.835420
72.
Papailiou
,
K. O.
,
1995
, “
Bending of Helically Twisted Cables Under Variable Bending Stiffness Due to Internal Friction, Tensile Force and Cable Curvature
,” Ph.D. thesis, Eidgenossische Technische Hochschule Zurich, Zurich, Switzerland.
73.
Lanteigne
,
J.
,
1986
, “
Theoretical Estimation of the Response of Helically Armored Cables to Tension, Torsion, and Bending
,”
ASME J. Appl. Mech.
,
52
(
2
), pp.
423
432
.10.1115/1.3169064
74.
Hong
,
K.
,
Der Kiureghian
,
A.
, and
Sackman
,
J. L.
,
2005
, “
Bending Behavior of Helically Wrapped Cables
,”
J. Eng. Mech.
,
131
(
5
),
pp
.
500
511
.10.1061/(ASCE)0733-9399(2005)131:5(500)
75.
Jayakumar
,
C. V.
,
Sathikh
,
S.
,
Jebaraj
,
C.
, and
Jolicoeur
,
C.
,
1999
, “
Discussion of ‘Comparative Study of Two Semicontinuous Models for Wire Strand Analysis’
,”
J. Eng. Mech.
,
125
(
3
), pp.
369
370
.10.1061/(ASCE)0733-9399(1999)125:3(369)
76.
Johansen
,
V.
,
Ersdal
,
S.
,
Sørensen
,
A. J.
, and
Leira
,
B.
,
2006
, “
Modeling of Inextensible Cable Dynamics With Experiments
,”
Int. J. Nonlinear Mech.
,
41
(
4
), pp.
543
555
.10.1016/j.ijnonlinmec.2006.01.002
77.
Cardou
,
A.
,
2006
, “
Discussion of ‘Bending Behavior of Helically Wrapped Cables’
by Kee-Jeung Hong, Armen Der Kiureghian, and Jerome L. Sackman,”
J. Eng. Mech.
,
132
, pp.
790
791
.10.1061/(ASCE)0733-9399(2006)132:7(790)
78.
Filiatrault
,
A.
, and
Stearns
,
C.
,
2005
, “
Flexural Properties of Flexible Conductors Interconnecting Electrical Substation Equipment
,”
J. Struct. Eng.
,
131
(
1
), pp.
151
160
.10.1061/(ASCE)0733-9445(2005)131:1(151)
79.
Yamaguchi
,
H.
, and
Adhikari
,
R.
,
1994
, “
Loss Factors of Damping Treated Structural Cables
,”
J. Sound Vib.
,
176
(
4
), pp.
487
495
.10.1006/jsvi.1994.1391
80.
Yamaguchi
,
H.
, and
Adhikari
,
R.
,
1995
, “
Energy-Based Evaluation of Modal Damping in Structural Cables With and Without Damping Treatment
,”
J. Sound Vib.
,
181
(
1
), pp.
71
83
.10.1006/jsvi.1995.0126
81.
Barbieri
,
N.
,
de Souza
,
O. H.
, and
Barbieri
,
R.
,
2004
, “
Dynamical Analysis of Transmission Line Cables. Part 1—Linear Theory
,”
Mech. Syst. Signal Process.
,
18
, pp.
659
669
.10.1016/S0888-3270(02)00217-0
82.
Krenk
,
S.
, and
Hogsberg
,
J. R.
,
2004
, “
Damping of Cables by a Transverse Force
,”
J. Eng. Mech.
,
131
(
4
), pp.
340
348
.10.1061/(ASCE)0733-9399(2005)131:4(340)
83.
Weber
,
F.
, and
Boston
,
C.
,
2010
, “
Energy Based Optimization of Viscous—Friction Dampers on Cables
,”
Smart Mater. Struct.
,
19
, p.
045025
.10.1088/0964-1726/19/4/045025
84.
Noiseux
,
D. U.
,
1992
, “
Similarity Laws of the Internal Damping of Stranded Cables in Transverse Vibrations
,”
IEEE Trans. Power Delivery
,
7
(
3
), pp.
1574
1581
.10.1109/61.141877
85.
Kauffman
,
J. L.
,
Lesieutre
,
G. A.
, and
Babuska
,
V.
,
2012
, “
Damping Models for Shear Beams With Applications to Spacecraft Wiring Harnesses
,”
Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
,
Honolulu, HI
, pp.
1
10
.
86.
Lesieutre
,
G. A.
,
2010
, “
Frequency-Independent Modal Damping for Flexural Structures via a Viscous Geometric Damping Model
,”
J. Guid. Control Dyn.
,
33
(
6
), pp.
1931
1935
.10.2514/1.49864
You do not currently have access to this content.