Review Articles

Cable Modeling and Internal Damping Developments

[+] Author and Article Information
Kaitlin Spak

Virginia Polytechnic Institute,
310 Durham Hall,
Blacksburg, VA 24060
e-mail: kspak@vt.edu

Gregory Agnes

Jet Propulsion Laboratory,
California Institute of Technology,
Pasadena, CA 91109

Daniel Inman

University of Michigan,
Ann Arbor, MI 48109

Manuscript received September 6, 2012; final manuscript received January 18, 2013; published online March 20, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 65(1), 010801 (Mar 21, 2013) (18 pages) Paper No: AMR-12-1048; doi: 10.1115/1.4023489 History: Received September 06, 2012; Revised January 18, 2013

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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Triantafyllou, M. S., 1984, “Linear Dynamics of Cables and Chains,” Shock Vib. Dig., 16(3), pp. 9–17. [CrossRef]
Starossek, U., 1994, “Cable Dynamics—A Review,” Struct. Eng. Int., 3, pp. 171–176. [CrossRef]
Rega, G., 2004, “Nonlinear Vibrations of Suspended Cables—Part I: Modeling and Analysis,” ASME Appl. Mech. Rev., 57(6), pp. 443–478. [CrossRef]
Rega, G., 2004, “Nonlinear Vibrations of Suspended Cables—Part II: Deterministic Phenomena,” ASME Appl. Mech. Rev., 57(6), pp. 479–514. [CrossRef]
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.
Feyrer, K., 2007, Wire Rope: Tension, Endurance, Reliability, Springer, New York.
Chiang, Y. J., 1996, “Characterizing Simple-Stranded Wire Cables Under Axial Loading,” Finite Elem. Anal. Des., 24, pp. 49–66. [CrossRef]
Costello, G. A., 1990, Theory of Wire Rope, Springer, New York.
Rawlins, C. B., 2009, “Flexural Self-Damping in Overhead Electrical Transmission Conductors,” J. Sound Vib., 323, pp. 232–256. [CrossRef]
Triantafyllou, M. S., 1987, “Dynamics of Cables and Chains,” Shock Vib. Dig., 19(12), pp. 3–5. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Hagedorn, P., and Schafer, B., 1980, “On Non-Linear Free Vibrations of an Elastic Cable,” Int. J. Nonlinear Mech., 15, pp. 333–340. [CrossRef]
Koh, C. G., and Zhang, Y., 1999, “Low-Tension Cable Dynamics: Numerical and Experimental Studies,” J. Eng. Mech., 125(3), pp. 347–354. [CrossRef]
Luongo, A., Rega, G., and Vestroni, F., 1984, “Planar Non-Linear Free Vibrations Elastic Cable,” Int. J. Nonlinear Mech., 19(1), pp. 39–52. [CrossRef]
Starossek, U., 1991, “Dynamic Stiffness Matrix of Sagging Cable,” J. Eng. Mech., 117(12), pp. 2815–2829. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Velinsky, S. A., 1985, “General Nonlinear Theory for Complex Wire Ropes,” Int. J. Mech. Sci., 27, pp. 497–507. [CrossRef]
Velinsky, S. A., 1989, “On the Design of Wire Rope,” ASME J. Mech. Trans., 111(3), pp. 382–388. [CrossRef]
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. [CrossRef]
Huang, N. C., 1978, “Finite Extension of an Elastic Strand With a Central Core,” ASME J. Appl. Mech., 45(4), pp. 852–858. [CrossRef]
Raoof, M., and Hobbs, R. E., 1988, “Analysis of Multilayered Structural Strands,” J. Eng. Mech., 114(7), pp. 1166–1182. [CrossRef]
Jolicoeur, C., and Cardou, A., 1996, “Semicontinuous Mathematical Model for Bending of Multilayered Wire Strands,” J. Eng. Mech., 122(7), pp. 643–650. [CrossRef]
Jolicoeur, C., 1997, “Comparative Study of Two Semicontinuous Models for Wire Strand Analysis,” J. Eng. Mech., 123(8), pp. 792–799. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Hover, F. S., and Triantafyllou, M. S., 1999, “Linear Dynamics of Curved Tensioned Elastic Beams,” J. Sound Vib., 228(4), pp. 923–930. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Sauter, D., 2003, “Modeling the Dynamic Characteristics of Slack Wire Cables in Stockbridge Dampers,” Ph.D. thesis, Technische Universität Darmstadt, Darmstadt, Germany.
Zhong, M., 2003, “Dynamic Analysis of Cables With Variable Flexural Rigidity,” M.S. thesis, University of Hawaii, Hilo, HI.
Liu, X., 2004, “Cable Vibration Considering Internal Friction,” M.S. thesis, University of Hawaii, Hilo, HI.
Knapp, R. H., and Liu, X., 2005, “Cable Vibration Considering Interlayer Coulomb Friction,” Int. J. Offshore Polar Eng., 15(3), pp. 229–234.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Lacarbonara, W., and Pacitti, A., 2008, “Nonlinear Modeling of Cables With Flexural Stiffness,” Math. Probl. Eng., 2008, pp. 1–22. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Papailiou, K. O., 1997, “On the Bending Stiffness of Transmission Line Conductors,” IEEE Trans. Power Delivery, 12(4), pp. 1576–1588. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Boston, C., Weber, F., and Guzzella, L., 2011, “Optimal Semiactive Damping of Cables With Bending Stiffness,” Smart Mater. Struct., 20, p. 055005. [CrossRef]
Yu, A., 1949, “Vibration Damping of Stranded Cable,” Ph.D. thesis, Lehigh University, Bethlehem, PA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Ramsey, H., 1990, “Analysis of Interwire Friction in Multilayered Cables Under Uniform Extension and Twisting,” Int. J. Mech. Sci., 32(8), pp. 709–716. [CrossRef]
Raoof, M., and Huang, Y. P., 1992, “Upper Bound Prediction of Cable Damping Under Cyclic Bending,” J. Eng. Mech., 117(12), pp. 2729–2747. [CrossRef]
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. [CrossRef]
Kumar, K., and Botsis, J., 2001, “Contact Stresses in Multilayered Strands Under Tension and Torsion,” ASME J. Appl. Mech., 68(3), pp. 432–440. [CrossRef]
Labrosse, M., Nawrocki, A., and Conway, T., 2000, “Frictional Dissipation in Axially Loaded Simple Straight Strands,” J. Eng. Mech., 126(6), pp. 641–646. [CrossRef]
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. [CrossRef]
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.
Goodding, J. C., 2008, “Spacecraft Electrical Cable Harness Structural Test and Analysis Methods,” IMAC: Conference and Exposition on Structural Dynamics, pp. 437–443.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
Hong, K., Der Kiureghian, A., and Sackman, J. L., 2005, “Bending Behavior of Helically Wrapped Cables,” J. Eng. Mech., 131(5), pp. 500–511. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Filiatrault, A., and Stearns, C., 2005, “Flexural Properties of Flexible Conductors Interconnecting Electrical Substation Equipment,” J. Struct. Eng., 131(1), pp. 151–160. [CrossRef]
Yamaguchi, H., and Adhikari, R., 1994, “Loss Factors of Damping Treated Structural Cables,” J. Sound Vib., 176(4), pp. 487–495. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Krenk, S., and Hogsberg, J. R., 2004, “Damping of Cables by a Transverse Force,” J. Eng. Mech., 131(4), pp. 340–348. [CrossRef]
Weber, F., and Boston, C., 2010, “Energy Based Optimization of Viscous—Friction Dampers on Cables,” Smart Mater. Struct., 19, p. 045025. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]


Grahic Jump Location
Fig. 1

(a) 7 × 7 cable side view and end view with core labeled and individual seven-wire strand identified. (b) 7 × 19 cable side view and end view; side views reprinted with permission from VER sales.

Grahic Jump Location
Fig. 2

Procedure for semicontinuous models in which individual wire properties are averaged or combined over an entire layer to make a model with homogeneous layers in order to simplify calculations

Grahic Jump Location
Fig. 3

Core wire with single helix wires in first layer and core of surrounding strands and double helix wire in first layer of surrounding strands [30]

Grahic Jump Location
Fig. 4

Wire-core contact, in which the core wire diameter is larger than the layer wires, and wire-wire contact, in which all wire diameters can be equal

Grahic Jump Location
Fig. 5

Simplified interwire contact forces. Tension on the cable, as a whole results, in pressure from the outer layer to each successive inner layer, causing normal forces between the wires. Sliding friction between the wires is proportional to the normal force and acts along the line of contact between the wires, shown by the dotted lines.

Grahic Jump Location
Fig. 6

Comparison of traditional Coulomb damping model with hysteretic Coulomb damping model

Grahic Jump Location
Fig. 7

Masing-based model used to incorporate frictional damping, where ki are spring values and hi are the maximum stiction forces for the Coulomb element

Grahic Jump Location
Fig. 8

Definition of wire contact types used in Gnanavel and Parthasarathy's work [70]

Grahic Jump Location
Fig. 9

Relationship between bending stiffness and curvature; bending stiffness is constant and maximum with minimal curvature when wires are not sliding against one another. Once the wires begin to slip, they enter the transition state, where some wires are slipping and some are sticking; Kslip is the critical curvature that represents the average curvature between stick and slip states. When the cable experiences high curvature, all wires have slipped and the bending stiffness approaches the minimum.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In