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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.

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Figures

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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.

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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

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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]

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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

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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.

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Fig. 6

Comparison of traditional Coulomb damping model with hysteretic Coulomb damping model

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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

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Fig. 8

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

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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.

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