The propagation of elastic waves along composite wire rope is considered. The rope is modeled as co-axial layers of cylindrically anisotropic material. Simple kinematical assumptions lead to a “rod theory” for the wire rope, consisting of three coupled one-dimensional wave equations. Solutions of these equations are found. Results for a particular aluminum conductor steel reinforced (ACSR) conductor are described in detail. The slowest mode is found to be mainly torsional and mainly nondispersive in character. The other two modes are dispersive and have small torsional components.
1.
Rawlins, C. B., 1979, “Fatigue of Overhead Conductors,” Transmission Line Reference Book: Wind-Induced Conductor Motion, Electric Power Research Institute, Palo Alto, CA, pp. 51–81.
2.
Berger
, J. R.
, Martin
, P. A.
, and McCaffery
, S. J.
, 2000
, “Time-Harmonic Torsional Waves in a Composite Cylinder With an Imperfect Interface
,” J. Acoust. Soc. Am.
, 107
, pp. 1161
–1167
.3.
Butson, G. J., Phillips, J. W., and Costello, G. A., 1980, “Stresses in Wire Rope due to Dynamic Loads Associated With Deep Shaft Hoisting Systems,” Proc. First Annual Wire Rope Symposium, Denver, CO, Engineering Extension Service, Washington State University, Pullman, WA, pp. 243–273.
4.
Costello, G. A., 1997, Theory of Wire Rope, 2nd Ed., Springer, New York.
5.
McConnell
, K. G.
, and Zemke
, W. P.
, 1982
, “A Model to Predict the Coupled Axial Torsion Properties of ACSR Electrical Conductors
,” Exp. Mech.
, 22
, pp. 237
–244
.6.
Lanteigne
, J.
, 1985
, “Theoretical Estimation of the Response of Helically Armored Cables to Tension, Torsion, and Bending
,” ASME J. Appl. Mech.
, 52
, pp. 423
–432
.7.
Sathikh
, S.
, Rajasekaran
, S.
, Jayakumar
, and Jebaraj
, C.
, 2000
, “General Thin Rod Model for Preslip Bending Response of Strand
,” J. Eng. Mech.
, 126
, pp. 132
–139
.8.
Raoof
, M.
, and Kraincanic
, I.
, 1994
, “Critical Examination of Various Approaches Used for Analysing Helical Cables
,” J. Strain Anal.
, 29
, pp. 43
–55
.9.
Samras
, R. K.
, Skop
, R. A.
, and Milburn
, D. A.
, 1974
, “An Analysis of Coupled Extensional-Torsional Oscillations in Wire Rope
,” J. Eng. Ind.
, 96
, pp. 1130
–1135
.10.
Graff, K. F., 1991, Wave Motion in Elastic Solids, Dover, New York.
11.
Cardou
, A.
, and Jolicoeur
, C.
, 1997
, “Mechanical Models of Helical Strands
,” Appl. Mech. Rev.
, 50
, pp. 1
–14
.12.
Hobbs, R. E., and Raoof, M., 1982, “Interwire Slippage and Fatigue Prediction in Stranded Cables for TLP Tethers,” Proceedings, 3rd Intl. Conf. Behavior of Offshore Structures, Hemisphere, Washington, DC, pp. 77–92.
13.
Blouin
, F.
, and Cardou
, A.
, 1989
, “A Study of Helically Reinforced Cylinders Under Axially Symmetric Loads and Application to Strand Mathematical Modelling
,” Int. J. Solids Struct.
, 25
, pp. 189
–200
.14.
Jolicoeur
, C.
, and Cardou
, A.
, 1994
, “Analytical Solution for Bending of Coaxial Orthotropic Cylinders
,” J. Eng. Mech.
, 120
, pp. 2556
–2574
.15.
Jolicoeur
, C.
, and Cardou
, A.
, 1996
, “Semicontinuous Mathematical Model for Bending of Multilayered Wire Strands
,” J. Eng. Mech.
, 122
, pp. 643
–650
.16.
Skop
, R. A.
, and Samras
, R. K.
, 1975
, “Effects of Coupled Extensional-Torsional Oscillations in Wire Rope During Ocean Salvage and Construction Operations
,” J. Eng. Ind.
, 97
, pp. 485
–492
.17.
Phillips
, J. W.
, and Costello
, G. A.
, 1977
, “Axial Impact of Twisted Wire Cables
,” ASME J. Appl. Mech.
, 44
, pp. 127
–131
.18.
Raoof
, M.
, Huang
, Y. P.
, and Pithia
, K. D.
, 1994
, “Response of Axially Preloaded Spiral Strands to Impact Loading
,” Comput. Struct.
, 51
, pp. 125
–135
.19.
Martin
, P. A.
, 1992
, “Boundary Integral Equations for the Scattering of Elastic Waves by Elastic Inclusions With Thin Interface Layers
,” J. Nondestruct. Eval.
, 11
, pp. 167
–174
.20.
Ting
, T. C. T.
, 1996
, “Pressuring, Shearing, Torsion and Extension of a Circular Tube or Bar of Cylindrically Anisotropic Material
,” Proc. R. Soc. London, Ser. A
, 452
, pp. 2397
–2421
.21.
Martin
, P. A.
, and Berger
, J. R.
, 2001
, “Waves in Wood: Free Vibrations of a Wooden Pole
,” J. Mech. Phys. Solids
, 49
, pp. 1155
–1178
.22.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University Press, Oxford, UK.
23.
Jones, R. M., 1999, Mechanics of Composite Materials, 2nd Ed., Taylor & Francis, Philadelphia, PA.
24.
Doocy, E. S., and Hard, A. R., 1979, “Introduction,” Transmission Line Reference Book: Wind-Induced Conductor Motion, Electric Power Research Institute, Palo Alto, CA, pp. 1–50.
25.
Young, W. C., 1989, Roark’s Formulas for Stress and Strain, 6th Ed., McGraw-Hill, New York.
26.
Abramowitz, M., and Stegun, I. A., eds., 1965, Handbook of Mathematical Functions, Dover, New York.
27.
Bostro¨m
, A.
, 2000
, “On Wave Equations for Elastic Rods
,” Z. Angew. Math. Mech.
, 80
, pp. 245
–251
.28.
Labrosse
, M.
, Nawrocki
, A.
, and Conway
, T.
, 2000
, “Frictional Dissipation in Axially Loaded Simple Straight Strands
,” J. Eng. Mech.
, 126
, pp. 641
–646
.29.
Fang
, J.
, and Lyons
, G. J.
, 1996
, “Structural Damping of Tensioned Pipes With Reference to Cables
,” J. Sound Vib.
, 193
, pp. 891
–907
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