0
TECHNICAL PAPERS

Equilibrium Solutions and Existence for Traveling, Arbitrarily Sagged Elastic Cables

[+] Author and Article Information
A. C. J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University, Edwardsville, IL 62034-1805

C. D. Mote

Office of the President, Main Administration Building, University of Maryland, College Park, MD 20742

J. Appl. Mech 67(1), 148-154 (Aug 10, 1999) (7 pages) doi:10.1115/1.321159 History: Received October 16, 1998; Revised August 10, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Rohrs,  J. H., 1851, “On the Oscillations of a Suspension Cable,” Trans. Cambridge Philos. Soc., 9, pp. 379–398.
Routh E. J., 1884, The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, 4th Ed., MacMillan and Co., London.
Pugsley,  A. G., 1949, “On Natural Frequencies of Suspension Chain,” Q. J. Mech. Appl. Math., 2, pp. 412–418.
Saxon,  D. S., and Cahn,  A. S., 1953, “Modes of Vibration of a Suspended Chain,” Q. J. Mech. Appl. Math., 6, pp. 273–285.
Simpson,  A., 1966, “Determination of the Inplane Natural Frequencies of Multispan Transmission Lines by a Transfer Matrix Method,” Proc. Inst. Electr. Eng., 113, pp. 870–878.
Irvine,  H. M., and Caughey,  T. K., 1974, “The Linear Theory of Free Vibrations of a Suspended Cable,” Proc. R. Soc. London, Ser. A, 341A, pp. 299–315.
Hagedorn,  P., and Schafer,  B., 1980, “On Nonlinear Free Vibrations of an Elastic Cable,” Int. J. Non-Linear Mech., 15, pp. 333–340.
Luongo,  A., Rega,  G., and Vestroni,  F., 1984, “Planar Non-linear Free Vibrations of an Elastic Cable,” Int. J. Non-Linear Mech., 19, pp. 39–52.
Perkins,  N. C., 1992, “Modal Interactions in the Nonlinear Response of Elastic Cables Under Parametric/External Excitation,” Int. J. Non-Linear Mech., 27, No. 2, pp. 233–250.
Simpson,  A., 1972, “On the Oscillatory Motions of Translating Elastic Cables,” J. Sound Vib., 20, No. 2, pp. 177–189.
Triantafyllou,  M. S., 1985, “The Dynamics of Translating Cables,” J. Sound Vib., 103, No. 2, pp. 171–182.
Perkins,  N. C., and Mote,  C. D., 1987, “Three-Dimensional Vibration of Traveling Elastic Cables,” J. Sound Vib., 114, No. 3, pp. 325–340.
Perkins,  N. C., and Mote,  C. D., 1989, “Theoretical and Experimental Stability of Two Translating Cable Equilibria,” J. Sound Vib., 128, No. 3, pp. 397–410.
Dickey,  R. W., 1969, “The Nonlinear String Under a Vertical Force,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 17, No. 1, pp. 172–178.
Antman,  S. S., 1979, “Multiple Equilibrium States of Nonlinear Elastic Strings,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 37, No. 3, pp. 588–604.
O’Reilly,  O. M., and Varadi,  P., 1995, “Elastic Equilibria of Translating Cables,” Acta Mech., 108, pp. 189–206.
Healey,  T. J., and Papadopoulos,  J. N., 1990, “Steady Axial Motions of Strings,” ASME J. Appl. Mech., 57, pp. 785–787.
O’Reilly,  O. M., 1996, “Steady Motions of a Drawn Cable,” ASME J. Appl. Mech., 63, pp. 180–189.
Irvine, H. M., 1974, Cable Structures, The MIT Press, Cambridge, MA.
Yu,  P., Wong,  P. S., and Kaempffer,  F., 1995, “Tension of Conductor Under Concentrated Loads,” ASME J. Appl. Mech., 62, pp. 802–809.
Luo,  A. C. J., Han,  R. P. S., Tyc,  G., Modi,  V. J., and Misra,  A. K., 1996, “Analytical Vibration and Resonant Motion of a Stretched, Spinning, Nonlinear Tether,” AIAA J. Guidance, Control Dyn., 19, No. 5, pp. 1162–1171.

Figures

Grahic Jump Location
Longitudinal (upper) and transverse (lower) displacements of a sagged elastic cable at equilibrium (xB=0.8) under its own weight (qy=−1) and various longitudinal loads for c=10:cp=740.87 and c0=0
Grahic Jump Location
Equilibrium and deformation of a traveling sagged cable under arbitrary loading
Grahic Jump Location
Longitudinal (upper) and transverse (lower) equilibrium displacements of a straight elastic cable under qx=0 and qy=−1 for c=10:cp=740.87 and c0=0
Grahic Jump Location
Displacement (upper) and tension (lower) versus traveling speed of a sagged elastic cable (xB=0.8) for qx=qy=−1 with various transverse loads: cp=740.87 and c0=0
Grahic Jump Location
Multiple equilibrium configurations (upper) and tension distributions (lower) of a sagged elastic cable (xB=0.8) under its own weight (qy=−1) and various longitudinal loads for c=1:cp=740.87 and c0=0
Grahic Jump Location
Displacement (upper) and tension (lower) versus chord ratio of a sagged elastic cable with various transverse loads for c=10:cp=740.87 and c0=0
Grahic Jump Location
Equilibrium configuration (upper) and tension-jump from segment 1 to segment 2 (lower) of a sagged elastic cable (xB=0.8) under its own weight (qy=−1) and a concentrated force (Fy=−2) for c=10:cp=740.87 and c0=0

Tables

Errata

Discussions

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