Advertisement

Archive of Applied Mechanics

, Volume 66, Issue 5, pp 315–325 | Cite as

Dynamic stiffness matrix of a general cable element

  • A. Sarkar
  • C. S. Manohar
Originals

Summary

A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.

Key words

Dynamic stiffness extensible cables earthquake loads 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Clough, R. W.;Penzien, J.: Dynamics of structures. Tokyo: McGraw-Hill Kogakusha 1992Google Scholar
  2. 2.
    Irvine, M.: Cable structures. New York: Dover Publications 1981Google Scholar
  3. 3.
    Iyengar, R. N.;Rao, G. V.: Free vibrations and parametric instability of a laterally loaded cable. J. Sound Vib. 127 (1988) 231–243Google Scholar
  4. 4.
    Lee, S. Y.;Kuo, Y. H.: Exact solutions for the analysis of general elastically restrained nonuniform beams. Trans. ASME/J. Appl. Mech. 59 (1992) 205–212Google Scholar
  5. 5.
    Manohar, C. S.;Keane, A. J.: Statistics of energy flows in spring coupled one dimensional subsystems. Phil. Trans. R. Soc. Lond. A 346 (1994) 525–542Google Scholar
  6. 6.
    Migliore, H.;Webster, R. L.: Current methods for analyzing cable response 1979 to the present. Shock Vib. Dig. 14 (1982) 19–24Google Scholar
  7. 7.
    Paz, M.: Structural dynamics. New Delhi: CBS Publishers 1985Google Scholar
  8. 8.
    Rao, G. V.: Vibration of cables under deterministic and random excitations. PhD thesis, Department of civil engineering, Indian Institute of Science, 1989Google Scholar
  9. 9.
    Rao, G. V.;Iyengar, R. N.: Seismic response of a long span cable. Earthquake Eng. Struct. Dyn. 20 (1991) 243–258Google Scholar
  10. 10.
    Starossek, U.: Dynamic stiffness matrix of sagging cable. J. Eng. Mech. 117 (1991) 2815–2829Google Scholar
  11. 11.
    Triantfyllou, M. S.: Dynamics of cables, towing cables and mooring systems. Shock Vib. Dig. 23 (1991) 3–8Google Scholar
  12. 12.
    Velestos, A. S.;Darbre, G. R.: Dynamic stiffness of parabolic cables. Earthquake Eng. Struct. Dyn. 11 (1983) 367–401Google Scholar
  13. 13.
    Vinogradov, O. G.; Pivovarov, I.: The phenomenon of damping in stranded cables. In: Proc. 26th SDM Conf., Orlando, Florida, USA, 1985 pp. 232–237 AIAAGoogle Scholar
  14. 14.
    Wickert, J. A.;Mote, C. D. Jr.: Current research on the vibration and stability of axially moving materials. Shock Vib. Dig. 20 (1988) 3–13Google Scholar
  15. 15.
    Yang, B.: Transfer functions of constrained/combined one-dimensional continuous dynamic systems. J. Sound Vib. 156 (1992) 425–443Google Scholar
  16. 16.
    Yang, B.: Distributed transfer function analysis of complex distributed parameter systems. Trans. ASME Appl. Mech. 61 (1994) 84–92Google Scholar
  17. 17.
    Zerva, A.: Effect of spatial variability and propagation of seismic ground motions on the response of multiply supported structures. Probabilistic Eng. Mech. 6 (1991) 212–221Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • A. Sarkar
    • 1
  • C. S. Manohar
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations