Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 231726, 11 pages
http://dx.doi.org/10.1155/2014/231726
Research Article

The Static WKB Solution to Catenary Problems with Large Sag and Bending Stiffness

Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei City 10607, Taiwan

Received 30 June 2014; Accepted 11 September 2014; Published 28 September 2014

Academic Editor: Bruno Briseghella

Copyright © 2014 Yuhung Hsu and Chanping Pan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. M. Irvine, Cable Structures, Dover Publications, 1992.
  2. J. J. Burgess, “Bending stiffness in a simulation of undersea cable deployment,” International Journal of Offshore and Polar Engineering, vol. 3, no. 3, pp. 197–204, 1993. View at Google Scholar · View at Scopus
  3. E. J. Hinch, Perturbation Methods, Cambridge University Press, Cambridge, UK, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods, Springer, Berlin, Germany, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, NY, USA, 2011.
  6. M. S. Triantafyllou and G. S. Triantafyllou, “The paradox of the hanging string: an explanation using singular perturbations,” Journal of Sound and Vibration, vol. 148, no. 2, pp. 343–351, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. P. Wolfe, “The effect of bending stiffness on inextensible cables,” International Journal of Engineering Science, vol. 30, no. 9, pp. 1187–1192, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. M. Irvine, “Local bending stresses in cables,” International Journal of Offshore and Polar Engineering, vol. 3, no. 3, pp. 172–175, 1993. View at Google Scholar · View at Scopus
  9. D. M. Stump and W. B. Fraser, “Bending boundary layers in a moving strip,” Nonlinear Dynamics, vol. 21, no. 1, pp. 55–70, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. D. M. Stump and G. H. M. van der Heijden, “Matched asymptotic expansions for bent and twisted rods: applications for cable and pipeline laying,” Journal of Engineering Mathematics, vol. 38, no. 1, pp. 13–31, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. V. Denoël and E. Detournay, “Multiple scales solution for a beam with a small bending stiffness,” Journal of Engineering Mechanics, vol. 136, no. 1, Article ID 006001QEM, pp. 69–77, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. V. Denoël and T. Canor, “Patching asymptotics solution of a cable with a small bending stiffness,” Journal of Structural Engineering, vol. 139, no. 2, pp. 180–187, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. A. B. Mehrabi and H. Tabatabai, “Unified finite difference formulation for free vibration of cables,” Journal of Structural Engineering, vol. 124, no. 11, pp. 1313–1322, 1998. View at Publisher · View at Google Scholar · View at Scopus