Skip to main content
SpringerLink
Log in

Torsional asymmetry in suspension bridge systems

  • Published:
Applications of Mathematics Aims and scope Submit manuscript

Abstract

In this paper a dynamic linear model of suspension bridge center spans is formulated and three different ways of fixing the main cables are studied. The model describes vertical and torsional oscillations of the deck under the action of lateral wind. The mutual interactions of main cables, center span, and hangers are analyzed. Three variational evolutions are analyzed. The variational equations correspond to the way how the main cables are fixed. The existence, uniqueness, and continuous dependence on data are proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N.U. Ahmed, H. Harbi: Mathematical analysis of dynamic models of suspension bridges. SIAM J. Appl. Math. 58 (1998), 853–874.

    Article  MathSciNet  MATH  Google Scholar 

  2. Y. An: Nonlinear perturbations of a coupled system of steady state suspension bridge equations. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 51 (2002), 1285–1292.

    Article  MATH  Google Scholar 

  3. Y. An, C. Zhong: Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load. J. Math. Anal. Appl. 279 (2003), 569–579.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Berkovits, P. Drábek, H. Leinfelder, V. Mustonen, G. Tajčová: Time-periodic oscillations in suspension bridges: existence of unique solutions. Nonlinear Anal., Real World Appl. 1 (2000), 345–362.

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. S. Choi, K. C. Jen, P. J. McKenna: The structure of the solution set for periodic oscillations in a suspension bridge model. IMA J. Appl. Math. 47 (1991), 283–306.

    Article  MathSciNet  MATH  Google Scholar 

  6. Z. Ding: Multiple periodic oscillations in a nonlinear suspension bridge system. J. Math. Anal. Appl. 269 (2002), 726–746.

    Article  MathSciNet  MATH  Google Scholar 

  7. Z. Ding: Nonlinear periodic oscillations in a suspension bridge system under periodic external aerodynamic forces. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 49 (2002), 1079–1097.

    Article  MATH  Google Scholar 

  8. P. Drábek, H. Leinfelder, G. Tajčová: Coupled string-beam equations as a model of suspension bridges. Appl. Math., Praha 44 (1999), 97–142.

    Article  MATH  Google Scholar 

  9. R. E. Edwards: Functional Analysis. Theory and Applications. Holt Rinehart and Winston, New York, 1965.

    MATH  Google Scholar 

  10. A. Fonda, Z. Schneider, F. Zanolin: Periodic oscillations for a nonlinear suspension bridge model. J. Comput. Appl. Math. 52 (1994), 113–140.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Gajewski, K. Gröger, K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Mathematische Lehrbücher und Monographien. II. Abteilung. Band 38, Akademie-Verlag, Berlin, 1974. (In German.)

    MATH  Google Scholar 

  12. J. Glover, A. C. Lazer, P. J. McKenna: Existence and stability of large scale nonlinear oscillations in suspension bridges. Z. Angew. Math. Phys. 40 (1989), 172–200.

    Article  MathSciNet  MATH  Google Scholar 

  13. G. Holubová, A. Matas: Initial-boundary value problem for the nonlinear string-beam system. J. Math. Anal. Appl. 288 (2003), 784–802.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. C. Lazer, P. J. McKenna: Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. SIAM Rev. 32 (1990), 537–578.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Malík: Generalized nonlinear models of suspension bridges. J. Math. Anal. Appl. 324 (2006), 1288–1296.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Malík: Nonlinear models of suspension bridges. J. Math. Anal. Appl. 321 (2006), 828–850.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Malík: Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge. J. Sound Vib. 332 (2013), 3772–3789.

    Article  Google Scholar 

  18. P. J. McKenna: Large torsional oscillations in suspension bridges revisited: fixing an old approximation. Am. Math. Mon. 106 (1999), 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  19. P. J. McKenna, W. Walter: Nonlinear oscillations in a suspension bridge. Arch. Ration. Mech. Anal. 98 (1987), 167–177.

    Article  MathSciNet  MATH  Google Scholar 

  20. R. H. Plaut: Snap loads and torsional oscillations of the original Tacoma Narrows Bridge. J. Sound Vib. 309 (2008), 613–636.

    Article  Google Scholar 

  21. R. H. Plaut, F. M. Davis: Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges. J. Sound Vib. 307 (2007), 894–905.

    Article  Google Scholar 

  22. A. Pugsley: The Theory of Suspension Bridges. Edward Arnold, London, 1968.

    Google Scholar 

  23. R. H. Scanlan: The action of flexible bridges under wind, I: Flutter theory. J. Sound Vib. 60 (1978), 187–199.

    Article  MATH  Google Scholar 

  24. R. H. Scanlan: The action of flexible bridges under wind, II: Buffeting theory. J. Sound Vib. 60 (1978), 201–211.

    Article  MATH  Google Scholar 

  25. E. Simiu, R. H. Scanlan: Wind Effects on Structures: Fundamentals and Applications to Design. Wiley, New York, 1996.

    Google Scholar 

  26. G. Tajčová: Mathematical models of suspension bridges. Appl. Math., Praha 42 (1997), 451–480.

    Article  MATH  Google Scholar 

  27. E. Zeidler: Nonlinear Functional Analysis and Its Applications. II/A: Linear Monotone Operators. Springer, New York, 1990.

    Book  MATH  Google Scholar 

  28. http://www.youtube.com/watch?v=3mclp9QmCGs.

  29. http://www.youtube.com/watch?v=j-zczJXSxnw.

Download references

Author information

Authors and Affiliations

  1. Institute of Geonics, The Czech Academy of Sciences, Studentská 1768, 708 00, Ostrava-Poruba, Czech Republic

    Josef Malík

Authors
  1. Josef Malík
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Josef Malík.

Additional information

The paper was prepared in connection with project Institute of Clean Technologies, areg. no. CZ.1.05/2.1.00/03.0082 supported by Research and Development for Innovations Operational Program financed by Structural Funds of European Union and from the means of the state budget of the Czech Republic.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Malík, J. Torsional asymmetry in suspension bridge systems. Appl Math 60, 677–701 (2015). https://doi.org/10.1007/s10492-015-0117-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10492-015-0117-3

Keywords

MSC 2010

Search

Navigation