Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A method to evaluate the frequencies of free transversal vibrations in self-anchored cable-stayed bridges

  • Monaco, Pietro (Civil and Environmental Engineering Department, Polytechnic of Bari) ;
  • Fiore, Alessandra (Civil and Environmental Engineering Department, Polytechnic of Bari)
  • Received : 2003.11.07
  • Accepted : 2005.03.25
  • Published : 2005.04.25
⟨ Previous Next ⟩

Abstract

The objective of this paper is setting out, for a cable-stayed bridge with a curtain suspension, a method to determine the modes of vibration of the structure. The system of differential equations governing the vibrations of the bridge, derived by means of a variational formulation in a nonlinear field, is reported in Appendix C. The whole analysis results from the application of Hamilton's principle, using the expressions of potential and kinetic energies and of the virtual work made by viscous damping forces of the various parts of the bridge (Monaco and Fiore 2003). This paper focuses on the equation concerning the transversal motion of the girder of the cable-stayed bridge and in particular on its final form obtained, restrictedly to the linear case, neglecting some quantities affecting the solution in a non-remarkable way. In the hypotheses of normal mode of vibration and of steady-state, we propose the resolution of this equation by a particular method based on a numerical approach. Respecting the boundary conditions, we derive, for each mode of vibration, the corresponding frequency, both natural and damped, the shape-function of the girder axis and the exponential function governing the variability of motion amplitude in time. Finally the results so obtained are compared with those deriving from the dynamic analysis performed by a finite elements calculation program.

Keywords

References

  1. Abdel-Ghaffar, A. M. (1976), Dynamic Analyses of Suspension Bridge Structures, California Institute of Tecnology-Earthquake Engineering Research Laboratory.
  2. Abdel-Ghaffar, A. M. (1991), "Cable-stayed bridges under seismic action", Cable-stayed Bridges-Recent Developments and their Future, Proceedings of the Seminar, Yokohama, Japan, 10-11 December 1991, edited by Ito, M., et al., Elsevier Science Publishers B.V., Amsterdam.
  3. Abdel-Ghaffar, Ahmed, M. and R., Lawrence, I. (1982), "Multiple-support excitations of suspension bridges", J. Eng. Mech., ASCE, 108(EM2).
  4. Albi Marini, A., Augenti, N., Raithel, A. (1979), Introduzione alla Dinamica dei ponti strallati, Atti dell'Istituto di Costruzioni di Ponti, Facolta di Ingegneria della Universita di Napoli, Italy.
  5. Bartoli, G., Ricciardelli, F., Sepe, V. (2004), WINDERFUL Wind and INfrastructures: Dominating Eolian Risk For Utilities and Lifelines, Firenze University Press, Firenze (Italy).
  6. Bartoli, G., Cluni, F., Gusella, V., Procino, L. (2004), "Dinamica del cavo sotto l'azione del vento: analisi sperimentale in galleria del vento", Proceedings of IN-VENTO-2004 $8^{\circ}$ Convegno Nazionale di Ingegneria del Vento, Reggio Calabria (Italy), Giugno.
  7. De Miranda, F., Grimaldi, A., Maceri, F., Como, M. (1979), Basic Problems in Long Span Cable Stayed Bridges, University of Calabria, Italy.
  8. Gimsing, N. J. Technical University of Denmark (1983), Clable Supported Bridges, John Wiley & Sons, New York.
  9. Greenspan, D. and Casulli, V. (1988), Numerical Analysis for applied mathematics, Science, and Engineering, Addison-Wesley Publishing Company, New York.
  10. Ito, M., Fujino, Y., Miyata, T. and Narita, N. (1991), Cable-stayed Bridges-Recent Developments and Their Future, Elsevier Science Publishers B.V., Amsterdam.
  11. Leonhardt, F. and Zellner, W. (1970), Cable-Stayed Bridges: Report on Latest Developments, Canadian Structural Engineering Conference, Toronto.
  12. Leonhardt, F. and Zellner, W. (1991), "Past, present and future of cable-stayed bridges", Cable-stayed Bridges- Recent Developments and their Future, Proceedings of the Seminar, Yokohama, Japan, 10-11 December 1991, edited by Ito, M., et al., Elsevier Science Publishers B.V., Amsterdam.
  13. Monaco, P. and Fiore, A. (2003), "Free transversal vibrations in self-anchored cable-stayed bridges with a curtain suspension", Proceedings of the Fifth International Symposium on Cable Dynamics, Santa Margherita Ligure (Italy), September.
  14. Monaco, P. (1995), I ponti strallati. 1a e 2a parte, Rassegna tecnica pugliese 1/2.1995, Ass. Reg. Ing. e Arch. di Puglia, Italy.
  15. Salvatori, L., Spinelli, P. (2004), "Influenza delle non-linearità strutturali sulla risposta dei ponti sospesi all'azione eolica: simulazioni numeriche su strutture semplificate", Proceedings of IN-VENTO-2004 $8^{\circ}$ Convegno Nazionale di Ingegneria del Vento, Reggio Calabria (Italy), Giugno.
  16. Thomson, W. T. (1965), Theory of Vibration and applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
  17. Warburton (1976), The Dynamical Behaviour of Structures, Pergamon Press Ltd, Headington Hill Hall, Oxford OX3 0BW, England.
  18. Wells, D. A. (1984), Collana SCHAUM. Teoria e problemi di Dinamica Lagrangiana, Etas Libri, Milano (Italy).

Cited by

  1. Enhanced finite element modeling for geometric non-linear analysis of cable-supported structures vol.22, pp.5, 2006, https://doi.org/10.12989/sem.2006.22.5.575
  2. Computational method for determining the mechanical tension in a self-anchored suspension bridge during construction and its engineering application vol.34, pp.5, 2017, https://doi.org/10.1108/EC-03-2016-0107
  3. An approximate solution for the rheological behavior of non-homogeneous structures changing the structural system during the construction process vol.46, 2013, https://doi.org/10.1016/j.engstruct.2012.08.014
  4. POD-based representation of the alongwind Equivalent Static Force for long-span bridges vol.12, pp.3, 2005, https://doi.org/10.12989/was.2009.12.3.239