Amplitudes of vibration for a parametrically excited inclined cable close to two-to-one internal resonance

MR Marsico, V Tzanov, DJ Wagg, SA Neild, B Krauskopf

Research output: Working paper

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This paper presents a study of how different vibration modes contribute to the dynamics of an inclined cable that is parametrically excited close to a 2:1 internal resonance. The behaviour of inclined cables is important for the design and analysis of cable-stay bridges. In this work the cable vibrations are modelled by a four-mode model. This type of model has been used previously to study the onset of cable sway motion caused by internal resonances which occur due to the nonlinear modal coupling terms. A bifurcation study is carried out with numerical continuation techniques applied to the scaled and averaged modal equations. As part of this analysis, the amplitudes of the cable vibration response to support inputs is computed. These theoretical results are compared with experimental measurements taken from a 5.4 m long inclined cable with a vertical support input at the lower end. In general this comparison shows a very high level of agreement.
Original languageEnglish
Publication statusPublished - Jul 2010

Bibliographical note

Sponsorship: The authors would like to acknowledge the support from the Engineering and Physical Sciences Research Council (EPSRC) of the research of M.R. Marsico and V. Tzanov under grant EP/F030711/1. We would like to thank
Dr. M.S. Dietz for assisting with the experimental set-up, and the technicians
at the Earthquake Engineering Laboratory for their assistance. We are also grateful to Dr J.H.G. Macdonald who gave us feedback on the experimental results and the manuscript.


  • bifurcation analysis
  • cable vibration
  • sway motion
  • modal interaction
  • internal resonance


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