Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge

D. Cao, M. Song, W. Zhu, R. Tucker, C. H. Wang

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

The in-plane vibration of a complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of the cables and transverse vibrations of segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge are determined, and orthogonality relations of the mode shapes are established. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for various symmetrical and non-symmetrical bridge cases with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies when the bridge model is symmetrical and/or partially symmetrical, and the mode shapes tend to be more localized when the bridge model is less symmetrical. The relationships between the natural frequencies and mode shapes of the cable-stayed bridge and those of a single fixed–fixed cable and the single simply-supported deck beam are analyzed. The results, which are validated by commercial finite element software, demonstrate some complex classical resonance behavior of the cable-stayed bridge.
Original languageEnglish
Pages (from-to)5685–5714
Number of pages30
JournalJournal of Sound and Vibration
Volume331
Issue number26
Early online date28 Aug 2012
DOIs
Publication statusPublished - 17 Dec 2012

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Cable stayed bridges
cables
Natural frequencies
Cables
vibration
modal response
resonant frequencies
transverse oscillation
Towers
Partial differential equations
Numerical analysis
orthogonality
towers
partial differential equations
numerical analysis
boundary conditions
computer programs

Cite this

Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge. / Cao, D.; Song, M.; Zhu, W.; Tucker, R.; Wang, C. H.

In: Journal of Sound and Vibration, Vol. 331, No. 26, 17.12.2012, p. 5685–5714 .

Research output: Contribution to journalArticle

Cao, D. ; Song, M. ; Zhu, W. ; Tucker, R. ; Wang, C. H. / Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge. In: Journal of Sound and Vibration. 2012 ; Vol. 331, No. 26. pp. 5685–5714 .
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AB - The in-plane vibration of a complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of the cables and transverse vibrations of segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge are determined, and orthogonality relations of the mode shapes are established. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for various symmetrical and non-symmetrical bridge cases with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies when the bridge model is symmetrical and/or partially symmetrical, and the mode shapes tend to be more localized when the bridge model is less symmetrical. The relationships between the natural frequencies and mode shapes of the cable-stayed bridge and those of a single fixed–fixed cable and the single simply-supported deck beam are analyzed. The results, which are validated by commercial finite element software, demonstrate some complex classical resonance behavior of the cable-stayed bridge.

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