Keywords: cable-stayed bridges, wind-rain induced vibration, vortex-induced vibration, Cosserat methods.

A review will be given of the application of Cosserat approximations with emphasis on the dynamical behaviour of undersea marine risers responding to vortex-induced vibration and the motion of cable-stayed bridges that are excited to vibrate in light-wind-rain conditions. In the latter the motion of the cable section is coupled with the motion of a mobile rivulet on its surface via aerodynamic fluid-structure interactions. These complex interactions are modelled in two distinct ways and the resulting cable motions compared. The first employs an approximation that permits the use of data extrapolated from wind-tunnel measurements. The second approaches the aerodynamic interaction in terms of a sub-critical vortex description. Such mathematical modelling offers a useful means to understand how marine risers respond to under-sea currents and how rain-wind-induced vibrations of stay cables can arise and persist in terms of more realistic approaches than have been considered before in the literature.

Based on the early work of the Cosserat brothers and others, the mathematical theory of Cosserat media is now well established. The essential idea is to exploit the geometry of the structure to reduce the dimension of its configuration space. Cosserat rod models can be used to determine the spectrum of linearized excitations about an equilibrium configuration under purely static gravitational forces [1]. In many engineering applications, where free vibration is dominated by a single harmonic mode, such a model can be used to determine the nature of forced vibrations due to the environment.

Long stay cables are important components of cable-stayed bridges and, due to their large flexibility and small structural damping, are prone to vibration induced by motion of their supports and/or aerodynamic forces such as wind and rain loadings. Under the simultaneous occurrence of light-to-moderate wind and rain, large amplitude vibrations of stay cables have been observed in a number of cable-stayed bridges worldwide  [2,3,4,5]. Rain rivulets snaking along the cables alter their aerodynamic profile and thus affect the aerodynamic forces on the structure. A cable section model is employed to investigate this phenomenon. Two recent methods of modelling the fluid-structure interaction [6] are discussed. The wind-tunnel approach involves measurements of the forces and torques on a static cylinder with an adhered solid rivulet. Careful attention is paid to the range of validity of this approach in dynamic contexts. It is noted that, for sufficiently small motions, the air flow outside of the moving cable section should be similar to that in the static case. Linearization of the section model is therefore mandatory in this context. Since the Reynolds number associated with the system is in the sub-critical range dynamic vortex shedding should play a role. This is investigated using a dynamic point-vortex model to represent the air flow field where the aerodynamic forces and torques on the structure are obtained from pressure integrals. A method, recently presented in [7], for applying the model to more that one cable section is summarized.

1

R. W. Tucker and C. Wang, "An integrated model for drill-string dynamics", Journal of Sound and Vibration, 224, 123-165, 1999. doi:10.1006/jsvi.1999.2169

2

Y. Hikami and N. Shiraishi, "Rain-wind induced vibration of cables in cable stayed bridges", Journal of Wind Engineering and Industrial Aerodynamics, 29, 409-418, 1988. doi:10.1016/0167-6105(88)90179-1

3

R. W. Poston, "Cable-stay conundrum" Civil Engineering, 68, 58-61, 1998.

4

J. H. G. Macdonald, E. L. Dagless, B. T. Thomas and C. A. Taylor "Dynamic measurements of the Second Severn Crossing", Proceedings of the Institution of Civil Engineers (Transport), 123, 241-248, 1997. doi:10.1680/itran.1997.29978

5

J. A. Main and N. P. Jones, "Full-scale measurements of stay cable vibration", Wind Engineering into the 21st Century, Larsen, Larose and Livesey (eds.), Balkeman, Rotterdam, 963-970, 1999.

6

D. A. Burton, D. Q. Cao, R. W. Tucker and C. Wang, "On the stability of stay cables under light wind and rain conditions", Journal of Sound and Vibration, to appear. doi:10.1016/j.jsv.2003.10.038

7

D. A. Burton, J. Gratus and R. W. Tucker, "Hydrodynamic forces on two moving discs", submitted to the Proceedings of The Royal Society of Edinburgh.

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