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### Abstract

The dissertation investigates the phenomenon of wind induced vibration of bridge cables under varying meteorological conditions. A twin research approach is adopted, where wind tunnel investigation of full-scale bridge cable section models is paralleled with theoretical modelling.

A literature review on bridge cable vibration mechanisms under the three surface states possibly achieved by cables, i.e. dry, wet and iced, was first undertaken. The study helped to systematize the understanding of the excitation phenomena occurring in the different climatic conditions, based on results of full-scale monitoring, wind tunnel testing and theoretical modelling.

An extensive wind tunnel test campaign was then undertaken in order to further understand the onset conditions and characteristics of instability in the different climatic conditions described in the literature. Tests were separated into two different categories, i.e. static and passive-dynamic.

Static wind tunnel tests were performed in dry surface conditions, for varying Reynolds number, turbulence intensity, cable-wind angle, and angleof- attack. It was understood that dry instability is very sensitive to microscopic imperfections of the cable surface, such as deviations from the nominal shape of the external HDPE tubing or alterations of its inherent surface roughness. It was in fact observed that in the critical Reynolds number range, while the drag coefficient is consistent with changes in the angle-of-attack, the lift coefficient exhibits marked variations. This variation is sufficient to generate negative quasi-steady aerodynamic damping, and thus to potentialy lead to galloping instability.

Passive dynamic wind tunnel tests were subsequently undertaken for a cable section model of the same type as the one tested in static conditions. Tests were undertaken at a critical cable-wind angle for the occurrence of dry inclined galloping, for varying Reynolds numbers and angles-of-attack. As confirmation of the findings from the static tests, it was observed that the dynamic response of the cable section, i.e. in terms of peak-to-peak amplitudes and aerodynamic damping, changes consistently with Reynolds number, for the tested wind angles-of-attack. In fact, for selected angles-of-attack, the response was stable thoughout the whole tested range of Reynolds number, while for other angles, negative aerodynamic damping, accompanied by large amplitude peak to peak amplitudes, occurred. This latter behaviour was likely to be associated to dry inclined galloping.

Passive dynamic wind tunnel tests were finally undertaken in presence of rain, using the same cable model as adopted in the dry state. The tests served to improve the current understanding of the phenomenon of rainwind induced vibration. Test results showed that when the a critical surface tension is achieved for the cable sheating, an oscillating lower and upper water rivulet form on its surface. The angular oscillation of the rivulets contribute to amplify the vertical vibration of the cable, which becomes large in amplitude and is accompanied by negative aerodynamic damping. On the other hand, when the surface tension of the cable is too low a steady upper and lower non-coherent water rivulets form. These are not sufficient for the excitation to get started, independently of the cable mass. The cable model was in fact manifestly stable and exhibited positive aerodynamic damping throughout the whole range of tested Reynolds number, being accompanied by limited peak-to-peak amplitude.

A generalized quasi-steady 3 DOF analytical model for the prediction of the aerodynamic instability of a slender prism with generic cross section, i.e. either bluff or streamlined, immersed in unsteady wind flow, and characterized by a general spatial orientation with respect to the wind direction, was finally developed. The model accounted for variation of the force coefficients, i.e. drag, lift, and moment, with Reynolds number based on the relative flow velocity, with relative angle-of-attack, and relative cable-wind angle. The aerodynamic forces acting on the structure were linearized about zero structural velocities, structural rotation and about the steady component of the total wind velocity. Based on the analytical solution of the eigenvalue problem, by applying the Routh-Hurwitz criterion, an expression of the minimum structural damping and structural stiffness required to prevent aerodynamic instabilities of galloping- and static divergence-type respectively are given.

A literature review on bridge cable vibration mechanisms under the three surface states possibly achieved by cables, i.e. dry, wet and iced, was first undertaken. The study helped to systematize the understanding of the excitation phenomena occurring in the different climatic conditions, based on results of full-scale monitoring, wind tunnel testing and theoretical modelling.

An extensive wind tunnel test campaign was then undertaken in order to further understand the onset conditions and characteristics of instability in the different climatic conditions described in the literature. Tests were separated into two different categories, i.e. static and passive-dynamic.

Static wind tunnel tests were performed in dry surface conditions, for varying Reynolds number, turbulence intensity, cable-wind angle, and angleof- attack. It was understood that dry instability is very sensitive to microscopic imperfections of the cable surface, such as deviations from the nominal shape of the external HDPE tubing or alterations of its inherent surface roughness. It was in fact observed that in the critical Reynolds number range, while the drag coefficient is consistent with changes in the angle-of-attack, the lift coefficient exhibits marked variations. This variation is sufficient to generate negative quasi-steady aerodynamic damping, and thus to potentialy lead to galloping instability.

Passive dynamic wind tunnel tests were subsequently undertaken for a cable section model of the same type as the one tested in static conditions. Tests were undertaken at a critical cable-wind angle for the occurrence of dry inclined galloping, for varying Reynolds numbers and angles-of-attack. As confirmation of the findings from the static tests, it was observed that the dynamic response of the cable section, i.e. in terms of peak-to-peak amplitudes and aerodynamic damping, changes consistently with Reynolds number, for the tested wind angles-of-attack. In fact, for selected angles-of-attack, the response was stable thoughout the whole tested range of Reynolds number, while for other angles, negative aerodynamic damping, accompanied by large amplitude peak to peak amplitudes, occurred. This latter behaviour was likely to be associated to dry inclined galloping.

Passive dynamic wind tunnel tests were finally undertaken in presence of rain, using the same cable model as adopted in the dry state. The tests served to improve the current understanding of the phenomenon of rainwind induced vibration. Test results showed that when the a critical surface tension is achieved for the cable sheating, an oscillating lower and upper water rivulet form on its surface. The angular oscillation of the rivulets contribute to amplify the vertical vibration of the cable, which becomes large in amplitude and is accompanied by negative aerodynamic damping. On the other hand, when the surface tension of the cable is too low a steady upper and lower non-coherent water rivulets form. These are not sufficient for the excitation to get started, independently of the cable mass. The cable model was in fact manifestly stable and exhibited positive aerodynamic damping throughout the whole range of tested Reynolds number, being accompanied by limited peak-to-peak amplitude.

A generalized quasi-steady 3 DOF analytical model for the prediction of the aerodynamic instability of a slender prism with generic cross section, i.e. either bluff or streamlined, immersed in unsteady wind flow, and characterized by a general spatial orientation with respect to the wind direction, was finally developed. The model accounted for variation of the force coefficients, i.e. drag, lift, and moment, with Reynolds number based on the relative flow velocity, with relative angle-of-attack, and relative cable-wind angle. The aerodynamic forces acting on the structure were linearized about zero structural velocities, structural rotation and about the steady component of the total wind velocity. Based on the analytical solution of the eigenvalue problem, by applying the Routh-Hurwitz criterion, an expression of the minimum structural damping and structural stiffness required to prevent aerodynamic instabilities of galloping- and static divergence-type respectively are given.

Original language | English |
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Publisher | DTU Tryk |
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Number of pages | 206 |

Publication status | Published - 2014 |

## Projects

- 1 Finished

## Understanding of bridge cable vibration mechanisms under varying meteorological conditions

Matteoni, G., Georgakis, C. T., Koss, H., Fischer, G., Jakobsen, J. B., Macdonald, J. H. G., Arentoft, M. & Ricciardelli, F.

01/05/2010 → 23/06/2014

Project: PhD