Investigation of the Dynamic Performance of a Cable-Stayed Footbridge

The developments in conceptual design, material technology and efficient construction techniques enabled the creation of longer, lighter, slender and stylish Cable-Stayed Foot Bridges (CSFB). Hence, modern CSFB can be characterized by interacting phenomena like cable nonlinearities, deck dynamic instability and deck lateral oscillations due to pedestrian walking. These phenomena, if intertwined, may bring these structures out of service or to failure. In view of a better performance, additional damping can be provided by passive dampers. However, amplitude dependent behaviour of dampers and slip in connections can make them effective only above a threshold amplitude. Hence, due to high uncertainties in the complex CSFB-damper system, usually, dynamic tests are performed to investigate the performance of the overall system. In this thesis, the effectiveness of the passive vibration reduction system in a complex cablestayed footbridge characterised by two curved decks was investigated. The amplitude dependent behaviour was found both with the output-only ambient vibration and free decay tests. In order to clarify these outcomes, modal quantities were calculated instantaneously,based on time-frequency identification techniques. A thorough analysis of dynamic response signals revealed that the structure with dampers actually behaved like a threshold system: i) for low vibration levels the dampers were still, so that they performed as constraints that stiffened the structure; ii) for high vibration levels, the dampers became fully working. Moreover, a deckcable interaction between one of the longest cables and the first global mode was detected. Initially, the modal properties estimated from the dynamic tests did not match those of the numerical model. In order to have a robust FE model capable to simulate the actual behaviour of the footbridge, model updating was performed. The sensitivity-based model updating techniques and Powell's Dog-Leg method of optimisation based on the Trust-Region approach were used. The final updated model showed a considerable reduction in the percentage error of frequencies. The updated model was able to reproduce the response of the footbridge under actual wind conditions. The revealed cable-deck interaction phenomenon was a motivation to investigate in depth the dynamics of long stay cables. Therefore, efforts were made towards the identification of the nonlinear behaviour of stay cables from measured response data. In view of the fact that actual measured data contained the response of a MDoF system, the first step in this direction was to investigate the feasibility of the nonlinear identification method, i.e. a nonparametric approach applied to a SDoF cable system. The results revealed a good fitting between identified and numerical data, where only a cubic type of nonlinearity was identified. Moreover, an increase of the parameter related to damping and a decrease of the parameter relevant to linear-frequency were observed versus the loading amplitude. However, the values of the parameters stabilised at higher load amplitudes and superharmonics were present in the response. The proposed non-parametric method exhibited a good capability in the nonlinear parameter identification of cables. Approaching towards a more complete understanding of the performance of cable-stayed footbridges, it was realized that the modern footbridges are more prone to pedestrian-induced vibrations that, eventually, degrades their serviceability performance. Moreover, several researchers tried to investigate the problem of synchronous lateral excitation of footbridges, but there is no general consensus on pedestrian models. Therefore, a model of pedestrian-footbridge interaction was proposed. In detail, pedestrian was represented by a modified hybrid Van der Pol/Rayleigh (MHVR) self-sustained oscillator. Amplitude, stability and phase of the MHVR oscillator solution under a harmonic external force associated with the floor motion were analytically evaluated by the harmonic balance method and was compared with numerical results. It was shown that the phase difference tended to become constant at high excitation amplitudes. Moreover, the stability domain was found useful in predicting the percentage of pedestrians synchronized to a given oscillating floor. The numerical results of MHVR oscillator was, then, compared with the experimental result of a shake table with harmonic floor motion. A good agreement in amplitude ratio was found, however, the phase difference resulted to be underestimated by the MHVR model.