Robust vibration serviceability design of structures subjected to human-induced loading.

The use of high strength materials and advanced calculation methods facilitates the design of slender footbridges, often resulting in low natural frequencies of the structure in the range of the loading frequencies of human-induced excitation. In combination with a low modal damping, these structures are sensitive to human-induced loading. Therefore, a vibration serviceability assessment of structures subjected to human-induced loading has become an important design issue. A reliable response estimation requires a description of both the human-induced loading and the dynamic behaviour of the structure. If the calculated response exceeds a predefined limit for vibration comfort, the installation of vibration mitigation devices such as Tuned Mass Dampers (TMDs) can be desired. However, both the vibration serviceability assessment and the TMD parameter tuning are subject to a high degree of uncertainty since they require an accurate description of human-induced loading and the dynamic behaviour of the structure. Due to these uncertainties, an acceptable behaviour after construction cannot always be guaranteed sometimes resulting in modifications of the structure or the unexpected installation of vibration mitigation devices leading to additional costs.

The innovative approach of this doctoral study is to introduce the concept of robustness in the vibration serviceability assessment and TMD design. The main objective is to design footbridges which are minimally sensitive to the effect of the uncertainties in the modal parameters and to variability in the loading, resulting in safe and cost-effective designs.

A generic methodology for the robust vibration serviceability assessment of footbridges to walking loading is proposed. By considering multiple levels of uncertainty in the modal parameters, a gradual evaluation of the vibration response is performed. Additional variation on the stochastic models for walking loading is also included. It is shown that human-structure interaction effects considerably affect the response and therefore must be considered. It is also indicated how the multi-interval assessment provides a measure for the sensitivity of the response of the footbridge to the effect of uncertainties.

The presented methodology for the robust vibration serviceability assessment is implemented in the TMD design. The TMD design problem is defined as a robust optimisation problem. By minimising a cost function, the TMD mass, stiffness and damping constants are tuned. Design constraints are implemented for operability of the TMD and for vibration serviceability considering uncertainties in the dynamic behaviour of the footbridge. The effect of human-induced walking loading is directly accounted for in the response. The design can be performed for a selected range of uncertainty. If multiple designs are performed at different levels of uncertainty, the sensitivity of the TMD design to the range of uncertainties can be verified. It is concluded that for designs considering a wider range of uncertainty, the total TMD mass increases. However, its performance is ensured with respect to uncertainties. It is also shown that the TMD mass can be strongly reduced in comparison with conventional designs by tuning the TMD mass, stiffness and damping independently from each other.