Keywords: multiple tuned mass damper (MTMD), passive control, suspension bridges, tower, tuned mass dampers (TMD).

Today slender structures are usual implementations for tall-buildings and suspension bridges. They offer low damping and large deformability. Their design is mainly performance based with limitations on displacements and vibrations. High and slender structures are quite sensitive to wind action. One must account for static effects, turbulence, von Karman vortexes (with consequent transversal vibrations) and secondary aero-elastic coupling phenomena. The action of the wind dominates the design, mainly because of limitations imposed by induced motion.

Recent structural engineering developments were also recorded in the area of structural control devices. These devices can improve performance, comfort, efficiency and fatigue durability of the structures on which they are mounted. Within the civil application of structural engineering, passive control techniques are enlarging their diffusion mainly in the areas of seismic base isolation and mitigation of wind-induced vibrations [1]. The main drawbacks of the many alternative semi active [2] or active types of [3] strategies are high maintenance costs and the low they reliability offer. Semi-active and active devices are therefore allowed as redundant tools capable of providing the same performance as a passive control scheme even when the active component fails.

The design of complex structural systems such as suspension bridges [4] relies on the efficient organisation of the components, on their suitable selection (in terms of geometry and material) and on robust hierarchies of dependency established between these components. Nevertheless, performance and comfort can be pursued or simply improved by strategies of vibration mitigation and structural control.

Several theoretical and experimental studies on scaled models and full-scale schemes can be found in the literature to confirm the efficiency of tuned mass dampers (TMD) toward the mitigation of the response of wind action. Nevertheless, TMD devices are not intrinsically robust. Their performance could be strongly reduced even in the presence of modest perturbations of the frequency ratio (mistuning). This ratio is affected by ignorance of the actual mechanical properties of the structure, by the foundation soil characteristics and their deterioration during the structure lifetime, by aero-elastic effects and aerodynamic damping and, of course, by the deterioration (alteration) of the device with respect to the one originally designed. The associated contingency scenarios are therefore deterministic, rather than random, since they occur as mistuning situations.

Multiple TMD (MTMD) systems offer a better performance during the operation lifetime, when mounted in the towers of suspension bridges. Indeed, they result in effectiveness and robustness, and make response mitigation redundant.

Ignoring robustness in favour of mistuning can only pursue effectiveness maximisation. For this purpose, a policy of data collection during the construction stage is quite important. It allows one to reduce the uncertainties and, hence, the robustness requirements are limited to the time variability of the main design parameters during the bridge lifetime. This paper reports the results of numerical analyses under the ultimate limit state wind action. When comparing the response in serviceability conditions with the response in ultimate conditions, the contribution of the TMD could have critical results. The simplest solution is to make the TMD device adaptive, driven by the feedback of suitable sensors. This aspect, however, is the matter of a deep further investigation.

1

Soong T.T., Dargush G.F., Passive Energy Dissipation Systems in Structural Engineering, John Wiley & Sons, Chichester, UK, 1997

2

Casciati F., Magonette G., Marazzi F., Semi active Devices and Applications in Vibration Mitigation, John Wiley & Sons, Chichester, UK, 2006.

3

Fujino, Y., "Vibration, Control and Monitoring of Long-Span Bridges - Recent Research, Developments and Practice in Japan", Journal of Constructional Steel Research 58, 71-97, 2002. doi:10.1016/S0143-974X(01)00049-9

4

Gimsing N.J., Cable Supported Bridges, Concept and Design. NY: J. Wiley & Sons, Chichester, UK, 1983.

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