An adaptive pendulum for evolving structures
Résumé
Tuned mass dampers (TMDs) supplement existing structures with damping while preserving stability. As evolutions of the structure to be controlled may pull down the performance of this kind of device, large bridges under construction in windy areas are rather equipped with active devices such as AMDs that prove efficient (7th International Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures, Assisi, Italy, 2001). However, active devices suffer from several drawbacks such as the necessity to carefully prevent from instability, especially in the case of noncollocated control. Therefore, a natural question arises: how to adapt a TMD in such a way to make its performance independent of the structural evolution? A new type of semi-active control system matching this requirement is presented. It builds upon a TMD of pendulum type. In order to damp the torsional mode of a bridge under construction, a gear with an alternator would connect the pendulum to the structure. As the bridge starts vibrating, the pendulum begins to oscillate and the alternator converts the mechanical energy into electrical energy to be dissipated through an exterior resistor via the Joule effect. Given an optimal design of a passive tuned pendulum damper (TPD) for the structure in its current configuration, the semi-active control strategy consists in changing the resistor in real-time in such a way to lock the apparent stiffness and damping of the real TPD at their desired optimal values no matter the current construction step. Resistor tuning is mandatory even when only one construction step is considered since a constant resistor within the alternator would yield a time-varying effective damping coefficient of the pendulum, whereas the desired optimal damping assumes a given value, which does not change until the structure or load type changes. The semi-active control law easily adapts to any change of the structure provided this change is known. The control algorithm relies on the knowledge of the pendulum rotation, of the frequency of the mode to be controlled and of its modal participation factor at the TPD location. These modal parameters are computed during the construction process, or can be viewed as outputs of a SHM system. How to get these parameters has already received a lot of attention in the SHM literature and is not discussed here. Experimental validations on a small-scale bridge mock-up confirm the interest of the approach.