Passive and active vibration damping of suspension bridges

In this paper, we consider passive and active vibration damping of suspension bridges. We explore two classical techniques: (i) Tuned Mass Dampers (TMD), optimized for the damping of several modes; and (ii) active control using thin stay cables (added to the structures) controlled with active tendons. An active tendon consists of a displacement actuator collocated with a force sensor monitoring the tension in the stay cable. The active tendons are controlled with decentralized Integral Force Feedback (IFF). For the considered suspension bridge, we target the damping of the first few modes of the deck (the most excited modes). In first part of this study, we explore the feasibility of damping several modes using several tuned mass dampers. When a single mode is targeted, a single TMD is attached at the location of the mode antinode in order to maximize the energy absorption; when two modes are targeted for the damping, two TMDs are attached at the locations corresponding to the antinodes of the two targeted modes etc. For each mode, a TMD is needed, leading to a high number of TMDs and a penalty of mass. For the modes whose antinodes are at the same location, e.g. first flexural and torsional modes, we suggest to use only a single TMD with 2 degrees of freedom (instead of two), such that the first mode of the TMD is flexural and the second is torsional. With the same mass as a single TMD, the simulation confirms that it is possible to target two modes at the same time with a single TMD, and thus, 4 modes with the mass of only 2 TMDs,... The performances of the TMDs are then compared to those of active control with decentralized IFF. The robustness of the TMD is also discussed. In the second part of this study, the tuned mass dampers are implemented experimentally on a laboratory mock-up. The 2 d.o.f. TMD is realized with a cantilever beam equipped with two movable masses attached at its end. The active control is performed using 4 control stay cables equipped with piezoelectric actuators and force sensors. In very good agreement with the predictions, the experimental results confirm the simplicity of the proposed TMDs, and the excellent performance and robustness of the active control system. Of course, although the active control technique performs better than the passive one, the comparison between the two techniques should be made under real conditions (excitation bandwidth, thermal loading, model variation, etc).