A novel methodology for designing a multimodal tuned mass damper applied to a suspension bridge model

Abstract

Suspension bridges are vital infrastructure for transportation systems worldwide, and their stability and safety under dynamic loads, such as wind and seismic excitation, are critical concerns for bridge engineers. To improve their performance when undergoing such phenomena, some designers propose the use of Single-Degree of Freedom (DOF) Tuned Mass Dampers (TMDs) to dampen its first bending mode. Nonetheless, these devices have a single frequency band of operation, and many studies have shown that bridges present many critical vibration modes. Therefore, this work developed a novel methodology for designing Multimodal Tuned Mass Dampers (MTMDs) to simultaneously target the bending and torsional vibration of a suspension bridge’s deck. The research methodology was divided in two parts, and follows a step-wise approach, starting with a basic analytic model up to a laboratory prototype. The first part was the conception of an idealized model of a suspension bridge’s deck with a Multimodal Tuned Mass Damper (MTMD) attached, in Matrix Laboratory® (MATLAB®). Each member’s characteristics, such as material properties, and boundary conditions, were considered in this representation. This model was used to simulate simple dynamic loads, such as harmonic and pulse inputs, to determine the primary structure’s behavior and the MTMD’s geometric properties. In order to reduce the vibration levels of the targeted modes, the “Equal Peak Design" technique was applied and a complete physical decoupling between the modes was considered. Next, the analytic model was developed into a Finite Element’s in Analysis System Incorporated® (ANSYS®). The dynamic response of the deck, whilst the MTMD is attached thereon was simulated, through Harmonic and Transient Analysis. The results for the initial part of the study showed the employed method as effective, for the structure’s vibration levels were mitigated for both frequencies by more than 70%. Finally, in the second part, to validate the theoretical procedure, a physical prototype for the MTMD and the bridge’s deck were built in the laboratory and adjusted to its numerical equivalents. This second model was then subjected to dynamic excitation, and a modal analysis was carried by the Rational Fractional Polynomial (RFP) Method. The experimental results, concerning this second system, were compared to their FE counterpart. The findings suggest that MTMDs have the potential to reduce the dynamic response of a complex structure, since, in this study, the device was able to split both of the targeted modes. Moreover, there was a significant movement reduction of around 5dB and 1dB for the bending and torsional modes, respectively, even without the insertion of optimal damping.