Performance and efficiency oriented optimal design of tuned inerter damper for seismic response control of building structures

Characterized by mass and damping enhancement effects, inerter-based dampers (IBDs) have recently been applied in structural vibration control as efficient vibration control devices. Prior studies have demonstrated the applicability of IBDs in various control objects, where two typical IBDs, the tuned viscous mass damper, and tuned inerter damper (TID), are considered. Research has proposed optimization procedures to determine the design parameters of IBDs, and most of the optimization objects are indices related to the magnitude or mitigation ratio of the structural response. This study investigates the damping enhancement and optimal design from the equivalent damping ratio supplied by the TID because the supplemental equivalent damping ratio (SEDR) is commonly utilized in the design of energy dissipation devices. Based on the indices related to the SEDR and the installation position of the TID, the control performance and damping enhancement effect are investigated. Two closed-form solutions for the optimal parameters are developed to achieve the best control performance and highest damping enhancement effect. The proposed optimization methods are verified by a time history analysis of single- and multi-degree-of-freedom structures. In addition, the proposed methods are compared with conventional optimization approaches based on a fixed-point strategy. When the mass ratio was less than 20%, the TID optimized by the proposed method achieved a similar control performance but a better damping enhancement effect compared with those by the conventional optimization approaches. Installing the TID in the story with the largest interstory drift improved the deformation uniformity of the primary structure and achieved a better damping enhancement effect.