Tuned inerter dampers for civil structures subjected to earthquake ground motions: optimum design and seismic performance

•Optimum design formulas for TID are derived for seismic response control.•Seismic control performance of the optimally designed TID is demonstrated.•TID outperforms the conventional TMD for seismic response control.•TID can prolong the fundamental period of a structure-TID system.•TID greatly reduces acceleration response of short-to-moderate period structures. Tuned inerter damper (TID) is a promising passive vibration control device in earthquake engineering because it achieves a large inertance-to-mass ratio without requiring a large space and thus can effectively decrease the cost. This paper presents a theoretical and numerical study of a structure-TID system subjected to earthquake ground motions. Using the fixed-point theory, we derived simple design formulas for the TID when it attached to a single-degree-of-freedom system subjected to ground acceleration excitations. Analytical and numerical results demonstrate that the optimally designed TID using the proposed parameters is capable of suppressing the displacement response of structures with natural period ranging from 0.3 s to 5 s, and the performance positively relates to the inertance-to-mass ratio used. Particularly, a TID with a large inertance-to-mass ratio can significantly prolong the fundamental period of a structure-TID system, which is similar to a seismic isolation system. The optimally designed TID can effectively mitigate the absolute acceleration response of short-to-moderate period structures, but is far less likely to be effective for long-period structures. It is suggested that a value of less than one is used for the inertance-to-mass ratio of long-period structures if one intended to mitigate both displacement and absolute acceleration responses. In addition, numerical results illustrate that an optimal inertance-to-mass ratio exists when a single TID is applied to a multi-degree-of-freedom building structure. The results also indicate that the emerging TID outperforms the conventional tuned mass damper for seismic response control because the former device introduce no additional seismic energy to the system and is more robust due to large inertance-to-mass ratio used.