Closed-form optimal design of the tuned inerter damper (TID) connecting adjacent flexible buildings

Abstract

The tuned inerter damper (TID) is a viable solution for addressing the vibration issue of the adjacent-building system. However, the conventional optimal calibration of the TID is conducted based on the classic 3-degree-of-freedom (3-DOF) model with one resonant DOF for each structure, which ignored the background flexibility contribution that comes from non-resonant modes of each one, and thus leads to non-optimal control performance. This paper developed a novel analogue 3-DOF model, in which the background flexibility contribution of each flexible building at the damper attachment location is represented by an equivalent stiffness element. An enhanced formula for the TID optimal frequency is developed accordingly (targeting the fundamental mode of the taller building) using the ‘root-locus’ method, where the background flexibility as well as the resonant mode contributions that come from both buildings are accounted for. For completeness, the optimal frequency formula that ignores the background flexibility contribution is derived based on the classic 3-DOF model. A robust approach is adopted to determine the optimal damping ratio based on the classic model. Numerical analysis is conducted based on a 25-15 floors adjacent-building system. Results demonstrate that when the enhanced frequency-tuning formula is used, a much more balanced frequency response curve of the taller building is achieved. Further, time-domain seismic analysis indicates that the TID performance is consistently improved when background flexibility is accounted for in the design formulas.