Design and performance evaluation of toroidal TLCDs in bidirectional seismic control of structures using a modified dynamic model

In this study, a modified dynamic model which distinguishes between liquid oscillation and sloshing in vertical columns is derived for toroidal tuned liquid column dampers (TLCDs). In the modified model of toroidal TLCDs, the primary sloshing mode within vertical columns is modeled as mass–spring-dashpot systems, whereas the oscillatory behavior of the liquid is analyzed employing the conventional theory of TLCDs. The accuracy of the modified dynamic model in capturing bidirectional liquid responses is verified by computational fluid dynamics (CFD)-based simulations. A large number of CFD-based simulations are performed to establish a ready-to-use suggested formula for a newly introduced parameter (which is related to the geometric configuration of liquid containers and the initial liquid depth) in the modified model. Subsequently, considering the maximum allowable liquid displacement in vertical columns, an optimized design approach for toroidal TLCDs installed in symmetric and asymmetric structures is illustrated. On the basis of the proposed optimization design method, the bidirectional vibration control effects of toroidal TLCDs are comprehensively analyzed under El Centro, Loma Prieta, Northridge, and Chi–Chi seismic excitations in both the time and frequency domains. The results demonstrate the effectiveness of toroidal TLCDs for bidirectional seismic control of structures.