Optimized parameters of toroidal tuned liquid column dampers for multidirectional pitching vibration mitigation of structures

Toroidal tuned liquid column dampers (TLCDs) are recently designed devices that extend the application of TLCDs to multidirectional vibration control. Toroidal TLCDs are promising in suppressing the horizontal vibration response of structures. This study further explores the potential and optimization scheme of toroidal TLCDs for multidirectional pitching vibration mitigation. Firstly, equations of motion for a toroidal TLCD-structure system in pitching motion are presented. A non-iterative analytical closed-form solution for calculating the dynamic response of the system under harmonic loading is developed. Subsequently, optimized frequency tuning ratio and flow resistance coefficient can be obtained. The optimization results theoretically confirm the direction-independent control performance of toroidal TLCDs. A design example of toroidal TLCDs is presented in detail as a reference. Finally, a pendulum rotational structure for TLCDs testing in pitching motion is constructed. The multidirectionality, effectiveness and robustness of toroidal TLCDs in mitigating pitching vibration are verified by free vibration tests.