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.

环形调谐液柱阻尼器 (TLCD) 是最近设计的设备，可将 TLCD 的应用扩展到多向振动控制。环形 TLCD 有望抑制结构的水平振动响应。本研究进一步探讨了环形 TLCD 用于多方向俯仰振动缓解的潜力和优化方案。首先，给出了俯仰运动中环形TLCD结构系统的运动方程。开发了一种用于计算系统在谐波载荷下的动态响应的非迭代解析封闭式解决方案。随后，可以获得优化的频率调谐比和流阻系数。优化结果理论上证实了环形 TLCD 的方向无关控制性能。详细介绍了环形 TLCD 的设计示例作为参考。最后，构建了一种用于 TLCD 俯仰运动测试的钟摆旋转结构。通过自由振动测试验证了环形 TLCD 在减轻俯仰振动方面的多向性、有效性和鲁棒性。