This research explores the effectiveness of tuned liquid dampers (TLDs) in mitigating structural vibrations under dynamic loading. The dampers are modeled as rigid shells of rotation, partially filled with liquid and rigidly attached to an elastic structure. These damper geometries are of particular interest because their sloshing dynamics differ from those of conventional rectangular containers, offering potential advantages for energy dissipation. The elastic structure is represented as a single-degree-of-freedom oscillator (SDOF), with explicit inclusion of its interaction with the TLD. Fundamental sloshing frequencies are evaluated using the reduced boundary element method, which ensures both computational efficiency and accuracy in fluid-structure interaction analysis. The novelty of this work lies in demonstrating the applicability of arbitrary shells of revolution as TLDs, enabling a more realistic assessment of vibration mitigation performance. The results show that cylindrical shell-type dampers can markedly enhance structural resilience against intensive dynamic excitations. These findings offer important guidance for designing and optimizing TLDs in engineering contexts.