Numerical and experimental investigations of the sloshing modal properties of sloped-bottom tuned liquid dampers for structural vibration control

•A general theoretical framework based on modal expansion technique is presented for modeling sloped-bottom TLDs mounted on structures.•A generalized eigenvalue problem (EVP) of the sloped-bottom TLD is established using finite difference scheme.•Full-scale tests of TLDs are performed for validating numerical models.•Sloshing modal properties are quite different between shallow- and deep-water sloped-bottom TLDs.•The sloshing eigenfrequencies vary with damper geometries in a nonlinear manner. Tuned liquid dampers (TLDs) utilize the liquid sloshing to damp vibrations of civil and mechanical structures. Rectangular tank with flat-bottom has been widely used for passive structural control. A recent experimental study, on the other hand, indicates that a TLD with sloped bottom achieves better performance than its flat-bottom counterpart, considering the improved vibration mitigation and reduced liquid mass. This work investigates the sloshing modal properties (sloshing frequencies and sloshing mode shapes) of sloped-bottom TLD using finite difference method, which is validated by full-scale tests. It is observed that the sloshing mode shapes are quite different comparing the shallow-water sloped-bottom TLD with the deep-water one. To further reveal the influence of damper geometries on the sloshing modal properties of the sloped-bottom TLD, three different geometrical parameters have been considered for parametric study, e.g. the mean water level of the liquid, the slope angle, and the ratio between the horizontal projection length of the slope and the total bottom length. It is found that the sloshing eigenfrequencies increase as the mean water level increases, as the slope angle decreases and as the length ratio increases. The eigenfrequencies vary with damper geometries in a nonlinear manner, and the results from flat-bottom TLD always act as upper limit of those from sloped-bottom TLD. The developed numerical model in the present study can be used for tuning and preliminary design of structural-mounted sloped-bottom TLDs.