Numerical investigation of the response of structures equipped with a limited freeboard tuned liquid damper

The tuned liquid damper (TLD) uses liquid sloshing in a tank to suppress unwanted wind-induced vibration of a flexible structure. The tank interior height is traditionally selected such that sloshing waves do not impact the tank ceiling by providing sufficient freeboard between the free surface and the tank ceiling. To optimize a TLD for a space with height constraints, it is possible to design the tank to have intentionally limited freeboard. This study numerically investigates the response of a structure equipped with a limited freeboard TLD using an incompressible smoothed particle hydrodynamics (SPH) model. Seven excitation force intensities are studied at nine different freeboard heights. The SPH results are used to assess the performance of the limited freeboard TLD. In general, limiting freeboard is found to reduce the effectiveness of the TLD. When the fundamental sloshing mode is not constrained by the tank ceiling, the TLD performs comparably well to its unlimited freeboard counterpart. If the fundamental sloshing mode is constrained by the tank ceiling, the motion reduction performance of the TLD is affected. The equivalent damping ratio of the fundamental sloshing mode is evaluated from the SPH results. An equivalent linear mechanical model that can be used for preliminary feasibility studies of the system with limited freeboard is presented. Additional TLD damping due to ceiling impact proportional to the reduction in wave height is introduced. The mechanical model is found to reasonably capture the structure response when compared to the SPH results.