Characterization and design of tuned liquid dampers with floating roof considering arbitrary tank cross-sections

A recently proposed new type of liquid mass damper, called Tuned Liquid Damper with Floating Roof (TLD-FR), is the focus of this paper. The TLD-FR consists of a traditional TLD (tank filled with liquid) with the addition of a floating roof. The sloshing of the liquid within the tank counteracts the motion of the primary structure it is placed on, offering the desired energy dissipation in the vibration of the latter, while the roof prevents wave breaking phenomena and introduces an essentially linear response. This creates a dynamic behavior that resembles other types of linear Tuned Mass dampers (TMDs). This investigation extends previous work of the authors to consider TLDs-FR with arbitrary tank cross-sections, whereas it additionally offers new insights on a variety of topics. In particular, the relationship between the tank geometry and the resultant vibratory characteristics is examined in detail, including the impact of the roof on these characteristics. An efficient mapping between these two is also developed, utilizing Kriging metamodeling concepts, to support the TLD-FR design. It is demonstrated that the overall behavior can be modeled through introduction of only four variables: the liquid mass, the frequency and damping ratio of the fundamental sloshing mode of the TLD-FR, and the efficiency index, which is related to the portion of the total mass that participates in this mode. Comparisons between TLDs-FR and other types of mass dampers are established through the use of the latter index. A design example is presented considering the dynamic response of a structure under stationary excitation. It is illustrated in this example that for complex tank cross-sectional geometries there exists a manifold of tank configurations leading to the same primary vibratory characteristics and therefore same efficiency of the TLD-FR. Considerations about excessive displacements of the roof can be then incorporated to indicate preference towards some of these candidate configurations.