The mathematical modeling of a Tuned Liquid Damper

Abstract

The goal of this research is the simplification of the mathematical modeling process of a Tuned Liquid Damper. In an environment of increasingly flexible and lightly damped structures, the suppression of structural vibrations is an important topic. The use of secondary mass systems (generally mass and liquid dampers) to control the displacements and accelerations in one or more vibration modes of the structure is a viable and popular solution. The development of a mathematical model to successfully model the response of a Tuned Liquid Damper will encourage its more frequent use in building systems. Using a simplified mathematical model, the secondary liquid system can be effectively 'linked' to the primary structural system model in specific locations, as necessary. The model is derived from conventional dynamic theories and fluid fundamentals to present an approximate solution for the response forces generated by a rectangular liquid tank subjected to an arbitrary excitation. The mathematical model is shown to generate stable solutions which correlate well with the results of extensive experimental work. The mathematical Tuned Liquid Damper model developed in this study is based on existing theoretical descriptions of wave action in a tank, and is calibrated and tested with data from a laboratory investigation. This laboratory study used a relatively massive (approximately 1000 pound) dynamic system consisting of two rigid masses, associated springs and dampers, and the attached Tuned Liquid Damper. Considerable effort has been directed towards the development of system identification methods for the structural model, as well as for the Tuned Liquid Damper. Mathematical parametric studies have then been used to further refine the mathematical model and to predict the effectiveness of the Tuned Liquid Damper for structures and excitations not tested in the laboratory. Finally, preliminary designs have been developed for hypothetical deployment of Tuned Liquid Dampers in two real high-rise buildings.