Shallow rectangular TLD for structural control implementation

A simple and practical model for the application of shallow rectangular tuned liquid damper (TLD) in structural vibration control is presented in this paper. The dynamic properties of shallow liquid in rectangular containers subjected to forced horizontal oscillation are analysed directly from the continuity and momentum equations of fluids. Following some practical assumptions, the nonlinear partial differential equations describing the wave movement of shallow liquid in rectangular containers are established and a numerical procedure for the solutions of these equations is proposed based on the finite element method. The formula for determining the control force provided by a shallow rectangular TLD is presented. The advantage of the proposed approach for the modeling of shallow rectangular TLD is that it simplifies a three-dimensional problem into a one-dimensional problem and therefore reduces the computation efforts significantly. The whole process forms a solid foundation and provides a simplified procedure for the design and analysis of shallow rectangular TLD.