Nonlinear multimodal model for TLD of irregular tank geometry and small fluid depth

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy. TLDs of irregular or complex tank geometry may be required in practice to avoid tank interference with fixed structural or mechanical components. The literature offers few analytical models to predict the response of this type of TLD, particularly when the fluid depth is small. In this paper, a multimodal model is developed utilizing a Boussinesq-type modal theory which is valid for small TLD fluid depths. The Bateman–Luke variational principle is employed to develop a system of coupled nonlinear ordinary differential equations which describe the fluid response when the tank is subjected to base excitation. Energy dissipation is incorporated into the model from the inclusion of damping screens. The fluid model is used to describe the response of a 2D structure–TLD system when the structure is subjected to external loading and the TLD tank geometry is irregular.Shake table experiments are conducted on a rectangular and chamfered tank subjected to unidirectional base excitation. Comparisons of the experimental and predicted sloshing forces and energy dissipation per cycle indicate that the model is able to predict the fluid response at fluid depth ratios greater than h/L=0.10. Next, structure–TLD system tests are conducted and it is found that the model can predict the structural and TLD responses. The simulated and experimental results show that the TLD tank transfers energy between orthogonal structural sway modes.