Nonlinear modelling of tuned sloshing dampers with large internal obstructions: Damping and frequency effects

Internal obstructions are commonly employed in tuned sloshing damper (TSD) tanks to increase the inherent damping of the sloshing liquid closer to its optimal value for the targeted excitation amplitude. However, these obstructions also produce added mass, which acts to decrease the natural sloshing frequency of the tank. Using potential flow theory, this study develops both a linearized equivalent mechanical model and a fourth-order nonlinear multimodal model that are capable of accommodating the fluid drag and added mass that are generated by the paddles. The linearized equivalent mechanical model represents the sloshing liquid as an equivalent spring–mass–dashpot system with amplitude-dependent damping. The fourth-order nonlinear multimodal model captures the nonlinear coupling that occurs among the first four sloshing modes. Shake table tests are then conducted on a scale model TSD tank equipped with vertical paddles of cruciform plan section. The sloshing forces predicted by the linearized and nonlinear models are in reasonable agreement with the experimental results. The nonlinear model is generally in good agreement with the experimental wave heights, whereas the linearized model often underestimates the peak wave heights considerably. A plot is created which shows the frequency shift produced by the paddles as a function of the width of the paddles. If the paddles’ widths are greater than approximately 5% of the tank width, the effect on the natural sloshing frequency is noticeable.