Analysis of Two-Dimensional Nonlinear Sloshing in a Rectangular Tank by Using a Concentrated Mass Model

Abstract Major problems can occur when liquid sloshes in a tank, such as occurs in liquid storage tanks during an earthquake, and this is an important engineering problem to address. To analyze this phenomenon, semi-analytical methods such as the perturbation method, the multimodal method, and the finiteelement method are generally used. However, semi-analytical methods involve quite complicated equations, and the finite-element method involves many degrees of freedom when the tank is large. In this paper, a nonlinear numerical model with relatively few degrees of freedom is established for vertical and horizontal two-dimensional nonlinear sloshing in a rectangular tank excited horizontally. The model comprises concentrated masses of liquid connected by nonlinear springs and dampers. The connecting springs have characteristics based on the static and dynamic pressures of the liquid. In addition, a method is proposed for reducing the number of degrees of freedom in the two-dimensional model. The natural frequencies, modes, and frequency responses are then compared among the concentrated-mass model, theoretical calculations, and experimental results. Good agreement was achieved among them, thus demonstrating the validity of the model.