Sloshing phenomenon analysis by using concentrated mass model (1st Report, Proposition of linear analytical model for small amplitude wave and free vibration analysis)

Sloshing phenomena in containers during earthquakes often cause serious accidents. For oil tanks with a floating roof, sloshing and structural vibration should be treated as a coupled problem. A Lagrangian fluid finite element method has been used to analyze the coupled problem because the compatibility and the equilibrium conditions are automatically satisfied at the boundary between the fluid and the structure. However, the number of degrees of freedom of the Lagrangian method becomes large because the fluid particles move vertically and horizontally. In addition, the Lagrangian model has physically meaningless spurious modes caused by redundancy in the degrees of freedom. In this paper, liquid in a rectangular container is modeled with a linear concentrated mass model to establish an efficient, accurate analytical model for the coupled problem. The model consists of masses and connecting springs. The masses move horizontally and the vertical liquid motion is considered as vertically movable points. The masses are governed by the equations of motion. The vertical displacements of the moving points are determined from the displacements of the masses based on the incompressibility of the liquid. The characteristics of the connecting springs are derived from the static and dynamic pressures of the liquid. In the proposed model, there are fewer degrees of freedom than in the Lagrangian model and the spurious modes do not occur. The proposed model is validated by comparing the calculated natural frequencies and natural modes with the theoretical values.