Semi-analytical model for frequency-domain analysis of sloshing in rocking excitation containers with bottom-mounted structures

This study develops a semi-analytical framework based on the Scaled Boundary Finite Element Method (SBFEM) to analyze frequency-domain liquid sloshing in rocking-excited rectangular containers. By reducing the governing partial differential equations to second-order ordinary differential equations, the method avoids the fundamental solution requirements of boundary element approaches while improving numerical stability and meshing flexibility for complex geometries. After validation, the framework is applied to bottom-mounted rigid baffles and rectangular obstacles. Results show that resonance suppression is governed mainly by changes in effective hydrodynamic inertia. A critical baffle-height ratio of 0.4 is identified, corresponding to the penetration depth of the fundamental sloshing mode; lower baffles are ineffective because near-bed fluid motion is weak. Increasing baffle density yields diminishing benefits due to flow-obstruction saturation. For rectangular obstacles, free-surface elevation is more sensitive to height than width because wave energy decays exponentially with depth. These findings support the design of passive sloshing-control devices.