Frequency Characteristics of Sloshing Resonance in a Three-Dimensional Shallow-Water Rectangular Tank

Abstract

The frequency characteristics of free surface elevation time histories of shallow-water sloshing in a three-dimensional rectangular tank is presented. The numerical model for sloshing motion uses an accurate velocity potential Boussinesq-type equation. A particular solution is adopted to express the external excitations and a linear damping term is introduced to replace a friction effect produced by tank walls. The excitation amplitude of the forced movement of the tank is tiny, while the excitation frequency varies around the first resonance frequency. The numerical results show that the wave energy in the rectangular tank under resonance is concentrated in the integer multiple of excitation frequencies, the sum excitation frequencies, and the difference excitation frequencies.

Keywords

• spectral analysis
• shallow-water sloshing
• Boussinesq-type equations