Coupled shallow-water fluid sloshing in an upright annular vessel

The coupled motion of shallow-water sloshing in a horizontally translating upright annular vessel is considered. The vessel motion is restricted to a single space dimension, such as for Tuned Liquid Damper systems. For particular parameters, the system is shown to support an internal 1 : 1 resonance, where the frequency of coupled sloshing mode which generates the vessel motion is equal to the frequency of a sloshing mode which occurs in a static vessel. Using a Lagrangian Particle Path formation, the fully nonlinear motion of the system is simulated using an efficient numerical symplectic integration scheme. The scheme is based upon the implicit-midpoint-rule which conserves energy and preserves the energy partition between the fluid and the vessel over many timesteps. Linear and nonlinear results are presented, including those showing the system transitioning to higher frequency eigenmodes as the fluid depth is reduced