Experiments on the synchronous sloshing in suspended containers described by shallow-water theory

The synchronous interaction between a sloshing fluid and its container may take place when the motion of the container is not prescribed a priori. When a partially-filled container is suspended as a bifilar pendulum, the fluid contributes to the restoring force by its weight through the wire suspensions and may either augment or diminish the restoring force through hydrodynamic interaction with the container. Here we report on linearized shallow-water theory and experiments for multi-chamber box containers, a cylinder and an upright 90◦ wedge. The nature of system response at low fluid mass is analyzed in detail using linear theory and shallow-water simulations. These results show that the system frequency smoothly transitions through successive higher frequency eigenmodes so that, in the limit where the fluid mass tends to zero, the system frequency is that of the dry container.