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The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio h>1). This behavior type is supported by the existing experimental data. The wave elevations at the vertical wall are satisfactorily predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.

Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion