Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 3. Base ratio perturbations

Abstract

Previous parts studied nonlinear resonant sloshing in a prismatic tank under the academic assumption of a square base. However, a representative industrial tank may have an ‘almost’ rather than a ‘precisely’ square base. The present paper generalizes the multimodal technique of Part 1 to examine this complication. The main focus is on resonant sloshing due to lateral harmonic excitations, but several known theoretical results about free-standing waves have also been re-derived. The analysis shows that, although disturbances of the square base do not lead to new types of steady-state wave regimes, the frequency domains, where these wave regimes are stable, change considerably even with small perturbations of the breadth/width ratio around 1. The modifications of the effective frequency domains are compared with the results of two experimental series.