Hydrodynamic forces on a two-dimensional multihull structure in waves: application of the scattering matrix theory

Abstract

The diffraction and radiation problems of a two dimensional multihull structure were investigated by application of the scattering matrix theory. The scattering matrix theory is widely used to analyze wave interaction problems in various scientific fields. The research is focused on the zeros of the wave exciting force near resonance, which occurs both in the diffraction problem and the radiation problem. At the zeros of the wave exciting force, the wave exciting force for the overall structure is zero, but each demihull undergoes wave excitation. At near-resonant frequencies, the amplitude of the traveling wave between adjacent demihulls becomes very large and the demihulls experience very large wave forces. A number of simple equations for representing the hydrodynamic properties of the multihull structure at the zeros and near-resonant frequencies are obtained. Numerical examples show that these simple equations well explain the hydrodynamic forces and the wave system in the spaces between the demihulls.