船の転覆限界のフラクタル性に及ぼす強制力の位相の影響について

概要

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In the previous papers, we examined a simple capsize equation of forced softening Duffing's type. This equation had four control paramerters, i.e. damping coefficient κ, forcing amplitude B, forcing frequency Ω and forcing phase δ, and was solved under initial conditions composed of rolling angle ψ(0) and rolling velocity ψ(0). It was clarified that the capsize boundaries which separated the capsizing and non-capsizing regions had very complicated and fractal-like characteristics in both the control space and the initial value plane. This result was obtained for one forcing phase δ=0, but at real sea the phase should have random value. In this paper, we have investigated the effects of the forcing phase on the capsize boundaries. As a result, it has been clarified that the capsize boundaries in both the control space and the initial value plane are metamorphosed complicatedly and in a fractal way as the forcing phase is varied. The effects of the duration of the external force on the capsize boundaries have also been examined. It has been clarified that as the duration time gets shorter, the capsize boundaries have simpler shapes and are closer to the bifurcation boundaries. This implies that there is a possibility that the bifurcation boundaries are used as a safety criterion.
社団法人日本船舶海洋工学会の論文
1991-09-04