船の転覆限界のフラクタル性に及ぼす復原力変動の影響

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The stability of a ship travelling in following or quartering seas varies with the relative position of the ship to the wave. In general, it is decreased when the wave crest is amidship and increased when the wave trough is amidship. If we use a polynomial with a linear term and a cubic term in rolling angle φ to fit the stability curve in still water, there are two simple expressions for such stability variation. One is an expression that all terms of the polynomial are varied with an encounter period, and another is only the linear term of the polynomial is varied. In this paper, we call the former N type variation and the latter L type one. In both cases the single-degree-of-freedom equation of motion for roll results in a forced Mathieu type capsize equation. In the previous paper, on the basis of the nonlinear dynamical systems theory the authors studied numerically the forced Mathieu type capsize equation with the N type stability variation. It was clarified that there were many different characteristics from the non-Mathieu type capsize equation without stability variation in phenomena such as bifurcation diagrams, metamorphoses of safe basin in the initial value plane and fractal-like capsize boundaries in the control parameter plane. In this paper, in order to clarify the difference between the two expressions for stability variation, we have carried out similar numerical studies for the L type forced Mathieu capsize equation and compared with the result of the N type. It is showed that although for the same magnitude of the stability variation, the result for the L type variation is more dangerous for capsizing than that for the N type, yet the difference between the two types is not essential. And some examples of super-subharmonics rolling in the fourth and fifth unstable regions and bifurcation diagrams with the slowly varied forcing frequency are also illustrated. By these numerical studies the totality of the global and local characteristics of the solution of the forced Mathieu type capsize equation has been more clarifed.
社団法人日本船舶海洋工学会の論文
1992-09-04

船の転覆限界のフラクタル性に及ぼす復原力変動の影響

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