EFFECTS OF THE VARIATION OF STABILITY ON FRACTAL CAPSIZE BOUNDARIES OF A SHIP

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 a polynomial with a linear term and a cubic term in rolling angle phi is used 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, the former N type variation and the latter L type are called one. In both cased the single-degree-of- freedom equation of motion for roll results in a forced Mathieu type capsize equation. In a 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, similar numerical studies were carried out for the L type forced Mathieu capsize equation and compared with the result of the N type. It is shown 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. Some examples of super-subharmonics rolling in the fourth and fifth unstable regions and bifurcation diagrams with the slowly varied forcing frequency are illustrated.

  • Supplemental Notes:
    • Trans Soc Naval Arch West Japan, n 84, Aug 1992, p 107 [14 p, 11 ref, 11 fig]
  • Authors:
    • Taguchi, H
    • Kan, M
  • Publication Date: 1992

Language

  • Japanese

Subject/Index Terms

Filing Info

  • Accession Number: 00716270
  • Record Type: Publication
  • Source Agency: British Maritime Technology
  • Files: TRIS
  • Created Date: Feb 28 1996 12:00AM