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The International Maritime Organization is still developing second generation intact stability criteria for the roll motion of ships. For level 2 vulnerability criteria for parametric roll that require no expert knowledge about nonlinear dynamics, various analytical approaches are proposed in this study based on averaging methods. Firstly, an averaging method is applied to an uncoupled roll equation without fitting a polynomial to the calm-water GZ curve, thereby taking into account more accurate effect of the restoring arm. Secondly, the parametric roll amplitude is estimated more accurately using an averaging method that takes into account the effect of superharmonic roll motion. Thirdly, the critical speed for parametric roll is estimated, which is expected to reduce calculation processes in the design stage. Fourthly, the averaging method is extended to parametric roll in oblique waves, thereby taking into account the effect of both the ship's speed and course, which are helpful for an operational decision. Finally, the proposed analytical approaches are verified against an existing averaging method, numerical simulations, and free-running model experiments.

Determination of Total Anthocyanin and ProanthocyanidinContents in Black Soybeans (Glycine max (L.) Merr.

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