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Study of the Influence of Nonlinear Moments upon Intensity of Parametric Roll

Hydrodynamical analysis of the conditions for the occurrence of chaotic ship roll, leading in some cases to the capsizing of the vessel, showed that such conditions are most likely to occur in the zone of the main parametric resonance of the roll when its period is sequentially doubled, and subharmonic oscillations turn into chaotic ones. This circumstance necessitates special attention to the regime of parametric roll resonance, issues of its occurrence, development, and establishment as well as to the methods of calculation of its amplitudes. In the present paper, the study of the parametric ship roll is conducted on the basis of the Lugovsky formula. An account is taken of the additional nonlinear moments M¯X23 and M¯X24, obtained through the application of the small parameter method. Presented are the calculation results for the parametric roll of five different ships performing motions at various course angles both with and without account of the aforementioned nonlinear moments. Demonstrated therewith is a significant influence of the nonlinear moments upon the maximum amplitudes of the parametric roll, especially in the case of beam waves.