PhD Dissertation

Reliability Assessment of Hull Forms Susceptible to Parametric Roll in Irregular Seas

Abhilash Somayajula


Traditionally ships are designed to be symmetric about their centerline which makes head seas a very safe heading for roll motion stability. However, in the recent years several incidents of large amplitude roll motion in head seas have been reported which have later been attributed to parametric roll. Parametric roll motion is a phenomenon in which a ship exhibits a large amplitude of roll motion even when it is moving into head seas with no direct excitation. This phenomenon is particularly an issue for modern high-speed fine form container ships and has gained attention relatively recently.

This instability is dangerous because of its manifestation in counter-intuitive headings. Also the roll amplitude during parametric roll rises exponentially with time which gives ship captains and masters very less time to react. While this instability has been studied extensively in regular waves, its manifestation in irregular seas has not received sufficient attention. This dissertation aims at the development of design criteria based on analytical techniques which can help a designer quickly quantify the stability of a vessel to parametric excitation.

For accurate simulation of parametric response of a vessel/platform in irregular seas, an in-house time domain simulation program has been developed and validated against available experiments. The roll equation of motion is then simplified into a single degree of freedom model for analytical assessment. The existing single degree of freedom models in the literature are compared against the time domain simulation tool to gain an understanding of the extent to which the simplified models capture the dynamics of the phenomenon. In order to improve the roll modeling, a new approach is suggested to overcome some of the limitations of the existing models.

This new model is then investigated using two analytical approaches, one from the theory of nonlinear dynamical systems and the other from stochastic dynamics to come up with two independent measures of stability. Both of these measures are used to demonstrate their potential as a design criteria which can be used by a ship designer. A comparison of the two methods for a variety of cases is undertaken to demonstrate the similar trends they exhibit.

Keywords: Parametric roll; 6-Degree of Freedom nonlinear time domain simulation; Roll damping; Ergodicity; Parametric response of spar platforms; Improved Grim effective wave; Volterra GM method, Volterra GZ method, Nonlinear dynamical systems; Melnikov analysis; Rate of phase space flux; Stochastic averaging; Markov approximation; Mean first passage time; Lyapunov exponent; Reliability analysis; Short term and long term analysis.

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