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This paper deals with the stability of an offshore barge when subjected to parametric rolling in longitudinal waves. The main aim of this paper is to understand the roll behaviour of an offshore barge under longitudinal waves, to predict the susceptibility of parametric rolling in longitudinal waves and to identify the region of instability when subjected to parametric rolling. The primary objective is to find the roll response of a geometrically modeled offshore barge in ANSYS AQWA for regular sea conditions followed by the calculation of roll response in a conservative way by the Linear Strip theory to validate with the results obtained from ANSYS AQWA. Two major cases were studied; once when the length of the waves is equal to the length of the barge and the other when the length of the encountering waves is four times the length of the barge The severity of the parametric rolling for the offshore barge is calculated by the mathematical modeling for solution of Mathieu's Differential equation using Matlab programming, taking in account the stability parameters for the offshore barge for which stability curves are plotted. This Graphical Ince-Strutt diagram was then verified by numerical modeling to illustrate the instability of barge. The boundary approximations for the instability zone for which frequencies prone to parametric roll resonance were identified and their threshold damping coefficient was then calculated.

This paper is the progressive research of the paper [1] titled "Stability of Offshore Barge Subjected to Parametric Rolling in Waves", and it deals with the boundary approximations for the instability zone of an offshore barge when subjected to parametric rolling in waves. The severity of the parametric rolling for the offshore barge is calculated by the mathematical modeling for solution of Mathieu's Differential equation using Matlab programming The frequencies prone to parametric roll resonance were identified and their threshold damping coefficient was then calculated. The susceptibility of parametric rolling including forward speed of ship was evaluated. Genetic Algorithm was implemented to find the most optimum angle of roll to enable us to determine the ratio of TCB to VCB for predefined upper limit of rolling

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