Mathematical Modelling of Roll Motion for a Floating Body in Regular Waves Using Frequency Based Analysis with Speed

This paper deals with the mathematical modelling and frequency-based analysis for uncoupled roll motions of a floating body in regular waves with the variation of speed. First we compute hydrodynamic coefficients by using strip theory formulation. Considering sinusoidal wave with frequency (ω) varying between 0.3 to 1.2 acts on beam to the floating body for zero and non-zero forward speed (U=0 and 12 m/s) governing equation is obtained. Using the normalization procedure and frequency based analysis; group based equations are formulated for each case. Based on relative importance of the hydrodynamic coefficients, analytical solutions are derived for zero and non-zero forward speed. The sensitivity analysis with respect to the effect of damping is also investigated. This study could be useful to understand the effect of waves on roll motion due to the variation of speed for various frequencies.