Determination of motion of a floating body with respect to the variations in degrees of freedom:An analytical study

The paper investigates the motion response of a floating body under the action of small amplitude regular waves and determines the influence of uncoupled as well as coupled systems through an analytical approach. The governing equations of motion describing the overall balance between the wave-exciting force with the linear form of inertial, damping and restoring forces are transformed into frequency domain by applying Laplace transform technique. The closed-form solution is sought for three specific cases: (i) Case I: when only the roll motion is considered, (ii) Case II: when coupled roll and yaw motions are considered and (iii) Case III: when coupled sway, roll and yaw are considered. To get an insight, we consider a floating body of displacement 19,190 tonnes under the action of beam waves with wave frequencies 0.56 and 0.74 rad/s. The analytical result indicates that roll amplitude increases with the increase of vessel speed for the case of single degree of freedom. All three motions show harmonic behaviour and attain dynamic equilibrium for time t > 100 s. Model result indicates that the reduction in degrees of freedom enhances phase lag and exhibits artificial increase in amplitude for roll. The importance of this study lies in terms of obtaining closed-form solution for a linear system while evaluating damping factor and critical encountering frequency for uncoupled and coupled motions.