Modelling and analysis of coupled nonlinear oscillations of a floating body in two degrees of freedom

Abstract

We describe a mathematical model to investigate the effect of coupled nonlinear oscillations of a floating body in time domain under the influence of sinusoidal waves. To account for hydrodynamic forces, a mathematical formulation for added mass moments of inertia, damping and restoring moments is presented for roll and yaw. Using perturbation technique, we obtain order wise solutions in the normalized domain wherein the assumption on small distortion holds. On applying Laplace transform, a zeroth-order solution is obtained in closed form whereas for higher order solutions we resort to the Runge-Kutta method with adaptive step size algorithm. For analyzing the model result we perform numerical experiments for a vessel of mass 19190 tons under the action of a beam wave of frequency 0.74 rad/sec and 1.0 m wave height. The validity of the numerical scheme is checked by comparing with the analytical solution for uncoupled zeroth-order roll and then we proceed to examine the effect of coupled behavior of roll and yaw for higher-order approximations. The inter-dependence between wave frequency (ω), system frequency (β) and damping factor (ζ) is obtained to reveal system stability. Model results indicate an artificial increase in amplitude for uncoupled roll, and also emphasize the contribution of viscous damping in roll in contrast to added mass in yaw.