Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 96373, 17 pages
doi:10.1155/2007/96373
Abstract
A mathematical model is described to investigate the damping moment of
weakly nonlinear roll and yaw motions of a floating body in time domain
under the action of sinusoidal waves. The mathematical formulation for added
mass moment of inertia and damping is presented by approximating
time-dependent coefficients and forcing moments when small distortion holds.
Using perturbation technique, we obtain orderwise equations wherein the
closed-form solution is obtained for zeroth-order case, and for higher-order
cases we resort to numerical integration using Runge-Kutta method with
adaptive step-size algorithm. In order to analyze the model result, we
perform numerical experiment for a vessel of 19190 tons under the beam wave
of 1 m height and frequency 0.74 rad/s. Closer inspection in damping
analysis reveals that viscous effect becomes significant for roll damping;
whereas for yaw damping, contribution from added mass variation becomes
significant.