Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 96373, 17 pages
Research Article

Modeling of Coupled Roll and Yaw Damping of a Floating Body in Waves

S. K. Das1 and S. N. Das2

1CFD-AIT Program, International Institute of Information Technology (I2IT), P-14 Pune Infotech Park, Hinjewadi, Pune 411 057, India
2Central Water and Power Research Station, Khadakwasla, Pune 411 024, India

Received 20 April 2005; Revised 21 November 2006; Accepted 28 February 2007

Academic Editor: Semyon M. Meerkov

Copyright © 2007 S. K. Das and S. N. Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.