International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 41, Pages 2181-2197

Determination of coupled sway, roll, and yaw motions of a floating body in regular waves

S. N. Das1 and S. K. Das2

1Central Water and Power Research Station, Khadakwasla, Pune 411 024, Maharashtra, India
2Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan

Received 21 May 2003

Copyright © 2004 S. N. Das and S. K. 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.


This paper investigates the motion response of a floating body in time domain under the influence of small amplitude regular waves. The governing equations of motion describing the balance of wave-exciting force with the inertial, damping, and restoring forces are transformed into frequency domain by applying Laplace transform technique. Assuming the floating body is initially at rest and the waves act perpendicular to the vessel of lateral symmetry, hydrodynamic coefficients were obtained in terms of integrated sectional added-mass, damping, and restoring coefficients, derived from Frank's close-fit curve. A numerical experiment on a vessel of 19190 ton displaced mass was carried out for three different wave frequencies, namely, 0.56 rad/s, 0.74 rad/s, and 1.24 rad/s. The damping parameters (ςi) reveal the system stability criteria, derived from the quartic analysis, corresponding to the undamped frequencies (βi). It is observed that the sway and yaw motions become maximum for frequency 0.56 rad/s, whereas roll motion is maximum for frequency 0.74 rad/s. All three motions show harmonic behavior and attain dynamic equilibrium for time t>100 seconds. The mathematical approach presented here will be useful to determine seaworthiness characteristics of any vessel when wave amplitudes are small and also to validate complex numerical models.