Mathematical model for coupled roll and yaw motions of a floating body in regular waves under resonant and non-resonant conditions

Abstract

The prediction of resonance is very important with respect to the vessels stability in the early stages of design. In this paper, an efficient modeling approach is presented to determine coupled roll and yaw motions of a symmetric and slender floating body when the influences of small amplitude regular waves are dominant. The angular motions described in time domain by considering all internal and external forces are transformed into frequency domain to obtain motion characteristics. We adopt a semi-analytical treatment to obtain roll and yaw motions and derive system instability due to roll resonance. To compute hydrodynamic forces, we employ strip theory method where frequency dependent sectional added-mass, damping and restoring coefficients are derived from the FrankÕs close-fit curve. Numerical experiments carried out for a vessel of mass 19,190 ton under the action of wave of frequencies 0.56 and 0.76 rad/s with zero and non-zero initial conditions are reported and the effect of various parameters on system stability is investigated. Model results indicate that damping factor (1) plays a pivotal role when wave encountering frequency (x) and undamped natural frequency (b) are nearly equal. The essence of this study lies in the efficient modeling technique to evaluate damping factor and critical encountering frequency regime for a given ship particulars when experimentally derived resonance zone is absent.

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

“…where f 40 (s) and f 60 (s) are the angular displacements and α i , β i , and γ i are the corresponding coefficients. The detailed solution procedure can be obtained from the investigations of Das and Das [23]. After solving two equations of (4.4), we obtain…”

“…This scheme controls the growth of rounding errors efficiently and is stable with respect to the nonlinearity. The detailed description of model development and its validation are given in [23]. A computer program "SHIPMOT-RY-N" consisting of three main modules and several submodules is developed to implement detailed computational procedures of roll and yaw motions.…”

A new approach for measurement of pitch, roll and yaw angles based on a circular feature

“…In the field of shipping, research on the motion of the ship, especially the motion of roll and yaw, are significant for the safety of ship (Das and Das, 2005). The three angles were also used in the field of orthodontic diagnosis and treatment planning (Ackerman et al, 2007).…”

CFD prediction of ship capsize

“…Das and Das (2004) studied the harmonic response of a floating body by developing a mathematical model for coupled sway, roll and yaw motions. They simplified their method for coupled roll and yaw motions to study roll resonance excitation in beam waves (Das and Das, 2005). Bifurcation is studied by Eissa and EI-Bassiouny (2003) applying method of multiple time scales to study rolling response of a ship in regular beam seas.…”