Regular Beam Seas Research Articles

A Systematic Approach to Modeling Nonlinear Multi-DOF Ship Motions in Regular Seas

The modeling and dynamics of nonlinear, large-amplitude motions of vessels in regular beam seas are studied. By using a wave-fixed coordinate system, a three-degree-of-freedom ship model which contains roll, sway, and heave motions is obtained. This model systematically includes various factors that contribute to ship motions. After nondimensionalization and rescaling, it is transformed into a form that is amenable to analysis that takes advantage of various time scales in the problem. This analysis provides a systematic reduction of the full system to a single-degree-of-freedom (DOF) dynamics problem in which roll is dominant. The analysis is based on invariant manifold theory of dynamical systems, and allows one to account for coupling to the quasi-static heave dynamics and the sway velocity. Numerical simulations of a model for a typical fishing vessel are presented and demonstrate that the traditional single DOF roll model represents approximately the dynamics on a special subset—an invariant manifold—of the higher dimensional state space of the full three-DOF model. This work points the way towards a systematic means of modeling general, large-amplitude motions of vessels in a variety of sea states.

A Note on the Computation of Maximum Roll Amplitudes in Regular Beam Seas

Generalized methods for deriving the harmonic balance equations are illustrated using a ship roll model with angle dependent cubic damping, and cubic stiffness terms. The balance equations are then solved subject to a phase constraint which identifies the resonant solution only. The amplitude of the response at resonance, and the frequency at which resonance occurs, can therefore be obtained without needing to compute the response over a wide frequency range. This provides an efficient tool for investigating the dependence of the resonant response on the level of input excitation, with results which agree well with more time-consuming simulation methods.

On the effectiveness of constant coefficients roll motion equation

As known, the rolling motion characteristics, amplitudes and accelerations, greatly influence the ability of a ship to operate and survive in bad weather. On the other hand, traditional computer codes for seakeeping calculations fail the forecasting of large amplitude rolling. There is a great need of using semi-empirical damping models and coefficients. This stresses the importance of campaigns of measurements as described in the paper, to get a deeper insight into the physical-mathematical modelling of the different contributions to rolling equation. Experimental tests on nonlinear rolling in a regular beam sea of a Ro-Ro ship model have been conducted by varying both the wave steepness and the wave frequency. The use of a parameter estimation technique, based on the least squares fitting of the stationary numerical solution of the nonlinear rolling motion differential equation, allowed to obtain informations on the damping model and on the linear and nonlinear damping coefficients. These exhibit a quite strong dependence on frequency that reduces the efficiency of constant coefficients rolling equation to simulate large amplitude nonlinear rolling. The results indicate that a good quality prediction model of nonlinear rolling cannot be based on constant coefficients time domain simulations. These can infact lead to incorrect estimates of rolling amplitudes even when the parameters have been obtained through high level parameter estimation procedures based on experimental data. The analysis indicates also a marked dependence of the effective wave slope coefficient on wave amplitude. The introduction of both these dependences on the rolling equation allows to reproduce the experimental results with great accuracy even at large amplitudes.

Stability and Complicated Rolling Responses of Ships in Regular Beam Seas

An analytical procedure is presented for the prediction of the stability and complicated responses of a vessel rolling in regular seas. The effectiveness of the technique is demonstrated by considering unbiased and biased ships rolling in regular beam seas, where the relative waveslope and the frequency of encounter can be alternatively changed. The procedure generates bifurcation diagrams showing the regions of the parameter space where instabilities and deterioration of seaworthiness occur so that the designer can assess the dangers and overall seaworthiness of the craft under a variety of sea conditions.

Predicting Incipient Jumps to Resonance of Compliant Marine Structures in an Evolving Sea-State

When monitoring the wave-driven motions of a compliant offshore facility, be it an articulated mooring tower or a vessel, the engineer would like to be able to predict, in real time, any incipient jump to resonance that might be imminent due to the slowly evolving sea-state. We explore in this paper a study of some new possible prediction techniques for both a jump to a main fundamental resonance leading to capsize and a flip bifurcation to a subharmonic resonance. Stroboscopic Poincare´ mapping techniques based on discrete time sampling are used to give information about the approach to instability. The first application of these techniques is in the prediction of the jump in resonance and consequent capsize at a cyclic fold in the roll response of a vessel in regular beam seas. Secondly, the techniques are shown to work extremely well in a variety of computational situations when applied to the simulation of an articulated mooring tower during the approach to the potentially dangerous oscillations produced by the onset of subharmonic resonance at a flip bifurcation, in both regular and irregular ocean waves.

The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas

The rolling motion of a ship has been successfully modelled using a semi-empirical nonlinear differential equation by a number of researchers. Experimental data has been used to model nonlinear damping and righting lever characteristics and comparison with observed behaviour has been reasonably good. The present article describes a numerical, phenomenological approach to analyse this type of behaviour. The stability of the periodic motion, and in particular the possibility of capsize, is explored with reference to qualitative prediction techniques. The appearance of chaotic motions in regular beam seas is a new feature which should be of interest to designers. The inability of traditional quantitative methods, such as the perturbation technique, to detect chaos is a further justification for using numerical simulation guided by dynamical systems theory.

A multiscale analysis of nonlinear rolling

Abstract A new analysis of nonlinear rolling carried out by the multiscale perturbation method is herewith presented. The behaviour of a ship in a regular beam sea is considered and approximate analytical solutions in three nonlinear resonance regions are obtained. These concern the transient and the steady state roll oscillations. The latter fits in well with a previous one obtained through the averaging method and with the results of the numerical simulation. The obtained results appear to be particularly convenient due to their major mathematical simplicity. Moreover, they allow a simple estimation of the maximum roll amplitudes predictable for a given excitation intensity.

Nonlinear rolling of ships in regular beam seas

A second-order approximate solution is obtained for the nonlinear established harmonic roll of a ship in regular beam seas. The perturbation solutions are compared with solutions obtained by numerically solving the nonlinear governing equations. The

A stochastic model for the effect of wind on the roll of a ship

Most stochastic models so far devoted to ship motions are of the stationary type. In order to provide a non-stationary model representing the action of wind on ship motions the Authors have examined a stochastic non-stationary model for the effect of a Poisson-distributed wind on the roll of a ship in a regular beam sea; as a result of the examination, a majorizing function for the probability of capsizing was obtained and the results applied to a small cargo ship.

Slowly Varying Oscillations of Moored Vessels in Beam Seas (Part II)

This paper is mainly aimed to study the phenomena of slowly varying oscillations of moored vessels and to state the procedures for predicting their values in wind and waves.Model tests were conducted at IHI's ship model basin on the motions of a floating vessel moored by coil springs in regular and transient water waves, and theoretical calculations of dynamic behaviors of a moored vessel including slowly varying transient sway motions were also carried out. As a result of the studies, the following conclusions were reached;1. Slowly varying oscillations of moored vessels exist as transient sway motions for a long period in regular beam seas, which are directly propotional to the steady-state displacement due to the wave drifting forces.2. The calculation and the test results are in fairly good agreement showing the procedures for predicting slowly varying transient sway motions in regular beam seas.3. Slowly varying transient sway motions also exist in transient water waves after the time when the transient water waves pass through.

Slowly Varying Oscillations of Moored Vessels in Beam Seas (Part I)

This paper is mainly aimed to study the phenomena of slowly varying oscillations of moored vessels and to state the procedures for predicting their values in wind and waves.Model tests were conducted at IHI's ship model basin on the motions of a floating vessel moored by coil springs in regular and transient water waves, and theoretical calculations of dynamic behaviors of a moored vessel including slowly varying transient sway motions were also carried out. As a result of the studies, the following conclusions were reached;1. Slowly varying oscillations of moored vessels exist as transient sway motions for a long period in regular beam seas, which are directly propotional to the steady-state displacement due to the wave drifting forces.2. The calculation and the test results are in fairly good agreement showing the procedures for predicting slowly varying transient sway motions in regular beam seas.3. Slowly varying transient sway motions also exist in transient water waves after the time when the transient water waves pass through.