Kostas J. Spyrou

Designing against parametric instability in following seas

We investigate the characteristics of parametric instability when very large variations of restoring between the wave trough and the wave crest are taking place, creating a restoring that is alternating between negative (or nearly negative) and strongly positive values. The possible ways to consider the nonlinearities in damping and in restoring are discussed in detail. The boundary separating parametric instability from pure-loss is identified. In depth studies are carried out to ascertain the practical relevance of the parametric mechanism. Instability regions are identified in terms of transient motions, rather than in terms of the customary asymptotic stability chart associated with Mathieus equation. A basis for comparing parametric roll behavior for different representations of restoring is established. Asymmetric variation laws and bi-chromatic waves are considered.

The nonlinear dynamics of ship motions: a field overview and some recent developments

This opening article of the issue is intended to provide a review of the field of nonlinear ship dynamics and to demonstrate the importance of the subject in the context of naval architecture. A list of relevant research topics that have received attention in recent years is included in the first section of the paper. This sets the scene for a brief discussion about the content and contribution of the articles that make up the Theme Issue. In order to facilitate understanding by non-specialists, we include an outline of the general concepts of nonlinear dynamics. Furthermore, we provide a detailed review of the evolution of ship research of the considered type since the 1970s, including a rather lengthy bibliography. We discuss the latest ideas about ship capsize and we include a special section summarizing the recent advances with regard to the mechanisms of ship capsize in astern seas. We close the article by offering some ideas about future directions for research.

Review of Available Methods for Application to Second Level Vulnerability Criteria

The International Maritime Organization (IMO) has begun work on the development of next generation intact stability criteria. These criteria are likely to consist of several levels: from simple to complex. The first levels are expected to contain vulnerability criteria and are generally intended to identify if a vessel is vulnerable to a particular mode of stability failure. These vulnerability criteria may consist of relatively simple formulations, which are expected to be quite conservative to compensate for their simplicity. This paper reviews methods which may be applicable to the second level of vulnerability assessment, when simple but physics-based approaches are used to assess the modes of stability failure, including pure-loss of stability, parametric roll, surf-riding, and dead-ship condition.

Homoclinic connections and period doublings of a ship advancing in quartering waves

The large-amplitude motions of a ship running in waves are analyzed with a mathematical model reduced to a system of eight coupled nonlinear ordinary differential equations. Bifurcation analysis in relation to the surf-riding condition, with control parameter the angle of the rudder, shows the existence of a region of oscillatory behavior, containing also a chaotic domain. This region ends with a homoclinic connection and a dangerous jump toward the overtaking-wave mode, which can incur ship capsize. Addition of linear control removes the chaotic domain while giving rise to new regions of oscillation. (c) 1996 American Institute of Physics.

On the parametric rolling of ships in a following sea under simultaneous nonlinear periodic surging

A new approach to the study of the parametric rolling of ships in a following sea is presented. The new aspect is the consideration of the interference of surge with the roll dynamics. When the waves are long and steep, the oscillatory component of the surge velocity can become large when compared with the mean value. As the oscillatory surge grows in amplitude, it tends also to become asymmetric due to the existence of nonlinearity. The nature of asymmetric surging is such that a ship spends more time on the crests than on the troughs of the waves. This means, however, that the probability of capsize is increased because a ships roll-restoring capability around the crest is at a minimum. We propose a new second-order differential equation of roll which incorporates automatically the surge effect through appropriate position-dependent coefficients. We explore numerically how this asymmetry in surge influences the build up of parametric rolling. The layout of the stability transition lines of the coupled system was found to be notably different from that of a Mathieu-type system. We pay attention also to the vicinity of surf-riding, where the capsize is more of a ‘pure-loss’ type.

Surf-riding and oscillations of a ship in quartering waves

The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.

Updated vertical extent of collision damage

The probabilistic distribution of the vertical extent of collision damage is an important and somewhat controversial component of the proposed IMO harmonized damage stability regulations for cargo and passenger ships. The only pre-existing vertical distribution, currently used in the international cargo ship regulations, was based on a very simplified presumption of bow heights. This paper investigates the development of this damage extent distribution based on three independent methodologies; actual casualty measurements, world fleet bow height statistics, and collision simulation modeling. The results from the three methods are compared, and a proposed distribution for the new harmonized regulations is presented.

A Basis for Developing a Rational Alternative to the Weather Criterion: Problems and Capabilities

The feasibility of developing a practical ship dynamic stability criterion based on nonlinear dynamical systems’ theory is explored. The concept of “engineering integrity” and Melnikov’s method are the pillars of the current effort which can provide a rational connection between the critical for capsize wind/wave environment, the damping and the restoring characteristics of a ship. Some discussion about the dynamical basis of the weather criterion is given first before describing the basic theory of the new method. Fundamental studies are then carried out in order to ensure the validity, the potential and the practicality of the proposed approach for stability assessment of ships in a wider scale.

Nonlinear Dynamics of Ship Steering Behaviour Under Environmental Excitations

Theoretical investigations on the effect of wind on ship manoeuvring and course-keeping can be traced back to the days of wind sailing [1]. In the modern period the theme continued to attract attention due to its significance for ships that are characterised either by a high superstructure or by a substantial variation of their windage area between the full-load and ballast condition [2], [3], [4], [5], [6] and [7]. Especially when operating in or near restricted waters, wind loading could bear detrimental effects for ship safety. Nonetheless, one feels that deeper understanding about the nature of phenomena that determine the course stability and turning performance of ships, even in our days, is incomplete. From this perspective, in this paper will be presented some of our key research findings concerning the “horizontal-plane” nonlinear dynamics of a modern ferry subjected to strong unidirectional wind. In such an environment, deflection of the rudder serves dual purpose: either for setting the ship on turning motion; or for offsetting the wind effect so that a desired straight-line course is maintained. Knowledge of the domains of these principal types or response in state/parameter space and the possibility some conditions to play host to more complex types of behaviour is essential for eliciting the operational profile of the ship. A mathematical model was thus built by combining a detailed wind loading module with a standard hydrodynamic model of ship surge, sway, yaw and roll motions [8]. Course-keeping capability for any possible heading relatively to the wind was assessed firstly, by coupling the mathematical model with a well-known continuation algorithm. The stationary states that correspond to operation of the ship at specific headings were found to undergo stability changes: at saddle-nodes near to the beam wind condition; and at supercritical Hopf points that arise in head wind and lead to parasitic oscillatory yawing where the course is maintained in the mean. It was discovered that a “Bogdanov-Takens” phenomenon determines the highest wind velocity where the Hopf bifurcation can arise. Continuation of oscillatory yawing was

Simple Analytical Criteria for Parametric Rolling

Analytical design criteria are sought for predicting the parametric rolling behavior of ships, taking into account: the growth rate during the inception stage of parametric rolling; and the steady amplitude that is reached when regular parametric excitation is assumed. The connection with the shape of the restoring curve and the effect of roll damping are shown. The results of the current deterministic treatment are transferred to the domain of probabilistic analysis by use of the concept of wave groups which seems to provide a powerful basis for criteria development.