In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds The ingredients of the formulation are comprised of three main components These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification

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Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch

Designing against parametric instability in following seas

Abstract Parametrically excited roll motion has become a relevant technical issue, especially in recent years, due the increasing number of accidents related to this phenomenon. For this reason, its study has attracted the interest of researchers, regulatory bodies and classification societies. The objective of this thesis is the developing of nonlinear analytical models able to provide simplified tools for the analysis of parametrically excited roll motion in longitudinal regular and irregular long crested waves. The sought models will take into account the nonlinearities of restoring and of damping, in order to try filling the gap with the analytical modelling in beam sea. In addition, semi-empirical methodologies will be provided to try extending the usual static approach to ship stability based on the analysis of GZ curve, in a probabilistic framework where the propensity of the ship to exhibit restoring variations in waves is rationally accounted for. The thesis addresses three main topics: the modelling of parametric roll in regular sea (Chapter 2 to Chapter 5), the modelling of parametric roll motion in irregular long crested sea (Chapter 6 and Chapter 7) and the extension of deterministic stability criteria based on the analysis of geometrical GZ curve properties to a probabilistic framework (Chapter 8). Chapter 1 gives an introduction, whereas Chapter 9 reports a series of final remarks. For the regular sea case an analytical model is developed and analysed both in time domain and in frequency domain. In this latter case an approximate analytical solution for the nonlinear response curve in the first parametric resonance region is provided by using the approximate method of averaging. Prediction are compared with experimental results for four ships, and the analytical model is investigated with particular attention to the presence of multiple stable steady states and the inception of chaotic motions. The influence of harmonic components higher than the first one in the fluctuation of the restoring is also investigated. In the case of irregular sea, the Grim's effective wave concept is used to develop an analytical model for the long crested longitudinal sea condition, that allows for an approximate analytical determination of the stochastic stability threshold in the first parametric resonance region. Experimental results are compared with Monte Carlo simulations on a single ship, showing the necessity of a tuning factor reducing the hydrostatically predicted magnitude of parametric excitation. The non-Gaussianity of parametrically excited roll motion is also discussed. Finally, on the basis of the analytical modelling of the restoring term in irregular waves, an extension of the classical deterministic approach to ship static stability in calm water is proposed, to take into account, although is a semi-empirical form, restoring variations in waves. Classical calm water GZ curve is then extended from a deterministic quantity to a stochastic process. By limiting the discussion to the instantaneous ensemble properties of this process, it is shown how it is possible to extend any static stability criterion based on the geometrical properties of the GZ curve, in a rational probabilistic framework taking into account the actual operational area of the ship and the propensity of the ship to show restoring variations in waves. General measures of restoring variations are also discussed, such as the coefficient of variation of metacentric height, restoring lever and area under GZ . Both the short-term and long-term point of view are considered, and the method is applied to three different ships in different geographical areas.Parametrically excited roll motion has become a relevant technical issue, especially in recent years, due the increasing number of accidents related to this phenomenon. For this reason, its study has attracted the interest of researchers, regulatory bodies and classification societies. The objective of this thesis is the developing of nonlinear analytical models able to provide simplified tools for the analysis of parametrically excited roll motion in longitudinal regular and irregular long crested waves. The sought models will take into account the nonlinearities of restoring and of damping, in order to try filling the gap with the analytical modelling in beam sea. In addition, semi-empirical methodologies will be provided to try extending the usual static approach to ship stability based on the analysis of GZ curve, in a probabilistic framework where the propensity of the ship to exhibit restoring variations in waves is rationally accounted for. The thesis addresses three main topics: the modelling of parametric roll in regular sea (Chapter 2 to Chapter 5), the modelling of parametric roll motion in irregular long crested sea (Chapter 6 and Chapter 7) and the extension of deterministic stability criteria based on the analysis of geometrical GZ curve properties to a probabilistic framework (Chapter 8). Chapter 1 gives an introduction, whereas Chapter 9 reports a series of final remarks. For the regular sea case an analytical model is developed and analysed both in time domain and in frequency domain. In this latter case an approximate analytical solution for the nonlinear response curve in the first parametric resonance region is provided by using the approximate method of averaging. Prediction are compared with experimental results for four ships, and the analytical model is investigated with particular attention to the presence of multiple stable steady states and the inception of chaotic motions. The influence of harmonic components higher than the first one in the fluctuation of the restoring is also investigated. In the case of irregular sea, the Grim's effective wave concept is used to develop an analytical model for the long crested longitudinal sea condition, that allows for an approximate analytical determination of the stochastic stability threshold in the first parametric resonance region. Experimental results are compared with Monte Carlo simulations on a single ship, showing the necessity of a tuning factor reducing the hydrostatically predicted magnitude of parametric excitation. The non-Gaussianity of parametrically excited roll motion is also discussed. Finally, on the basis of the analytical modelling of the restoring term in irregular waves, an extension of the classical deterministic approach to ship static stability in calm water is proposed, to take into account, although is a semi-empirical form, restoring variations in waves. Classical calm water GZ curve is then extended from a deterministic quantity to a stochastic process. By limiting the discussion to the instantaneous ensemble properties of this process, it is shown how it is possible to extend any static stability criterion based on the geometrical properties of the GZ curve, in a rational probabilistic framework taking into account the actual operational area of the ship and the propensity of the ship to show restoring variations in waves. General measures of restoring variations are also discussed, such as the coefficient of variation of metacentric height, restoring lever and area under GZ . Both the short-term and long-term point of view are considered, and the method is applied to three different ships in different geographical areas.

Development of analytical nonlinear models for parametric roll and hydrostatic restoring variations in regular and irregular waves

Parametric rolling is a phenomenon of instability of a ship's upright state that can be realised in a longitudinal seaway and often leads to an oscillatory roll motion with moderate or large amplitude. In recent years it has been brought to the centre of attention following an accident and a discussion has been opened about the possibility of the adoption of relevant design criteria. Among ship parameters, roll damping has been singled out as the key factor governing the propensity toward this behaviour. This paper presents a review of the state of the art covering the various facets of parametric rolling for a deterministic, as well as for a probabilistic, environment. Furthermore, some new ideas about the development of practical design criteria are presented, based on the interfacing of deterministic transient responses with the probabilistic characteristics of wave groups.

http://shipdynamics.ntua.gr/publications/Oceanic_Engineering_International_2005_Spyrou.pdf

Design Criteria for Parametric Rolling

The influence of floating ice on the dynamic behavior of ships and offshore structures depends on many factors such as ice thickness and its relative speed with respect to the floating structure. The ice resistance to ship motion forms an essential problem in ship design and navigation. Furthermore, local or global ice loads acting on ocean systems are random and nonsmooth when impact interaction takes place. Impact loads on the bow of a ship navigating in solid ice may be modeled by a Poisson law. The measured stress amplitudes on the ship frame at the bow follow an exponential distribution. The nonhomogeneity and difference in ice microstructure, as well as the influence of salt and temperature, result in a great uncertainty in the ice strength. Therefore, the current review article aims at assessing the ice related problems encountered by offshore structures as well as by ships during their navigation. It also discusses the impacts of local and global ice loads on floating structures and reviews their existing probabilistic models. Moreover, this article covers the dynamic interaction of ice with flexible and rigid structures, and ships. In view of ice loads on marine systems, new design regulations have been introduced by international organizations that are involved in the design and building of ships as well as offshore structures. The ship stochastic stability and the first-passage roll stabilization problem associated with random ocean waves will also be described in an attempt to stimulate future research work dealing with ice impact loads. Moreover, due to the lack of research activities addressing the control problem of ships operating in icy waters, the current article will briefly discuss passive and active control schemes developed for controlling the ship roll motion. There are 529 references cited in this review article.

P.K. Muhuri

Papers

A study of the stability of the rolling motion of a ship in an irregular seaway