Analysis of roll motion and stability of a fishing vessel in head seas

The present paper describes an investigation on the relevance of parametric resonance for a typical fishing vessel in head seas. Results for different Froude numbers are discussed based on experimental, numerical and analytical studies.The first region of resonance is investigated. Distinct wave amplitudes are considered. Some intense resonances are found to occur. The paper compares the experimental results with non-linear time simulations of the roll motion. Very good agreement is found, even when large motions take place.Finally, in order to analyze the experimental/numerical results, analytic consideration is given to distinct parameters affecting the dynamic process of roll amplification. The influence of heave, pitch, wave passage effect, speed and roll restoring characteristics are discussed.     

Stability of small fishing vessels in longitudinal waves

The dynamic stability of fishing vessels in longitudinal regular waves is investigated, both analytically and experimentally. In particular, the influence of stern shape on the parametric stability of fishing vessels is studied. Vessels TS and RS have very similar main characteristics, but their sterns are different. Although their linear responses are comparable, both analytical and experimental investigations indicate substantial differences in their dynamic stability in longitudinal regular waves. Strong resonances are found for the vessel with the deep transom. The analytical method takes into consideration the effects of the heave and pitch motions and wave passage and shows good agreement with experimental results. Stability limits are obtained for different conditions and are used as an aid in the discussion of the results obtained in the tests when relevant parameters are changed, such as wave amplitude and frequency, metacentric height and roll damping moment.     

On the development of ship anti-roll tanks

This paper reviews the development of ship anti-roll tanks from the 1880s to the present day including their modelling and control strategies. Mention is also made of other ship roll stabilization systems and the application of the technology to stabilization of other structures. The potential for the use of roll stabilization tanks on modern, high speed multi-hull craft which also have a low speed operational requirement is also discussed.     

Influence of non-linearities on the limits of stability of ships rolling in head seas

The present paper describes an investigation on parametric resonance in head seas in which a new third-order coupled mathematical model is considered. The restored modes of heave, roll and pitch are contemplated. The discussion is illustrated for the case of a transom stern fishing vessel at different speeds. It is pointed out that numerical simulations employing the new model are successfully compared to experimental results previously obtained for the vessel.Considering that analyticity is an important tool when handling complex stability issues, some theoretical dynamic characteristics of the equations are discussed. By means of the analysis of the coupled linear variational equation derived from an extended third-order model, the appearance of super-harmonics and increased rigidity proportional to wave amplitude squared due to third-order terms is demonstrated.In the present paper, an important tool is explored, that is the analysis of the limits of stability obtained from the new model. Limits of stability are a well-known and practical way of looking into the problem of parametric resonance. New limits of stability are derived and compared to the more conventional Strut diagram. Dynamic characteristics associated with the new limits of stability are discussed. The influence of different parameters is investigated, including vessel speed, damping and tuning. Consistent and revealing results are obtained through the analysis of the new limits of stability for different speeds and damping.     

On the parametric rolling of ships using a numerical simulation method

This paper has shown a numerical motion simulation method which can be employed to study on parametric rolling of ships in a seaway. The method takes account of the main nonlinear terms in the rolling equation which stabilize parametric rolling, including the nonlinear shape of the righting arm curve, nonlinear damping and cross coupling among all 6 degrees of freedom. For the heave, pitch, sway and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonlinear motion equations coupled with the other 4 degrees of freedom. For computing righting arms in seaways, Grim's effective wave concept is used. Using these transfer functions of effective wave together with the heave and pitch transfer functions, the mean ship immersion, its trim and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle. The nonlinear damping moment and the effect of bilge keels are also taken into account. The numerical simulation tool has shown to be able to model the basic mechanism of parametric rolling motions. Some main characteristics of parametric rolling of ships in a seaway can be good reproduced by means of the method. Comprehensive parametric analyses on parametric rolling amplitude in regular waves have been carried out, with that the complicated parametric rolling phenomena can be understood better.     

Head-wave parametric rolling of a surface combatant

Complementary CFD, towing tank EFD, and nonlinear dynamics approach study of parametric roll for the ONR Tumblehome surface combatant both with and without bilge keels is presented. The investigations without bilge keels include a wide range of conditions. CFD closely agrees with EFD for resistance, sinkage, and trim except for Fr>0.5 which may be due to free surface and/or turbulence modeling. CFD shows fairly close agreement with EFD for forward-speed roll decay in calm water, although damping is over/under predicted for largest/smaller GM. Most importantly CFD shows remarkably close agreement with EFD for forward-speed parametric roll in head waves for GM=0.038 and 0.033 m, although CFD predicts larger instability zones at high and low Fr, respectively. The CFD and EFD results are analyzed with consideration ship motion theory and compared with Mathieu equation and nonlinear dynamics approaches. Nonlinear dynamics approaches are in qualitative agreement with CFD and EFD. The CFD and nonlinear dynamics approach results were blind in that the actual EFD radius of gyration k_xx was not known a priori.     

On unstable ship motions resulting from strong non-linear coupling

In this paper, the modelling of strong parametric resonance in head seas is investigated. Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are contemplated. A third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are analytically derived in terms of hull form characteristics.The main theoretical aspects of the new model are discussed. Numerical simulations obtained from the derived third-order non-linear mathematical model are compared to experimental results, corresponding to excessive motions of the model of a transom stern fishing vessel in head seas. It is shown that this enhanced model gives very realistic results and a much better comparison with the experiments than a second-order model.     

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 Mathieu's equation. A basis for comparing parametric roll behavior for different representations of restoring is established. Asymmetric variation laws and bi-chromatic waves are considered.     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.     

A Lagrangian approach to nonlinear modeling of anti-roll tanks

This paper presents two novel nonlinear models of u-shaped anti-roll tanks for ships, and their linearizations. In addition, a third simplified nonlinear model is presented. The models are derived using Lagrangian mechanics. This formulation not only simplifies the modeling process, but also allows one to obtain models that satisfy energy-related physical properties. The proposed nonlinear models and their linearizations are validated using model-scale experimental data. Unlike other models in the literature, the nonlinear models in this paper are valid for large roll amplitudes. Even at moderate roll angles, the nonlinear models have three orders of magnitude lower mean square error relative to experimental data than the linear models.     

Prediction potential of the parametric rolling behaviour of a post-panamax containership

A systematic investigation on the prediction of parametric rolling exhibited by a post-panamax containership is described, on the basis of several techniques. Analytical formulae that appear in current industrial guidelines are evaluated in a step-by-step process against various numerical predictions. The method of continuation of nonlinear dynamics is introduced in order to expedite the identification of the instability boundary and the prediction of steady amplitudes of roll oscillation. A well-known panel code is shown to be capable of reproducing parametric roll growth.     

Using wavelet transforms to analyze nonlinear ship rolling and heave-roll coupling

The use of wavelet transforms is explored to investigate the nonlinear dynamical characteristics of ship roll and coupled heave-roll motion. The harmonic character, double period character and chaotic character are observed via a time–frequency window of the wavelet transform. Typical wave parameters in different stability regions are considered. Features such as restoring rolling, divergence rolling, steady state and chaotic responses of ship roll are obtained as well. The investigation in this paper not only highlights the feasibility of using wavelet transforms in the analysis of nonlinear dynamic characteristics of ship rolling in waves, but also shows how it could enhance the analysis abilities.     

Theoretical, numerical and experimental study on the problem of ergodicity and ‘practical ergodicity’ with an application to parametric roll in longitudinal long crested irregular sea

This paper addresses the problem of ergodicity of stochastic processes starting from a theoretical point of view, with the aim of obtaining a deeper understanding for practical applications. The problem is tackled bearing in mind the concept of ‘practical ergodicity’, that is, the possibility of obtaining reliable information about ensemble averages by using temporal averages. Some general analytical tools are given to address the problem of accuracy of temporal averages and an example of their use in a possible design of experiments is given. A series of Monte Carlo numerical simulations are performed by means of an analytical non-linear 1.5-DOF model of parametrically excited roll motion. The outcomes of such simulations are analysed to show the effect of ship speed and sea spectrum shape. The effect of wave grouping phenomenon is discussed with particular attention to the Doppler effect. Qualitative indications given by the numerical simulations are then compared with experimental tests showing a good agreement. Practical ergodicity of generated sea in towing tank is also briefly addressed.     

Simplified model for predicting the onset of parametric rolling

The world container fleet shows the fastest growth of any ship type. The infrastructure for loading and unloading container ships are also growing in many ports around the world. Such a trend is due to the fact that the containerized transportation is becoming more and more attractive due to many factors. The increasing demand in container transportation is met by use of more number of container ships including Post-Panamax and Malacca-max containers. Loss of containers in seas and accidents of container vessels are reported from many parts of seas. New generation containers are severely hit by parametric rolling. Pure loss of stability, due to exponential increase of roll in either broaching—to or head sea conditions, is called parametric rolling, is subjected to rigorous investigation by many researchers. Algebraic expression based on well known Duffing's method is proposed for solutions in parametric rolling. The variation in GM and damping values from trough to crest conditions associated with bow flare immersion and emergence in head sea conditions with pitch resonance with the heading waves are said to be the prime reason for parametric rolling. A simple model to predict the beginning of parametric rolling is described in this paper.     

Application of the extended Melnikov's method for single-degree-of-freedom vessel roll motion

Traditionally, when using Melnikov's method to analyze ship motions, the damping terms are treated as small. This is typically true for roll motion but not always true for other and/or multiple degrees of freedom. In order to apply Melnikov's method to other and/or multiple-degree-of-freedom motions, the small damping assumption must be addressed. In this paper, the extended Melnikov method is used to analyze ship motion without the constraint of small linear damping. Two roll motion models are analyzed here. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is the model with biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of this method is demonstrated.     

On the parametric resonance of container ships

This work deals with parametric resonance which poses a great danger especially for container ships sailing in following or head seas. Important parameters that are effective in roll resonance are pointed out. For this purpose, a containership is taken as an example to analyze its stability in longitudinal waves based on the method worked out by American Bureau of Shipping (ABS). Unfavorable sailing conditions such as heading and speed, which directly depend on the environmental conditions, have been determined for this particular ship. These conditions may be reported to the master to guide him to keep his ship out of parametric resonance zones. Numerical details of the procedure have been worked out and provided as well.     

The effect of nonlinear damping and restoring in ship rolling

Many researchers have studied a wide range of nonlinear equations of motion describing a ship rolling in waves. In this study, a form of nonlinear equation governing the motion of a rolling ship subjected to synchronous beam waves is suggested and solved by the generalized Duffing's method in the frequency domain. Various representations of damping and restoring terms found in the literature are investigated and their solutions are analyzed by the above-mentioned method. Comparative results of nonlinear roll responses are obtained for four distinct vessel types at resonance conditions which constitute the worst situation. The results indicate the importance of roll damping and restoring, when constructing a nonlinear roll model. An inappropriate selection of damping and restoring terms may lead to serious discrepancies with reality, especially in peak roll amplitudes.     

An Experimental Investigation on the Dynamic Response of a Damaged Ship with a realistic arrangement of the flooded compartment

The dynamics of a damaged ship in waves is a complex phenomenon regarding fluid and structure interactions. Flooded water motions in the damaged compartment could be influenced by decks, obstructions and obstacles in the compartment. This becomes particularly relevant in case of flooding in the engine room that is usually characterized by the presence of large objects such as engines and machineries. In such cases the possibility to better understand the behavior of a damaged ship, influenced by the fluid and structure interactions, could provide novel outcomes and thus enhance the damaged ship safety.In this paper an experimental campaign is conducted on a passenger ferry hull. The effects of obstacles in the engine room compartment, such as decks and engines, on ship roll responses, are studied. Roll decay in still water and steady roll responses in beam regular waves at zero speed are measured for the empty compartment and for the compartment with obstructions, as defined above.The main outcomes from the conducted experiments disclose a mitigation of the resonant behavior of the coupled system, ship with damaged compartment, by having engine shapes occupying the flooded engine room. Moreover it is possible to observe how the resonant frequency of the ship modifies having a more realistic arrangement of damaged compartment and how motion RAOs and roll decay characteristics modify accordingly.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

An experimental investigation into the influence of the damage openings on ship response

Ship motions after damage are difficult to evaluate since they are affected by complex phenomena regarding fluid and structures interactions. The possibility to better understand how ship behavior in damage is influenced by these phenomena is important for improving ship safety, especially for passenger vessel.In this paper an experimental campaign is carried out on a passenger ferry hull, to show the effects of the water dynamics across damage openings on ship motions. Novel aspects of this research include the study of the effects of the damage position on the ship roll response. The study is carried out for still water and for beam regular waves at zero speed.Results from the experiments carried out underline that the roll behavior of a damaged ship is affected by the position of damage opening and not only by its size. Assuming the same final equilibrium conditions after flooding but characterized by different damage openings it is possible to observe how motions RAOs and roll decay characteristics modify according to the opening locations.