This research was done to develop tools to predict parametric roll motion of ships in regular and irregular sea and provide guidelines to avoid parametric roll during initial design stage. A post Panamax hull form (modified C11 Hull form, Courtesy of MARIN) was used to study parametric roll in ships. The approach of the study has been to simplify the roll equation of motion to a single degree of freedom equation so as to utilize the tools available to analyze the system retaining the non-linear character of the system. The Hill’ equation is used to develop highly accurate stability boundaries in the Ince-Strutt Diagram. The effect of non-linear damping has also been incorporated into the chart for the first time providing a simple method to predict the bounded roll motion amplitude. Floquet theory is also extended to predict parametric roll motion amplitude. Forward speed of the vessel has been treated as a bifurcation parameter and its effects studied both in head and following sea condition. In the second half of the research, parametric roll of the vessel in irregular sea is investigated using the Volterra Quadratic model. GM variation in irregular sea was obtained using transfer functions of the Volterra model. Heave and pitch coupling to roll motion was also studied using this approach. Sensitivity studies of spectral peak period and significant wave height on roll motion amplitude were also carried out. Forward speed effects were also evaluated using the Volterra approach. Based on the study, the Hill’s equation approach was found to give more accurate prediction of parametric roll in regular sea. The boundaries in the stability chart were more accurately defined by the Hill’s equation. The inclusion of non-linear damping in the stability chart gave reasonably accurate bounded motion amplitude prediction. The Volterra approach was found to be a good analytical prediction tool for parametric roll motion in irregular sea. Using the Volterra model, it was found that there is a high probability of parametric roll when the spectral modal period is close to twice the natural period of roll.

Parametric roll resonance is a dangerous resonance phenomenon affecting several types of ships, such as destroyers, RO-RO paxes, cruise ships, fishing vessels and especially container ships. Worst case, parametric roll is capable of causing roll angles of at least 50 degrees, and damage in the tens of millions of US dollars. Empirical and mathematical investigations have concluded that parametric roll occurs due to periodic changes in the waterplane area of the ship. If the vessel is sailing in longitudinal seas, with waves of approximately the same length as the ship, and encounter frequency of about twice the natural roll frequency, then parametric resonance can occur. While there is a significant amount of literature on the hydrodynamics of parametric roll, there is less on controlling and stopping the phenomenon through active control. The main goal of this thesis has been to develop controllers capable of stopping parametric roll. Two main results on control are presented. To derive, analyze and simulate the controllers, it proved necessary to develop novel models. The thesis thus contains four major contributions on modeling. The main results are (presented in order of appearance in the thesis): Six-DOF computer model for parametric roll One-DOF model of parametric roll for non-constant velocity Three-DOF model of parametric roll Seven-DOF model for ships with u-tanks of arbitrary shape Frequency detuning controller Active u-tank based controller for parametric roll

Modern Panamax Pure Car and Truck Carriers (PCTC) have become more vulnerable to critical roll responses as built in margins have been traded against increased transport efficiency. The research presented in this licentiate thesis aims at enhancing the predictability and control of these critical roll responses. The thesis presents the development of a new method for assessing the roll damping, which is a crucial parameter for predicting roll motions. The method involves a unique set up of full scale in-service trials and is straightforward, cost efficient and shows a good potential. The thesis also includes a demonstration of a new application for rudder control to be used for mitigation of parametric roll. This is performed by simulating real incidents that have occurred with PCTC’s in service. Simulations with rudder roll control show promising results and reveal that the approach could be very efficient for mitigation of parametric roll. Last but not least an approach for monitoring of roll induced stresses, so-called racking stresses in PCTC’s, is presented. The approach involves measurement of the ship motions and scaling of pre-calculated structural responses from global finite element analysis. Based on full scale motion and stress measurements from a PCTC in-service the approach is evaluated and demonstrated to be an efficient alternative to conventional methods. / <p>QC 20130424</p>

I samband med en växande befolkning och en ökande globalisering beslutadeinternationella sjöfartsorganisationen, IMO, att nya kriterier för stabilitet skulle in-föras. I de nya kriterierna beskrivs ett antal fenomen som kan orsaka haveri, dennarapport fokuserar på ett av dem, parametrisk rullning. Parametrisk rullning är ettfenomen som uppstår då stabiliteten hos ett fartyg varierar periodiskt. Den interna-tionella sjöfartsorganisationen definierar ett antal nivåer bestående av olika modellerför att undersöka risken för att parametrisk rullning ska uppstå och denna rapportbehandlar de första två nivåerna. Rapportens syfte var att bedöma om modellen,definierad av IMO, gick att implementera för att förutspå parametrisk rullning. Föratt modellera den första nivån i MATLAB byggdes ett program för att räkna utden rätande hävarmen som användes för att hitta jämvikter vilket gjordes med deninbyggda funktionen fzero. Samma program som konstruerades för den första ni-vån användes även på den andra nivån. Programmet utökades då den andra nivånevaluerades med en kvasistatisk modell som baserades på en, av IMO definierad, dif-ferentialekvation som löstes med den inbyggda funktionen ODE45. Resultatet frånden första och andra nivån jämfördes med, de av IMO definierade, referensvärdena.Resultaten visade att de två fartygen som tidigare uppvisat tecken på parametriskrullning överskred referensvärdena och de två fartygen som inte bör uppvisa någratecken på parametrisk rullning inte överskred referensvärdena. Slutsatsen blev alltsåatt modellen skapad av IMO korrekt bedömer om ett fartyg kommer kunna drabbasav parametrisk rullning.

Modern volume carriers such as container vessels, cruise ships and Pure Car and Truck Carriers (PCTC’s) have become more vulnerable to critical roll responses as built in margins have been traded against increased transport efficiency. The research presented in this doctoral thesis aims at enhancing the predictability and control of these critical roll responses. The thesis presents a holistic framework for predicting and assessing the roll damping, which is a crucial parameter for predicting roll motions, based on a unique combination of full scale trials, model tests, semi-empirical methods and computational fluid dynamics. The framework is intended to be used from the early design stage and gradually improved until delivery of the ship and finally to provide input for decision support in the operation. The thesis also includes a demonstration of a new application for rudder control to be used for mitigation of parametric roll. This is performed by simulating real incidents that have occurred with PCTC’s in service. Simulations with rudder roll control show promising results and reveal that the approach could be very efficient for mitigation of parametric roll. Finally, an approach for monitoring of roll induced stresses, so-called racking stresses in PCTC’s, is presented. The approach involves measurement of the ship motions and scaling of pre-calculated structural responses from global finite element analysis. Based on full scale motion and stress measurements from a PCTC in-service the approach is evaluated and demonstrated to be an efficient alternative to conventional methods. / <p>QC 20170516</p>

Les critères de stabilité à l’état intact de seconde génération sont en cours de finalisation par l’Organisation Maritime Internationale. Ils doivent compléter les critères actuels en apportant une sécurité accrue dans les vagues. Ils sont organisés en cinq modes de défaillance et trois niveaux d’évaluation dans chaque mode de défaillance. Le premier niveau est basé sur une approche déterministe simplifiée des phénomènes et assure des marges de sécurité importantes. Le second niveau requiert des calculs plus complexes basés sur des considérations hydrostatiques dans les vagues. Il est supposé assurer des marges de sécurité réduites. Le troisième niveau, actuellement en cours de développement, devrait consister en des simulations numériques du comportement du navire sur des états de mer réels réalisés par des instituts spécialisés. Les deux premiers niveaux des modes de défaillance perte pure de stabilité et roulis paramétrique ont été implémentés dans un code de stabilité. Les courbes de KGmax associées à ces critères sont calculées pour une sélection de navires civils et militaires de différents types ayant des comportements connus ou supposés différents vis-à-vis de ces modes de défaillance. Les exigences et la pertinence des critères sont analysées. La seconde vérification du critère de niveau deux en roulis paramétrique est étudiée en détail. Une méthode simplifiée de calcul de l’angle maximum de roulis paramétrique supposant un GZ linéaire est proposée et implémentée dans le critère correspondant. / The second generation intact stability criteria are currently under finalization by the International Maritime Organization. They are intended to improve the current intact stability rules by adding safety in waves. They are structured in five failure modes and three levels of assessment in each failure mode. The first level is based on a simplified deterministic approach of the phenomena and ensures high safety margins. The second level requires more complex computations based on hydrostatic considerations with regard to static waves and is expected to provide reduced safety margins. The third level, currently under development, would consist of numerical simulations of the ship’s behavior in real sea states performed by specialized institutes. Level-one and level-two criteria of both pure loss of stability and parametric roll failure modes have been implemented in a stability code. The KGmax curves associated with these future criteria are computed for a selection of different ships of different types, both civilian and military, expected or known to have different behaviors with regard to the considered failure modes. The requirement and the relevance of the criteria are analyzed. The second check of parametric roll level-two criterion is thoroughly analyzed. A simplified method providing the maximum parametric roll angle assuming a linear GZ is developed and implemented in the corresponding criterion.