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Stability and Safety of Ships: Risk of Capsizing

  • ID: 2166984
  • Book
  • December 2007
  • 445 Pages
  • Society of Naval Architects and Marine Engineers
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Naval Architects have recognized since the earliest times the importance of stability knowing well that ships have to survive the perils of the sea. The amount of knowledge on stability accumulated over the years is now enormous. There is, however, a lack of publications containing the review of the knowledge in this particular field. The intention of this book is to fill this gap and to present, as far possible, the state-ofthe- art focused on the regulatory, operational and future development aspects of intact stability. This book is addressed to readers who are interested in promoting safety against capsizing, who are involved in research on, and practical application of stability regulations on an international or national level, to ship operators and designers and members of the maritime administrations.

The book is divided in two volumes, 1 and 2. (These correspond to Volumes 9 and 10 of the Elsevier Ocean Engineering Series). The first volume (authored by L. Kobylinski and S. Kastner with subtitle “Regulation and Operation”) describes the state of the art in the field of intact ship stability. It is focused on how intact safety has been promoted; it considers stability regulations: their current state is given an historical perspective. The methods used to develop these regulations are carefully examined. Besides regulations, the first volume addresses the operational aspect of stability: ocean environment and ship behavior are described as they are seen from the bridge. Special attention is paid to onboard stability measurements and their accuracy.

The second volume (authored by V.L. Belenky and N.B. Sevastianov with the subtitle “Risk of Capsizing”) is a gathering of today’s knowledge for tomorrow’s development. It is focused on how risk and reliability can be applied for evaluation and regulation of the intact stability. First, the framework of future risk-based stability regulations is considered. Then the book examines physical phenomena associated with stability loss including broaching, greenwater influence and breaking waves action in order to evaluate the risk of capsizing in different situations. Much attention is paid to the mechanics of capsizing: as it seems to be necessary for interpretation and validation of numerical simulation results. The latter is meant to facilitate confident applicability of these methods for new ship designs.
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Preface to the Second Edition
Series Preface
Part 1. Probabilistic Approach to Stability and Risk Assessment
Chapter 1. Philosophy of Probabilistic Evaluation of Stability and Safety
1.1 General Concepts of Probabilistic Evaluation of Stability, Safety and Risk at Sea
1.2 Vectors of Assumed Situations and Loading Conditions. Risk Function
1.3 The Probability of Survival and Its Interpretation in the Task of Stability
1.4 The Problems of Criteria and Norms in the Probabilistic Approach to Stability
1.5 Algorithm of Averaging of Risk Function
Chapter 2. Probabilistic Evaluation of Environmental and Loading Conditions
2.1 Lightweight Loading Conditions
2.2 Time Varying Components of Loading Conditions
2.3 Meteorological Components of Assumed Situation
2.4 Operational Components of an Assumed Situation
Part 2. Dynamics of Capsizing
Chapter 3. Equations for Nonlinear Motions
3.1 General Equations of Fluid Motions
3.1.1 Forces and Stresses in Fluid
3.1.2 Relationship of Volume and Surface Integrals. Transport Theorem
3.1.3 Conservation of Mass and Momentum
3.1.4 Continuity Equation. Euler’s Equations
3.1.5 Navier-Stokes Equations
3.1.6 Boundary Conditions
3.2 Motions of Ideal Fluid
3.2.1 Model of Ideal Fluid
3.2.2 Potential. Laplace and Bernoulli Equations. Green’s Theorem
3.2.3 Hydrodynamic Pressure Forces
3.2.4 Forces on Moving Body in Unbounded Fluid. Added Masses
3.3 Waves
3.3.1 Free Surface Boundary Conditions
3.3.2 Linearized Free Surface Boundary Conditions. Theory of Small Waves
3.3.3 Plane Progressive Small Waves
3.4 Ship Response in Regular Small Waves
3.4.1 System of Coordinates
3.4.2 Formulation of the Problem
3.4.3 Hydrostatic Forces
3.4.4 Added Mass and Wave Damping
3.4.5 Wave Forces: Formulation of the Problem
3.4.6 Froude-Krylov Forces
3.4.7 Hydrodynamic or Diffraction Wave Forces
3.4.8 Body Mass Forces
3.4.9 Linear Equation of Motions
3.5 Linear Equation of Roll Motions
3.5.1 Adequacy of Linear Equation of Motions
3.5.2 Calculation of Forces and Motions
3.5.3 Isolated Linear Equation of Roll Motions
3.5.4 Other Forms of Linear Equation of Roll Motions
3.5.5 Solution of Linear Equation of Roll Motions
3.5.6 Linear Roll Motions in Calm Water
3.5.7 Linear Roll in Waves
3.5.8 Steady State Roll Motions. Memory Effect
3.6 Nonlinear Roll Equation
3.6.1 Classification of Forces
3.6.2 Inertial Hydrodynamic Forces and Moments
3.6.3 Hydrodynamic Wave Damping Forces
3.6.4 Viscous Damping Forces
3.6.5 Other Forces
3.6.6 Wave Excitation Forces
3.6.7 Hydrostatic Forces: Structure of Nonlinear Roll Equation
Chapter 4. Nonlinear Roll Motion in Regular Beam Seas
4.1 Free Roll Motion
4.1.1 Free Oscillations of Nonlinear System
4.1.2 Free Motions of Piecewise Linear System
4.2 Steady State of Forced Roll Motions
4.2.1 Equivalent Linearization
4.2.2 Harmonic Balance Method
4.2.3 Perturbation Method
4.2.4 Method of Multiple Scales
4.2.5 Numerical Method
4.2.6 Steady State Solution of Piecewise Linear System
4.3 Stability of Equilibrium
4.3.1 Identification of Equilibria
4.3.2 Original or “Normal” Equilibrium
4.3.3 Equilibrium at Angle of Vanishing Stability
4.3.4 Equilibrium at Capsized Position
4.3.5 Phase Plane in Vicinity of Equilibria
4.4 Stability of Roll Motion
4.4.1 Lyapunov Direct Method
4.4.2 Floquett Theory
4.4.3 Poincare Map and Numerical Method for Motion Stability
4.4.4 Motion Stability of Piecewise Linear System
4.5 Bifurcation Analysis
4.5.1 General
4.5.2 Fold Bifurcation
4.5.3 Period Doubling and Deterministic Chaos
4.5.4 Bifurcations of Piecewise Linear System
4.6 High Order Resonances
4.6.1 General
4.6.2 Ultra-harmonic Resonance
4.6.3 Sub-harmonic Resonance
Chapter 5. Capsizing in Regular Beam Seas
5.1 Classical Definition of Stability
5.1.1 Concept of Separatrix
5.1.2 Calculation of Separatrix
5.1.3 Separatrix, Eigenvalues and Eigenvectors
5.1.4 Numerical Validation of Classical Definition of Stability
5.2 Piecewise Linear Model of Capsizing
5.2.1 General
5.2.2 Capsizing in Piecewise Linear System
5.2.3 Piecewise linear System and Classical Definition of Stability
5.2.4 Shapes of Capsizing Trajectories
5.3. Nonlinear Dynamics and Capsizing
5.3.1 General
5.3.2 Sensitivity to Initial Conditions: Safe Basin
5.3.3 Concept of Invariant Manifold
5.3.4 Invariant Manifold and Erosion of Safe Basin. Melnikov Function
5.3.5 Loss of Motion Stability and Capsizing
Chapter 6. Capsizing in Regular Following and Quartering Seas
6.1 Variation of the GZ Curve in Longitudinal Waves. Pure Loss of Stability
6.1.1 Description of Phenomenon
6.1.2 Methods of Calculations
6.1.3 Pure Loss of Stability
6.1.4 Equation of Roll Motions
6.2 Parametric Resonance
6.2.1 Description of Phenomenon
6.2.2 Parametric Resonance in Linear System. Mathieu equation
6.2.3 Parametric Resonance in Nonlinear System
6.3 Surf-Riding in Following Seas
6.3.1 General
6.3.2 Forces and Equation of Motions
6.3.3 Equilibria
6.3.4 Stability of Equilibria
6.3.5 Bifurcation Analysis
6.4 Model of Ship Motion in Quartering Seas
6.4.1 General
6.4.2 Equations of Horizontal Ship Motions
6.4.3 Surging and Surge Wave Force
6.4.4 Swaying and Sway Wave Force
6.4.5 Yaw Motions and Yaw Wave Moment
6.4.6 Roll Equation for Broaching Study
6.4.7 Equation of Autopilot
6.4.8 Model for Broaching
6.5 Ship Behavior in Quartering Seas
6.5.1 Equilibria of Unsteered Vessel
6.5.2 Stability of Equilibria of Unsteered Ship
6.5.3 Stability of Equilibria of Steered Ship
6.5.4 Large Ship Motions in Quartering Seas
6.5.5 Global Analysis
6.5.6 Broaching as the Manifestation of Bifurcation of Periodic Motions
6.6 Broaching and Capsizing
6.6.1 Analysis of Equilibria
6.6.2 Invariant Manifold
6.6.3 Capsizing
Chpater 7. Other Factors Affecting Capsizing
7.1 Aerodynamic Forces and Drift
7.1.1 Steady Drift
7.1.2 Aerodynamic Forces
7.1.3 Hydrodynamic Drift Forces
7.1.4 Sudden Squall of Wind
7.1.5 Method of Energy Balance
7.2 Influence of Freeboard Height and Water on Deck
7.2.1 General
7.2.2 Experimental Observations. Pseudo-static Heel
7.2.3 Behavior of Water on Deck
7.2.4 Influence of Deck in Water
7.2.5 Model of Ship Motions
7.2.6 Behavior of Ship with Water on Deck
7.3 Stability in Breaking Waves
7.3.1 General
7.3.2 Geometry and Classification of Breaking Waves
7.3.3 Impact of Breaking Wave: Experiment and Theory
7.3.4 Probabilistic Approach to Capsizing in Breaking Waves
Chapter 8. Nonlinear Roll Motions in Irregular Seas
8.1 Fundamentals of Stochastic Processes
8.1.1 General
8.1.2 Moments of Stochastic Process. Autocorrelation
8.1.3 Stationary and Non-stationary Processes
8.1.4 Ergodicity
8.1.5 Spectrum and Autocorrelation Function
8.1.6 Envelope of Stochastic Process
8.2 Probabilistic Models of Wind and Waves
8.2.1 Gusty Wind
8.2.2 Squalls
8.2.3 Spectral Model of Irregular Waves
8.2.4 Method of Envelope
8.2.5 Autoregression Model
8.2.6 Non-Canonical Presentation
8.3 Irregular Roll in Beam Seas
8.3.1 Linear System. Weiner–Khinchin Theorem
8.3.2 Correlation of Irregular Roll
8.3.3 Statistical Linearization
8.3.4 Energy-Statistical Linearization
8.3.5 Method of Multiple Scales
8.3.6 Monte-Carlo Method
8.3.7 Non-Canonical Presentation and Monte-Carlo Method
8.3.8 Parametric Resonance in Irregular Beam Seas
8.4 Roll in Irregular Longitudinal Seas
8.4.1 Probabilistic Model of Irregular Longitudinal Seas
8.4.2 Surging in Irregular Seas
8.4.3 Changing Stability in Longitudinal Irregular Seas
8.4.4 Parametric Resonance in Irregular Longitudinal Seas
8.5 Influence of Gusty Wind
8.5.1 Distribution of Aerodynamic Pressures
8.5.2 Fourier Presentation for Aerodynamic Forces
8.5.3 Swaying and Drift in Beam Irregular Seas
8.5.4 Roll Under Action of Beam Irregular Seas and Gusty Wind
8.6 Probabilistic Qualities of Nonlinear Irregular Roll
8.6.1 Ergodicity of Nonlinear Irregular Roll
8.6.2 Distribution of Nonlinear Irregular Roll
8.6.3 Group Structure of Irregular Roll
8.6.4 Application of Markov Processes
Chapter 9. Probability of Capsizing
9.1 Application of Upcrossing Theory
9.1.1 General
9.1.2 Averaged Number of Crossings
9.1.3 Crossings as Poisson Flow
9.1.4 Time before Crossing
9.2 Probability of Capsizing in Beam Seas
9.2.1 Mathematical and Physical Modeling
9.2.2 Classical Definition of Stability
9.2.3 Method of Energy Balance
9.2.4 Piecewise Linear Method
9.2.5 Combined Piecewise-Linear-Numerical Method
9.2.6 Methods Based on Motion Stability
9.2.7 Methods Based on Nonlinear Dynamics
9.2.8 Markov Processes Application
9.3 Probability of Capsizing in Following Seas and Risk Caused by Breaking Waves
9.3.1 Classical Definition of Stability and Pure Loss of Stability
9.3.2 Piecewise Linear Method
9.3.3 Probability of Surf-Riding
9.3.4 Risk of Capsizing Caused by Breaking Waves
Appendix I. Nechaev Method
Appendix II. Basic Statistics and Ergodicity of Stochastic Process
A2.1 Statistical Estimates of Stochastic Process as Random Numbers
A2.2 Confidence Interval of Statistical Estimates
A2.3 Measure of Ergodicity
References for the Second Edition
Subject Index
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Note: Product cover images may vary from those shown