Dynamics of Offshore Structures

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Isaac Julius Sims
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1 - 7?// 3 Dynamics of Offshore Structures, Editor John Wiley & Sons, Inc.

2 Contents Preface Contributors Acknowledgments xi xiii xv 1 Structures in the Offshore Environment Historical Perspective, Platforms, 4 Fixed-Bottom Platforms, 4 Compliant Platforms, 7 Buoyant Platforms, Moorings, 9 Temporary Anchor Moorings, 9 Platform Pile and Single-Point Moorings, Pipelines, 11 Sea Floor Pipelines, 11 Vertical Pipelines, Challenges, 14 Environmental Forces, 14 Structural Materials, 14 Modeling and Analysis, 15 Experimental Evaluations, 15 References, 15 2 Structure-Environmental Force Interactions Single Degree of Freedom Structures, Fluid-Induced Structural Forces, 21 Classical Inviscid Fluid Flow, 21 Real Viscous Fluid Flow, 23 Conservation of Linear Momentum and Flow Superposition, 25 Buoyancy and Gravity, 28 Winds and Currents, Earthquakes, Ice Impact, and Wave Slamming, 36 Earthquake Forces, 36 Ice Impact Forces, 38 Wave Slamming Forces, Structural Mass, Damping, and Restraint, 40 Structural Mass and Stiffness, 40

3 vi CONTENTS Cable Restraints, 43 Soil Foundation Restraints, 52 Problems, 54 References, 56 3 Deterministic Descriptions of Offshore Waves 61 Bruce J. Muga 3.1 Description of Plane Waves, Linear Plane Waves, Nonlinear Waves, 68 Trochoidal Theory, 69 Cnoidal Theory, 69 Stokes Theory, 69 Solitary Theory, 72 Numerical Theory, Domains of Validity for Wave Theories, 75 Problems, 80 References, 81 4 Wave Forces on Structures Wave Loading of Flexible Cylinders, Classification of Fluid Load Regimes, Flow Regimes for Offshore Structures, Summary of Flow Coefficients CD and CM, Transfer Functions for Wave Loading, 94 Problems, 96 References, 98 5 Deterministic Responses for Single Degree of Freedom Structures Natural Frequencies of Linear Systems, 101 Direct Method, 101 The Rayleigh Method, Frequencies for Nonlinear Structures, Response Functions for Linear Structures, 115 Harmonic Response Function, 116 Impulse Response Function, 118 Convolution Integral, Response of Linear Structures to Earthquake Loading, Response Characteristics of Nonlinear Structures, 123 Responses to Harmonic Excitation, 123

4 CONTENTS vii Jumps, 126 Subharmonics, Nonlinear Responses for a SALM Buoy, 131 Physical Description and Dynamic Model, 132 Numerical Results and Conclusions, 136 Problems, 138 References, Statistical Descriptions of Offshore Waves 144 Bruce J. Muga 6.1 Introduction to Wave Spectra, Concept of the Significant Wave, 147 Wave Height Distributions, 148 Wave Height-Wave Spectrum Relationships, Descriptions of Wave Energy Spectra, 152 Alternative Definitions, 152 Empirical Forms, Selection of Design Wave Spectra, Synthesis of Time Histories from Spectra, 159 References, Statistical Responses for Single Degree of Freedom Linear Structures Averages and Probabilities, Stationary and Ergodic Hypotheses, Autocorrelation and Spectral Density, Structural Response Statistics: Part I, 173 The Fourier Transform, 174 The Autocorrelation Functions, 175 Response Parameters, 176 Approximate Responses, 180 Extensions, Structural Response Statistics: Part II, 183 State Variable Form, 184 Covariance Propagation Equation: Derivation, 185 Steady State Solutions, 187 A Closed Form Solution, 188 Problems, 190 References, Multi-Degree of Freedom Linear Structures Equations of Motion: General Form, 196

5 viii CONTENTS The Coordinate Vector,, 196 The Loading Vector, p, 198 The Mass Matrix, M, 199 The Stiffness Matrix, K, 201 The Damping Matrix, C, Equations of Motion: Newton's Method, Equations of Motion: Lagrange's Formulation, 208 System Energies, 208 Hamilton's Principle, 209 Derivation for a Simple System, 209 Comments, Free, Undamped Motion, 214 Frequencies, 214 Modal Vectors and Normalization, 214 Orthogonality of the Modal Vectors, Forced, Damped Motion, 216 The Mode Shape Matrix, X, 217 Modal Damping Matrix, C, 217 Uncoupling the Equations of Motion, 218 Steady State Solutions, Summary of the Normal Mode Method, 219 Problems, 220 References, Applications of Multi-Degree of Freedom Analysis A Fixed Leg Platform: Time Domain Responses, 224 Mathematical Model, 224 Frequencies, 225 Modal Vectors and Normalization, 226 Response to a Harmonic Wave, 227 Response to Earthquake Excitation, A Monopod Gravity Platform: Free Vibration and Stability, 233 Mathematical Model, 233 Frequencies and Mode Shapes, 236 Dynamic Stability, Structural Response Statistics for Wave Loading, A Fixed Leg Platform: Statistical Responses, 242 Problems, 246 References, Continuous Systems Modeling Beams and Cables, 250 Governing Equations, 250

6 CONTENTS ix Cable Frequencies and Mode Shapes, 252 Beam Frequencies and Mode Shapes, Cable Responses, 259 Transverse End Excitation, 259 Parametric Excitation, Beam Responses, 265 Transverse Excitation, 266 Parametric Excitation, 269 Statistical Wave Excitation, Deployment of an OTEC Pipeline, 275 Mathematical Model, 276 Pipe Excitations by Barge and Waves, 277 Numerical Results, 280 Problems, 284 References, Behavior of Piles Supporting Offshore Structures 289 Lymon C. Reese 11.1 Characteristics of Soil and Response to External Loading, Design of Single Piles under Axial Loading, Design of Single Piles under Lateral Loading, 296 Pile Model and Method of Solution, 297 Response of Soil, 298 Short-Term Static Loading, 299 Cyclic Loading, 299 Scour, 300 Solutions Using Nondimensional Parameters, 301 Computer-Aided Solutions, An Example: Lateral Pile Loading, 307 Problem Description, 308 Solutions Using Nondimensional Parameters, 310 Computer-Aided Solutions, 313 Conclusions, Response of Piles to Dynamic Loading, 316 Earthquakes, 316 Time-Dependent Loading Above the Mudline, 317 Problems, 318 References, 319 Conversion Table 321 Index 323

VIBRATION PROBLEMS IN ENGINEERING

VIBRATION PROBLEMS IN ENGINEERING FIFTH EDITION W. WEAVER, JR. Professor Emeritus of Structural Engineering The Late S. P. TIMOSHENKO Professor Emeritus of Engineering Mechanics The Late D. H. YOUNG Professor