Dynamic Behavior of Pipelines for Marine Applications

Preface
Contents
1 Introduction
	1.1 Land Based and Marine Pipelines
	1.2 Configurations and Operation of Marine Pipelines-Risers
		1.2.1 Operation
		1.2.2 Riser Configurations
	1.3 Pipeline Design Through Analysis (DTA)
	1.4 Dynamic Analysis as a Tool for Efficient Pipeline Design
2 Nonlinear Dynamics of a Curve in Three Dimensions
	2.1 General Remarks
	2.2 Fundamental Formulation
		2.2.1 Material Derivatives in Time and Space
		2.2.2 Euler Angles
		2.2.3 The Kinematics of an Element Along the Distorted Space Curve
		2.2.4 Balance of Moments
		2.2.5 Equations of Continuity
		2.2.6 Distributed Forces
		2.2.7 The Governing Dynamic System
	2.3 Static Equilibrium
	2.4 Two-Dimensional Dynamics
	2.5 Three-Dimensional Dynamic Behavior of an Originally Plane Beam with no Torsional Effects
	2.6 The Linearized System
	2.7 Decoupled In-Plane and Out-of-Plane Vibrations of an Initially Plane Beam
	2.8 The Last Simplification: Free Bending Vibrations of Horizontal or Vertical Beams
		2.8.1 Free Elastic Vibrations of Rods
		2.8.2 Free Elastic Vibrations of Beams
		2.8.3 Free Vibrations of Vertical Clamped Beams Under Tension, Using Perturbation Analysis
	Literature
3 Distributed Forces—Hydrodynamic Loads
	3.1 Description of the Distributed Forces
	3.2 The Morison Equation
		3.2.1 Introductory Information
		3.2.2 The Drag Forces
		3.2.3 A Further Significant Use of Morison’s Equation
	3.3 Variation of the Inertia and the Drag Coefficients
	3.4 Height Frequency Oscillations due to Vortex Shedding—The Vortex-Induced-Vibrations Phenomenon
		3.4.1 Brief Introduction
		3.4.2 Description of the VIV Phenomenon
		3.4.3 The Lock-In Condition
		3.4.4 Motions at Lock-In—The Van der Pol Oscillator
	Literature
4 Inner Flow Models
	4.1 Introduction
	4.2 Mathematical Formulation of Pipeline Dynamics with Internal Flow
		4.2.1 Dynamic Equilibrium of the Pipeline’s Element
		4.2.2 Dynamic Equilibrium of the Fluid’s Element
	4.3 Governing Differential Equations
		4.3.1 Equations of Motion
		4.3.2 Distributed Forces
		4.3.3 The Final System
	4.4 The Potential Flow Model
	4.5 Steady-State “Slug Flow” Model
		4.5.1 Two-Phase Steady-Steady Model
		4.5.2 The Cross Section
		4.5.3 The Friction Forces
		4.5.4 Hold-Up in the Liquid Slug Zone
		4.5.5 The Steady Translational Velocity of the Slug Unit
		4.5.6 The Bubble Velocity
		4.5.7 Liquid’s Velocity in the Slug
	4.6 Combining Pipeline Dynamics with the Inner Steady-State Two-Phase Flow
		4.6.1 Slug Flow Calculations
		4.6.2 Pipeline Dynamics with Internal Slug Flow
	4.7 Unsteady Two-Phase Flow
	Literature
5 Linear and Nonlinear Dynamics of Pipelines
	5.1 General Information
	5.2 Free Vibrations of Slender Structures
		5.2.1 Free Vibrations of a Straight, Hollow, Weightless Beam Assuming an Internal Flow
		5.2.2 Free Vibrations of Catenary, Cylindrical Pipelines
		5.2.3 Free Vibrations of Catenary Pipelines with Intermediate Buoyancy Sections
	5.3 Solution Method that Relies on Expansions of Eigenfunctions
	5.4 Solution of Nonlinear Systems in the Frequency Domain
		5.4.1 Introduction—The Fast Fourier Transformation (FFT)
		5.4.2 Nonlinear Dynamics of Catenary Pipelines—Solution in the Frequency Domain
	5.5 Dynamics of Pipes with Nonconventional End Conditions
		5.5.1 A Robin-Type Condition
		5.5.2 Statics
		5.5.3 Dynamics
	Literature
6 Local Discontinuities—Buoyancy Devises
	6.1 Introduction
	6.2 Buoys Attached Along the Pipeline
		6.2.1 General Information
		6.2.2 Point Connections of Buoys
		6.2.3 Drag Forces
		6.2.4 Added Masses
		6.2.5 Modification of the Dynamic Behavior
	6.3 Damping Due to the Motions of the Pipeline in the Wet Environment
		6.3.1 Introduction
		6.3.2 Calculation of Damping via the Linearized Problem
		6.3.3 Calculation of Damping in the Time Domain
	Literature
7 Extreme Loading—Dynamic Buckling
	7.1 Extreme Loading
	7.2 Mathematical Formulation
	7.3 Series Expansion
	7.4 Mathieu Equations
	7.5 Hill’s Equation
		7.5.1 The General Form
		7.5.2 Floquet Theory
	7.6 Identifying Instabilities via Perturbation Analysis
		7.6.1 Perturbation Expansions
		7.6.2 Identifying Nonlinear Resonances
	7.7 Dynamic Buckling in Catenary Pipelines
	7.8 Loss of Restoring Due to Tension Cancelation
	Literature