# Flexible floating breakwater

01 Sep 1991-Journal of Waterway Port Coastal and Ocean Engineering-asce (American Society of Civil Engineers)-Vol. 117, Iss: 5, pp 429-450

TL;DR: In this paper, the behavior of a flexible, floating breakwater consisting of a moored, compliant, beam-like structure anchored to the seabed and possessing a small buoyancy chamber at the tip was investigated.

Abstract: This study investigated the behavior of a flexible, floating breakwater consisting of a moored, compliant, beam-like structure anchored to the seabed and possessing a small buoyancy chamber at the tip. The fluid domain is treated utilizing the boundary integral equation method, modifications have been made to the basic formulation to account for the zero thickness of the idealized structure. The dynamic behavior of the breakwater is described through an appropriate Green's function and the coupled fluid-structure system is then solved numerically. Example results have been presented which illlustrate the effects of the various waves and structural parameters on the efficiency of the breakwater as a barrier to wave action. It was found that for typical wave conditions relatively stiff structures are required in order to obtain high wave reflection coefficients.

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TL;DR: In this paper, the hydrodynamic interaction of regular and irregular waves with floating breakwaters (FBs) in shallow and intermediate waters is examined experimentally in a large-scale facility.

Abstract: In the present study the hydrodynamic interaction of regular and irregular waves with floating breakwaters (FBs) in shallow and intermediate waters is examined experimentally in a large-scale facility. The experiments were conducted in the CIEM flume of the Catalonia University of Technology, Barcelona. The influence of incident wave characteristics and certain geometric characteristics, such as the width and the draught of the structure, on its efficiency is examined. Four different FBs configurations are examined: (a) single fixed FB, (b) heave motion FB, (c) single fixed FB with attached front plate (impermeable and permeable) and (d) double fixed FB. Results related to transmission, reflection, and energy dissipation of the incident (regular and irregular) waves on the structure are presented. For the single fixed FB, the efficiency of the structure is proportional to the width/wavelength and draught/water depth ratios. The single fixed FB operates in a highly reflective manner. On the other hand, the...

103 citations

### Cites methods from "Flexible floating breakwater"

...Linear models and analytical solutions, which describe the full hydrodynamic problem, have been developed by Hwang and Tang (1986), Williams and McDougal (1991), Drimer et al. (1992), Bhatta and Rahman (1993), Isaacson and Bhat (1998), Williams et al. (2000) and Kriezi et al. (2001)....

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01 Jan 2005

TL;DR: In this paper, the authors examined the hydrodynamic interaction of regular and irregular waves with floating breakwaters in shallow and intermediate waters in a large-scale facility, and the results related to transmission, reflection and energy dissipation of the incident (regular and irregular) waves on the structure were presented.

Abstract: In the present study the hydrodynamic interaction of regular and irregular waves with floating breakwaters (FBs) in shallow and intermediate waters is examined experimentally in a large-scale facility. The experiments were conducted in the CIEM flume of the Catalonia University of Technology, Barcelona. The influence of incident wave characteristics and certain geometric characteristics, such as the width and the draught of the structure, on its efficiency is examined. Four different FBs configurations are examined: (a) single fixed FB, (b) heave motion FB, (c) single fixed FB with attached front plate (impermeable and permeable) and (d) double fixed FB. Results related to transmission, reflection, and energy dissipation of the incident (regular and irregular) waves on the structure are presented. For the single fixed FB, the efficiency of the structure is proportional to the width/wavelength and draught/water depth ratios. The single fixed FB operates in a highly reflective manner. On the other hand, the heave motion FB operates in a dissipative manner with much lower reflection. The attached plate in the front part of the FB significantly enhances the efficiency of the structure. No significant differences are observed between the impermeable and the permeable plate cases. Generally, the most efficient configuration has been the double fixed FB. However, with regard to cost-effectiveness, the configuration of the FB with the attached plate should be considered the most efficient for design purposes. RESUME Dans la presente etude l’interaction hydrodynamique des vagues regulieres et irregulieres avec des brise-lames flottants (FBs) en eaux peu profondes

91 citations

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TL;DR: In this article, the reflection and transmission of small-amplitude waves by a flexible, porous, and thin beam-like breakwater held fixed in the seabed is studied.

Abstract: This is a theoretical study of the reflection and transmission of small‐amplitude waves by a flexible, porous, and thin beam‐like breakwater held fixed in the seabed. The fluid motion is idealized as a linearized, two‐dimensional potential flow and the breakwater is idealized as a one‐dimensional beam of uniform flexural rigidity and uniform mass per unit length. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free‐surface elevation, hydrodynamic force acting on the breakwater, and the overturning moment are determined. The dynamic response of the breakwater in terms of bending moment and shear force are also evaluated. It is found in general that hydrodynamic force increases as structural rigidity increases. The magnitude of the force is reduced dramatically for a stiffer porous breakwater. It is...

76 citations

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TL;DR: In this paper, the authors analyzed the scattering of oblique surface gravity waves due to the presence of multiple bottom-standing flexible porous barriers in finite water depth based on the linearized theory of water waves.

57 citations

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TL;DR: In this paper, the interaction of water waves with a tensioned, unstretchable, vertical flexible membrane extended to the seabed is solved in the context of two-dimensional linear wave theory.

Abstract: The interaction of water waves with a tensioned, unstretchable, vertical flexible membrane extended to the seabed is solved in the context of two-dimensional linear wave theory. First, analytic solutions are obtained based on the eigenfunction expansion of the velocity potential in two fluid domains and a continuous tensioned-string dynamic model. In contrast to the rigid-body hydrodynamics, the velocity potentials and membrane equation of motions are obtained simultaneously, since the membrane boundary condition is not known in advance. Second, a boundary element program based on a discrete membrane dynamic model and simple source distribution method is developed. Two different numerical methods, the iteration and whole matrix methods, are developed and both agree well with analytic solutions. Using those computer programs, the performance of a flexible-membrane wave barrier with varying initial tension, length, and mass density is investigated. It is found that almost complete reflection of incident wav...

54 citations

##### References

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01 Jan 1975

TL;DR: In this article, a single-degree-of-freedom (SDF) dynamic system is considered, and the effect of different degrees of freedom on the dynamics of the system is investigated.

Abstract: TABLE OF CONTENTS PREFACE 1 INTRODUCTION 1.1 Objectives of the Study of Structural Dynamics 1.2 Importance of Vibration Analysis 1.3 Nature of Exciting Forces 1.4 Mathematical Modeling of Dynamic Systems 1.5 Systems of Units 1.6 Organization of the Text PART I 2 FORMULATION OF THE EQUATIONS OF MOTION: SINGLE-DEGREE-OF-FREEDOM SYSTEMS 2.1 Introduction 2.2 Inertia Forces 2.3 Resultants of Inertia Forces on a Rigid Body 2.4 Spring Forces 2.5 Damping Forces 2.6 Principle of Virtual Displacement 2.7 Formulation of the Equations of Motion 2.8 Modeling of Multi Degree-of-Freedom Discrete Parameter System 2.9 Effect of Gravity Load 2.10 Axial Force Effect 2.11 Effect of Support Motion 3 FORMULATION OF THE EQUATIONS OF MOTION: MULTI-DEGREE-OF-FREEDOM SYSTEMS 3.1 Introduction 3.2 Principal Forces in Multi Degree-of-freedom Dynamic System 3.3 Formulation of the Equations of Motion 3.4 Transformation of Coordinates 3.5 Static Condensation of Stiffness matrix 3.6 Application of Ritz Method to Discrete Systems 4 PRINCIPLES OF ANALYTICAL MECHANICS 4.1 Introduction 4.2 Generalized coordinates 4.3 Constraints 4.4 Virtual Work 4.5 Generalized Forces 4.6 Conservative Forces and Potential Energy 4.7 Work Function 4.8 Lagrangian Multipliers 4.9 Virtual Work Equation For Dynamical Systems 4.10 Hamilton's Equation 4.11 Lagrange's Equation 4.12 Constraint Conditions and Lagrangian Multipliers 4.13 Lagrange's Equations for Discrete Multi-Degree-of-Freedom Systems 4.14 Rayleigh's Dissipation Function PART II 5 FREE VIBRATION RESPONSE: SINGLE-DEGREE-OF-FREEDOM SYSTEM 5.1 Introduction 5.2 Undamped Free Vibration 5.3 Free Vibrations with Viscous Damping 5.4 Damped Free vibration with Hysteretic Damping 5.5 Damped Free vibration with Coulomb Damping 6 FORCED HARMONIC VIBRATIONS: SINGLE-DEGREE-OF-FREEDOM SYSTEM 6.1 Introduction 6.2 Procedures for the Solution of Forced Vibration Equation 6.3 Undamped Harmonic Vibration 6.4 Resonant Response of an Undamped System 6.5 Damped Harmonic Vibration 6.6 Complex Frequency Response 6.7 Resonant Response of a Damped System 6.8 Rotating Unbalanced Force 6.9 Transmitted Motion due to Support Movement 6.10 Transmissibility and Vibration Isolation 6.11 Vibration Measuring Instruments 6.12 Energy Dissipated in Viscous Damping 6.13 Hysteretic Damping 6.14 Complex Stiffness 6.15 Coulomb Damping 6.16 Measurement of Damping 7 RESPONSE TO GENERAL DYNAMIC LOADING AND TRANSIENT RESPONSE 7.1 Introduction 7.2 Response to an Impulsive force 7.3 Response to General Dynamic Loading 7.4 Response to a Step Function Load 7.5 Response to a Ramp Function Load 7.6 Response to a Step Function Load With Rise Time 7.7 Response to Shock Loading 7.8 Response to a Ground Motion Pulse 7.9 Analysis of Response by the Phase Plane Diagram 8 ANALYSIS OF SINGLE-DEGREE-OF-FREEDOM SYSTEMS: APPROXIMATE AND NUMERICAL METHODS 8.1 Introduction 8.2 Conservation of Energy 8.3 Application of Rayleigh Method to Multi Degree of Freedom Systems 8.4 Improved Rayleigh Method 8.5 Selection of an Appropriate Vibration Shape 8.6 Systems with Distributed Mass and Stiffness: Analysis of Internal Forces 8.7 Numerical Evaluation of Duhamel's Integral 8.8 Direct Integration of the Equations of Motion 8.9 Integration Based on Piece-wise Linear Representation of the Excitation 8.10 Derivation of General Formulae 8.11 Constant Acceleration Method 8.12 Newmark's beta Method 8.13 Wilson-theta Method 8.14 Methods Based on Difference Expressions 8.15 Errors involved in Numerical Integration 8.16 Stability of the Integration Method 8.17 Selection of a Numerical Integration Method 8.18 Selection of Time Step 9 ANALYSIS OF RESPONSE IN THE FREQUENCY DOMAIN 9.1 Transform Methods of Analysis 9.2 Fourier Series Representation of a Periodic Function 9.3 Response to a Periodically Applied Load 9.4 Exponential Form of Fourier Series 9.5 Complex Frequency Response Function 9.6 Fourier Integral Representation of a Nonperiodic Load 9.7 Response to a Nonperiodic Load 9.8 Convolution Integral and Convolution Theorem 9.9 Discrete Fourier Transform 9.10 Discrete Convolution and Discrete Convolution Theorem 9.11 Comparison of Continuous and Discrete Fourier Transforms 9.12 Application of Discrete Inverse Transform 9.13 Comparison Between Continuous and Discrete Convolution 9.14 Discrete Convolution of an Infnite and a Finite duration Waveform 9.15 Corrective Response Superposition Methods 9.16 Exponential Window Method 9.17 The Fast Fourier Transform 9.18 Theoretical Background to Fast Fourier Transform 9.19 Computing Speed of FFT Convolution 9.16 Exponential Window Method 9.17 The Fast Fourier Transform 9.18 Theoretical Background to Fast Fourier Transform 9.19 Computing Speed of FFT Convolution PART III 10 FREE VIBRATION RESPONSE: MULTI-DEGREE-OF-FREEDOM SYSTEM 10.1 Introduction 10.2 Standard Eigenvalue Problem 10.3 Linearized Eigenvalue Problem and its Properties 10.4 Expansion Theorem 10.5 Rayleigh Quotient 10.6 Solution of the Undamped Free-Vibration Problem 10.7 Mode Superposition Analysis of Free-Vibration Response 10.8 Solution of the Damped Free-Vibration Problem 10.9 Additional Orthogonality Conditions 10.10 Damping Orthogonality 11 NUMERICAL SOLUTION OF THE EIGENPROBLEM 11.1 Introduction 11.2 Properties of Standard Eigenvalues and Eigenvectors 11.3 Transformation of a Linearized Eigenvalue Problem to the Standard Form 11.4 Transformation Methods 11.5 Iteration Methods 11.6 Determinant Search Method 11.7 Numerical Solution of Complex Eigenvalue Problem 11.8 Semi-definite or Unrestrained Systems 11.9 Selection of a Method for the Determination of Eigenvalues 12 FORCED DYNAMIC RESPONSE: MULTI-DEGREE-OF-FREEDOM SYSTEMS 12.1 Introduction 12.2 Normal Coordinate Transformation 12.3 Summary of Mode Superposition Method 12.4 Complex Frequency Response 12.5 Vibration Absorbers 12.6 Effect of Support Excitation 12.7 Forced Vibration of Unrestrained System 13 ANALYSIS OF MULTI-DEGREE-OF-FREEDOM SYSTEMS: APPROXIMATE AND NUMERICAL METHODS 13.1 Introduction 13.2 Rayleigh-Ritz Method 13.3 Application of Ritz Method to Forced Vibration Response 13.4 Direct Integration of the Equations of Motion 13.5 Analysis in the Frequency Domain PART IV 14 FORMULATION OF THE EQUATIONS OF MOTION: CONTINUOUS SYSTEMS 14.1 Introduction 14.2 Transverse Vibrations of a Beam 14.3 Transverse Vibrations of a Beam: Variational Formulation 14.4 Effect of Damping Resistance on Transverse Vibrations of a Beam 14.5 Effect of Shear Deformation and Rotatory Inertia on the Flexural Vibrations of a Beam 14.6 Axial Vibrations of a Bar 14.7 Torsional Vibrations of a Bar 14.8 Transverse Vibrations of a String 14.9 Transverse Vibration of a Shear Beam 14.10 Transverse Vibrations of a Beam Excited by Support Motion 14.11 Effect of Axial Force on Transverse Vibrations of a Beam 15 CONTINUOUS SYSTEMS: FREE VIBRATION RESPONSE 15.1 Introduction 15.2 Eigenvalue Problem for the Transverse Vibrations of a Beam 15.3 General Eigenvalue Problem for a Continuous System 15.4 Expansion Theorem 15.5 Frequencies and Mode Shapes for Lateral Vibrations of a Beam 15.6 Effect of Shear Deformation and Rotatory Inertia on the Frequencies of Flexural Vibrations 15.7 Frequencies and Mode Shapes for the Axial Vibrations of a Bar 15.8 Frequencies and Mode Shapes for the Transverse Vibration of a String 15.9 Boundary Conditions Containing the 15.10 Free-Vibration Response of a Continuous System 15.11 Undamped Free Transverse Vibrations of a Beam 15.12 Damped Free Transverse Vibrations of a Beam 16 CONTINUOUS SYSTEMS: FORCED-VIBRATION RESPONSE 16.1 Introduction 16.2 Normal Coordinate Transformation: General Case of an Undamped System 16.3 Forced Lateral Vibration of a Beam 16.4 Transverse Vibrations of a Beam Under Traveling Load 16.5 Forced Axial Vibrations of a Uniform Bar 16.6 Normal Coordinate Transformation, Damped Case 17 WAVE PROPAGATION ANALYSIS 17.1 Introduction 17.2 The Phenomenon of Wave Propagation 17.3 Harmonic Waves 17.4 One Dimensional Wave Equation and its Solution 17.5 Propagation of Waves in Systems of Finite Extent 17.6 Reection and Refraction of Waves at a Discontinuity in the System Properties 17.7 Characteristics of the Wave Equation 17.8 Wave Dispersion PART V 18 FINITE ELEMENT METHOD 18.1 Introduction 18.2 Formulation of the Finite Element Equations 18.3 Selection of Shape Functions 18.4 Advantages of the Finite Element Method 18.5 Element Shapes 18.6 One-dimensional Bar Element 18.7 Flexural Vibrations of a Beam 18.8 Stress-strain Relationship for a Continuum 18.9 Triangular Element in Plane Stress and Plane Strain 18.10 Natural Coordinates 19 COMPONENT MODE SYNTHESIS 19.1 Introduction 19.2 Fixed Interface Methods 19.3 Free Interface Method 19.4 Hybrid Method 20 ANALYSIS OF NONLINEAR RESPONSE 20.1 Introduction 20.2 Single-degree-of-freedom System 20.3 Errors involved in Numerical Integration of Nonlinear Systems 20.4 Multiple Degree-of-freedom System ANSWERS TO SELECTED PROBLEMS INDEX

5,044 citations

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01 Jan 1975

TL;DR: In this paper, an overview of structural dynamics analysis of free vibrations response to harmonic loading response, periodic loading response to impulse loading response and general dynamic loading -step by step methods, superposition methods generalized single degree-of-freedom systems.

Abstract: Part 1 Single-degree-of-freedom systems: overview of structural dynamics analysis of free vibrations response to harmonic loading response to periodic loading response to impulse loading responses to general dynamic loading - step by step methods, superposition methods generalized single degree-of-freedom systems. Part 2 Multi-degree-of-freedom systems: formulation of the MDOF equations of motion evaluation of structural-property matrices undamped free vibrations analysis of dynamic response using superposition vibration analysis by matrix iteration selection of dynamic degrees of freedom analysis of MDOF dynamic response - step by step methods variational formulation of the equations of motion. Part 3 Distributed parameter systems: partial differential equations of motion analysis of undamped free vibrations analysis if dynamic response. Part 4 Random vibrations: probability theory random processes stochastic response of linear SDOF systems stochastic response of non-linear MDOF systems. Part 5 Earthquake engineering: seismological background free-field surface ground motions deterministic structural response - including soil-structure interaction stochastic structural response.

1,627 citations

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TL;DR: In this article, boundary integral equation method (BIEM) is applied to examine the effectiveness of both the vertical and the inclined thin breakwater for free surface flow problems in both ground-water flows and water waves.

Abstract: The boundary integral equation method (BIEM) is applied to examine the effectiveness of both the vertical and the inclined thin breakwater. The BIEM has been used widely for free surface flow problems in both ground-water flows and water waves. For the present problems, modifications of the method are made to treat the velocity singularity at the tip of the breakwater and the zero thickness of the breakwater. The computational domain is truncated by introducing two auxiliary boundaries at some distance away from the break-water. Analytical solutions, which satisfy the governing equations and the radiation boundary condition, with unknown coefficients are used along the auxiliary boundaries. The accuracy of the numerical technique is demonstrated by comparing numerical results with analytical solutions for a vertical breakwater in a deep water. Numerical results in terms of both reflection coefficient and transmission coefficient are presented for both vertical and inclined thin breakwater.

80 citations

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TL;DR: In this article, the Goodyear and Wave-Guard floating tire breakwaters from measurements on ⅛-scale and ¼-scale models using regular and irregular waves were generated.

Abstract: Wave-transmission and peak-mooring force design curves were generated for the Goodyear and Wave-Guard floating tire breakwaters from measurements on ⅛-scale and ¼-scale models using regular and irregular waves, and found to be in good agreement with available full-scale data. These curves may be used to determine the breakwater size needed to attenuate a given regular design wave to an acceptable level, and also to determine the maximum mooring load associated with this. A simple semi-empirical energy-dissipation model was developed and found to simulate measured wave-transmission characteristics with sufficient precision to be useful in many engineering applications; e.g., the ratio of transmitted to incident wave height is stated as an exponential function of wave steepness, ratio of wavelength to breakwater-beam-size, breakwater porosity, and a drag coefficient. An empirical relationship for the peak mooring force was obtained.

44 citations