# Ocean waves and oscillating systems pdf

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Aitor J.

Hydraulic cylinders play a vital role in the energy output PTO system of an oscillating float-type wave energy converter, whose function is to convert the mechanical energy captured by the float from the waves into hydraulic energy. The performance of the hydraulic cylinder determines the conversion efficiency of mechanical energy to hydraulic energy in the system; therefore, it is necessary to study the working mechanism of the hydraulic cylinder. This paper takes a self-developed oscillating float-type wave energy converter as the research object, and studies the working mechanism of its hydraulic cylinder, and uses the linear analysis method to derive the critical self-excited vibration curve of the hydraulic cylinder. In addition, the effects of the external load, hydraulic cylinder load mass, stroke length, spring stiffness and piston area on the performance of the hydraulic cylinder were studied by AMESim simulation software.

## Ocean waves and oscillating systems.pdf

Mathematical Description of Oscillations 2. Interaction Between Oscillations and Waves 3. Gravity Waves on Water 4. Wave-Energy Absorption by Oscillating Bodies 6. Wave Interaction with Oscillating Water Columns 7. This book is intended to provide a thorough consideration of the interaction between waves and oscillating systems immersed bodies and oscillating water columns under conditions where amplitudes are sufciently small that linear theory is applicable.

In practice, this small-wave assumption is reasonably valid for most of the time, during which, for example, a wave-energy converter is generating most of its income. During the rather rare extreme-wave situations, however, non-linear effects may be signicant, and such situations inuence design loads, and hence the costs, for ships and other installations deployed at sea.

This matter is treated in several other books. The present book is mainly based on lecture notes from a postgraduate university course on water waves and extraction of energy from ocean waves, which I have taught many times since For the purposes of this book, I have selected those parts of the subject which have more general interest, rather than those parts of my course which pertain to wave-power conversion in particular.

I hope that the book is thus of interest to a much wider readership than just the wave-energy community.

Except in , my course has been taught every second year, mainly for doctorate students at the university in Trondheim, but other interested students have also attended. Moreover, a similar two-week course was given in with participants from Norwegian industry. Another two-week course, with international participation, was held at the Chalmers University of Technology in Gothenburg, Sweden, in In February , the lecture notes were issued in a bound volume entitled Hydrodynamisk teori for blgjekraftverk Hydrodynamic theory for wave power plants by L.

Iversen and me. Later I revised the lecture notes, while translating them into English. In this process resulted in a two-volume work entitled Theory for extraction of ocean-wave energy. I wish to thank the course participant Knut Bnke for his inspiring encouragement to have the lecture notes typed in and issued in a bound volume, and ix.

Moreover, I would like to thank Jrgen Hals, a course partcipant from , for working out the subject index of the present book.

I am also in debt to my other students for their comments and proof-reading. In this connection I wish to mention, in particular, the following graduate students the years they Kyllingstad completed their doctorate degrees are given : L. Iversen , A.

Malmo , G. Oltedal , A. Brendmo and H. Eidsmoen Also my collaborator over many years, P. Lillebekken, who attended the course in , has made many valuable comments. Most of all, I am in debt to my late colleague Kjell Budal , whose initiative inspired my interest in wave-power utilisation at an early stage. During the oil crisis at the end of , we started a new research project aimed at utilising ocean-wave energy. At that time we did not have a research background in hydrodynamics, but Budal had carried out research in acoustics, developing a particular microphone, whereas I had studied waves in electromagnetics and plasma physics.

During we jointly authored a Norwegian textbook Blgjelre Wave Science for the second-year undergraduate students in physics. This is an interdisciplinary text on waves, with particular emphasis on acoustics and optics. With this background our approach and attitude towards hydrodynamic waves have perhaps been more interdisciplinary than traditional.

In my view, this has inuenced our way of thinking and stimulated our contributions to the science of hydrodynamics. This background is also reected in the present book, notably in Chapter 3, where interaction between oscillations and waves is considered in general; water waves, in particular, are treated in subsequent chapters Chapters I am also grateful to Elsevier Science for permission to reuse, in Sections 4.

Moreover, I wish to thank Professor J. Newman and Dr. Alain Clement. I am also grateful to Dr. Stephen Barstow for permission to use Problem 4.

Finally, I wish to thank my wife, Dagny Elisabeth, for continuous support during the many years I have worked on this book. Our oldest son, Magne, took the photographs used in composition of the front cover of the book.

In this book, gravity waves on water and their interaction with oscillating systems having zero forward speed are approached from a somewhat interdisciplinary point of view. Before the matter is explored in depth, a comparison is briey made between different types of waves, including acoustic waves and electromagnetic waves, drawing the readers attention to some analogies and dissimilarities.

Oscillating systems for generating or absorbing waves on water are analogues of loudspeakers or microphones in acoustics, respectively. In electromagnetics the analogues are transmitting or receiving antennae in radio engineering, and lightemitting or light-absorbing atoms in optics. The discussion of waves is, in this book, almost exclusively limited to waves of sufciently low amplitudes for linear analysis to be applicable. Several other books see, e. In contrast, the purpose of this book is to convey a thorough understanding of the interaction between waves and oscillations, when the amplitudes are low, which is true most of the time.

For example, on one hand, for a wavepower plant the income is determined by the annual energy production, which is essentially accrued during most times of the year, when amplitudes are low, that is, when linear interaction is applicable. On the other hand, as with many other types of ocean installations, wave-power plants also have their expenses, to a large extent, determined by the extreme-load design.

The technological aspects related to conversion and useful application of wave energy are not covered in the present book. Readers interested in such subjects are referred to other literature. At the end of each chapter, except the rst, there is a collection of problems. Chapter 2 gives a mathematical description of free and forced oscillations in the time domain as well as in the frequency domain. An important purpose is to introduce students to the very useful mathematical tool represented by the complex representation of sinusoidal oscillations.

The mathematical connection 1. Linear systems are discussed in a rather general way, and for a causal linear system in particular, the Kramers-Kronig relations are derived. A simple mechanical oscillating system is analysed to some extent, the concept of mechanical impedance is introduced and a discussion of energy accounting in the system is included to serve as a tool for physical explanation, in subsequent chapters, of the so-called hydrodynamic added mass.

In Chapter 3 a brief comparison is made of waves on water with other types of waves, in particular with acoustic waves. The concepts of wave dispersion, phase velocity and group velocity are introduced. In addition the transport of energy associated with propagating waves is considered, and the radiated power from a radiation source wave generator is mathematically expressed in terms of a phenomenologically dened radiation resistance.

The radiation impedance, which is a complex parameter, is also introduced in a phenomenological way. For mechanical waves such as acoustic waves and waves on water its imaginary part may be represented by an added mass. Finally in Chapter 3, an analysis is given of the absorption of energy from a mechanical wave by means of a mechanical oscillation system of the simple type considered in Chapter 2.

The optimum parameters of this system for maximising the absorbed energy are discussed. The maximum is obtained at resonance. From Chapter 4 onward, a deeper hydrodynamic discussion of water waves is the main subject.

With an assumption of inviscid and incompressible uid and irrotational uid motion, the hydrodynamic potential theory is developed. With the linearisation of uid equations and boundary conditions, the basic equations for low-amplitude waves are derived.

In most of the following discussions, either innite water depth or nite, but constant, water depth is assumed. Dispersion and wave-propagation velocities are studied, and plane and circular waves are discussed in some detail. Also non-propagating, evanescent plane waves are considered. Another studied subject is wave-transported energy and momentum. The spectrum of real sea waves is treated only briey in the present book. The rather theoretical Sections 4. Whereas most of Chapter 4 is concerned with discussions in the frequency domain, the last section contains discussions in the time domain.

The subject of Chapter 5 is interactions between waves and oscillating bodies, including wave generation by oscillating bodies as well as forces induced by waves on the bodies. Initially six-dimensional generalised vectors are introduced which correspond to the six degrees of freedom for the motion of an immersed threedimensional body.

The radiation impedance, known from the phenomenological introduction in Chapter 3, is now dened in a hydrodynamic formulation, and, for a three-dimensional body, extended to a 6 6 matrix. In a later part of the chapter the radiation impedance matrix is extended to the case of a nite number of interacting, radiating, immersed bodies. For this case the generalised. From Greens theorem as mentioned in the summary of Chapter 4 several useful reciprocity theorems are derived, which relate excitation force and radiation resistance to each other or to far-eld coefcients or Kochin functions.

Subsequently these theorems are applied to oscillating systems consisting of concentric axisymmetric bodies or of two-dimensional bodies. The occurrence of singular radiation-resistance matrices is discussed in this connection.

Whereas most of Chapter 5 is concerned with discussions in the frequency domain, two sections, Sections 5. In the latter section motion response is the main subject. In the former section two hydrodynamic impulse-response functions are considered; one of them is causal and, hence, has to obey the Kramers-Kronig relations.

The extraction of wave energy is the subject of Chapter 6, which starts by explaining wave absorption as a wave-interference phenomenon. Toward the end of the chapter Section 6.

This discussion provides a physical explanation of the quite frequently encountered cases of singular radiation-resistance matrices, as mentioned above also see Sections 5. However, the central part of Chapter 6 is concerned with wave-energy conversion which utilises only a single body oscillating in just one degree of freedom.

With the assumption that an external force is applied to the oscillating system, for the purpose of power takeoff and optimum control of the oscillation, this discussion has a different starting point than that given in the last part of Chapter 3. The conditions for maximising the converted power are also studied for the case in which the body oscillation has to be restricted as a result of its designed amplitude limit or because of the installed capacity of the energy-conversion machinery.

Oscillating water columns OWCs are mentioned briey in Chapter 4 and considered in greater detail in Chapter 7, where their interaction with incident waves and radiated waves is the main subject of study.

## Wave power

Johannes Falnes, Adi Kurniawan. Ocean waves and oscillating systems : Linear interactions including wave-energy extraction. N2 - Understand the interaction between ocean waves and oscillating systems with this useful new edition. With a focus on linear analysis of low-amplitude waves, you are provided with a thorough understanding of wave interactions, presented to be easily accessible to non-specialist readers. Topics covered include the background mathematics of oscillations, gravity waves on water, the dynamics of wave-body interactions, and the absorption of wave energy by oscillating bodies and oscillating water columns. Featuring new content throughout, including three new chapters on oscillating-body wave energy converters, oscillating water columns and other types of wave energy converters, and wave energy converter arrays, this book is an excellent resource for students, researchers, and engineers who are new to the subject of wave energy conversion, as well as those with more experience.

This book examines the interaction between ocean waves and oscillating systems. With a focus on linear analysis of low-amplitude waves, the text is designed to convey a thorough understanding of wave interactions. Topics covered include the background mathematics of oscillations, gravity waves on water, the dynamics of wave-body interactions, and the absorption of wave energy by oscillating bodies. Linear algebra, complex numbers, differential equations, and Fourier transformation are utilized as bases for the analysis, and each chapter ends with problems. While the book's focus is on linear theory, the practical application of energy storage and transport is interwoven throughout. This book will be appropriate for those with backgrounds in elementary fluid dynamics or hydrodynamics and mathematical analysis.

## Wave Interaction with Oscillating Bodies and Water Columns

Mathematical Description of Oscillations 2. Interaction Between Oscillations and Waves 3. Gravity Waves on Water 4. Wave-Energy Absorption by Oscillating Bodies 6.

Roberto Frias , , Porto, Portugal. This new approach to harvest mechanical energy can produce high power outputs capable of supplying equipment and sensors deployed in remote offshore locations and of supporting offshore activities whilst being able to be used in conjunction with traditional energy harvesting technologies. This review describes the fundamentals of TENGs and the existing energy harvesting modes, with focus on those more suitable for marine applications. Moreover, the equipment and offshore activities whose energy needs can be satisfied by TENGs are described and implementation schemes presented. We conclude that TENGs have high potential for numerous maritime applications, ranging from the demand of electronics used for metocean monitoring, signalling and surveillance, to activities such as offshore aquaculture or oil and gas exploration.

Falnes, , J. January ; 56 1 : B3. ISBN

### Ocean Waves and Oscillating Systems - Ebook

Gratis? - по-прежнему увещевал бармен.  - За счет заведения. Превозмогая шум в голове, Беккер представил себе грязные улицы Трианы, удушающую жару, безнадежные поиски в долгой нескончаемой ночи.

Она безуспешно пыталась высвободиться. - Я сделал это ради нас обоих. Мы созданы друг для друга.

Мне был нужен человек, никак не связанный с государственной службой. Если бы я действовал по обычным каналам и кто-то узнал… - И Дэвид Беккер единственный, кто не связан с государственной службой. - Разумеется, не единственный. Но сегодня в шесть часов утра события стали разворачиваться стремительно. Дэвид говорит по-испански, он умен, ему можно доверять, к тому же я подумал, что оказываю ему услугу. - Услугу? - бурно отреагировала Сьюзан.

#### COMMENT 1

• Wave power is the capture of energy of wind waves to do useful work — for example, electricity generation , water desalination , or pumping water. Babette M. - 08.06.2021 at 15:05