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Chapter 2 starts by analysing free and forced oscillations in a simple mechanical system, and the method of complex representation of sinusoidal oscillation is introduced, including phasor diagram in the complex plane. Moreover, the concepts of active and reactive power for such a system are introduced. Then the method of state-space analysis is introduced and applied to a linear system. Further, the delta 'function' and other related distributions, as well as Fourier analysis, are introduced and applied to linear systems. Moreover, causal and noncausal systems are considered, as well as Kramers–Kronig relations and the Hilbert transform.
Chapter 5 is mainly devoted to the interaction between waves and immersed bodies. In general, an immersed body may oscillate in six different modes, three translating modes (surge, sway, heave) and three rotating modes (roll, pitch, yaw). An oscillating body radiates waves, and an incident wave may induce a corresponding excitation force for each one of the six modes. When a body oscillates, it radiates waves. Such radiated waves and excitation forces are related by so-called reciprocity relationships. Such relations are derived not only for a single oscillating body but even for a group (or 'array') of immersed bodies. Axisymmeric bodies and two-dimensional bodies are discussed in separate sections of the chapter. Although most of this chapter discusses wave-body dynamics in the frequency domain, a final section treats an immersed body in the time domain.
Chapter 1 mentions some previous books on ocean waves, and how the present book is different and serves as a source of supplementary information, which is mainly concerned with the utilisation of the energy of ocean waves. Then a short summary is given for each of the other chapters of the book.
Chapter 3 is a general, rather short and partly descriptive introduction to general wave theory, without application of any differential equation. The emphasis is on mechanical waves, e.g., acoustic waves.
Referring to a simple illustration, a verbal explanation is given by the essential, but perhaps paradoxical, statement that to absorb wave energy from a wave by means of an oscillating system, it is required that the system radiates a wave which interferes destructively with the incident wave. Then various mathematical relations are derived concerning the conditions for an oscillating body to remove energy from an incident wave. The mathematical conditions for wave-power absorption may be illustrated as a paraboloid-shaped 'island' on an infinite complex-plane 'ocean' surface. The top of this 'island' corresponds to maximum absorbed power. An additional matter is the optimum control of a wave-energy converter (WEC) body. Thus far, the WEC body's shape and oscillation mode have been taken into account, but not its physical size. The latter is an important parameter related to the cost of the WEC, when the Budal upper bound is explained and discussed. Another important phenomenon, related to the Keulegan–Carpenter number, is discussed, in relation to an example of a WEC body. In a final section of the chapter, a WEC body, oscillating in several modes of motion, is discussed.
Chapter 8 concerns a group of WEC units that may be realised in a more distant future, namely groups or arrays of individual WEC units and two-dimensional WEC units, which needs to be rather big structures. Firstly, a group of WEC bodies is analysed. Next a group consisting of WEC bodies as well as OWCs is analysed. Then the previous real radiation resistance needs to be replaced by a complex radiation damping matrix which is complex, but Hermitian, which means that its eigenvalues are real.
Chapter 4 introduces basic differential equations and boundary conditions for gravity waves propagating along a water surface. Assuming low wave amplitudes, equations are linearised. Then a quantitative discussion is given for harmonical (sinusoidal) waves propagating either on deep water, or otherwise on water of constant depth. Phase and group velocities are introduced, and then formulas are derived for the potential energy and the kinetic energy associated with a water wave. A closely related result is an important formula for the wave-power level, which equals the wave’s group velocity multiplied by the wave’s stored – kinetic + potential – energy per unit of sea surface. An additional subject is the wave’s momentum density. A section concerns real sea waves. Further, circular waves are mathematically described. Two sections of the chapter concern mathematical tools to be applied in Chapters 5–8 of the book. A final section considers water waves analysed in the time domain.
The first part of Chapter 7 deals with oscillating water columns (OWCs). The concepts of radiation conductance and susceptance are introduced. The former is related to the radiated power, whereas the latter represents the reactive power. Expressions for the power absorbed by the OWC are derived, which are analogous to those of the oscillating body WEC. The potential energy of the OWC is also discussed. The last part of Chapter 7 deals with wave energy converters that move in modes other than the six conventional rigid-body modes. The theory of generalised modes are described, and some examples are given to illustrate the utility of the theory.
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.
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