Handbook of Mathematical Techniques for Wave/Structure Interactions

Name: Handbook of Mathematical Techniques for Wave/Structure Interactions
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ISBN: 9781584881322

By: C. M. Linton, Philip McIver

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Hardcover Published: 26th February 2001
ISBN: 9781584881322
Number Of Pages: 320

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Table of Contents
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Although a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the most important techniques useful to applied mathematicians and engineers.

Each chapter is dedicated to a particular technique, such as eigenfunction expansions, multipoles, integral equations, and Wiener-Hopf methods. Other chapters discuss approximation techniques and variational methods. The authors describe all of the techniques in terms of wave/structure interactions, with most illustrated by application to research problems. They provide detailed explanations of the important steps within the mathematical development, and, where possible, physical interpretations of mathematical results.

Handbook of Mathematical Techniques for Wave/Structure Interactions effectively bridges the gap between the heavy computational methods preferred by some engineers and the more mathematical approach favored by others. These techniques provide a powerful means of dealing with wave/structure interactions, are readily applied to relevant problems, and illuminate those problems in a way that neither a purely computational approach nor a straight theoretical treatment can.

Preface
The water-wave problem	p. 1
Introduction	p. 2
The linearized equations	p. 3
Interaction of a wave with a structure	p. 5
The radiation condition	p. 7
The scattering problem	p. 8
The radiation problem	p. 8
Hydrodynamic forces and moments	p. 10
Limitations of the inviscid, linear theory	p. 11
Reciprocity relations	p. 12
Energy of the fluid motion	p. 19
Energy radiated to the far field	p. 19
Potential and kinetic energy	p. 20
Eigenfunction expansions	p. 23
Construction of vertical eigenfunctions	p. 24
Two-dimensional problems	p. 27
The wave-maker problem	p. 27
Forced oscillations of a rectangular tank	p. 28
Three-dimensional problems	p. 30
Sloshing in a rectangular tank	p. 30
Oblique waves	p. 31
Scattering by a symmetric obstacle	p. 32
Cylindrical polar coordinates	p. 33
Sloshing in a cylindrical tank	p. 35
The Helmholtz equation	p. 36
Scattering by a vertical circular cylinder	p. 37
Matched eigenfunction expansions	p. 39
Scattering by a vertical barrier	p. 39
A heaving truncated circular cylinder	p. 45
The finite dock problem	p. 49
Infinite depth	p. 52
Multipole expansions	p. 55
Isolated obstacles	p. 56
A submerged circular cylinder	p. 56
A heaving hemisphere	p. 64
Sloshing in a hemisphere	p. 67
Multiple bodies	p. 70
Two submerged circular cylinders	p. 70
A row of vertical circular cylinders	p. 73
Integral equations	p. 79
Source distributions	p. 80
Numerical solution	p. 82
Irregular values	p. 84
Green's theorem	p. 85
Scattering by a vertical cylinder	p. 88
Thin obstacles	p. 90
Numerical solution	p. 91
Interior problems	p. 94
Free-surface problems	p. 96
Numerical evaluation of Green's functions	p. 98
Green's functions for three-dimensional water-wave problems	p. 99
Channel Green's functions	p. 104
Diffraction by a breakwater	p. 107
Diffraction by a gap in a breakwater	p. 107
Diffraction by an insular breakwater	p. 112
Embedding formulas	p. 114
Numerical solutions	p. 117
Babinet's principle	p. 123
The Wiener-Hopf and related techniques	p. 129
The Wiener-Hopf technique	p. 130
The Sommerfeld problem	p. 132
High-frequency approximations	p. 136
A submerged horizontal plate	p. 141
Residue calculus theory	p. 148
Asymptotics of infinite products	p. 148
The finite dock problem	p. 151
Periodic coastlines	p. 157
Arrays	p. 167
An array of vertical circular cylinders	p. 168
A general interaction theory	p. 173
The wide-spacing approximation	p. 178
Scattering by equally-spaced identical structures	p. 182
Wave propagation through a periodic array	p. 183
Diffraction by multiple gratings	p. 187
A single grating	p. 188
Reciprocity relations	p. 190
Multiple gratings	p. 193
Wave interaction with small objects	p. 199
Introduction	p. 199
Diffraction by a breakwater	p. 200
Informal solution to the breakwater-gap problem	p. 201
A formal matching principle	p. 203
Formal solution to the breakwater-gap problem	p. 206
The insular breakwater	p. 213
Scattering by a vertical cylinder	p. 214
Radiation by a heaving cylinder	p. 217
A technique for eigenvalue problems	p. 220
Variational methods	p. 227
Scattering and radiation problems	p. 227
The variational principle	p. 228
Numerical implementation	p. 229
The Galerkin method	p. 231
Complementary approximations	p. 231
Eigenvalue problems	p. 233
Eigenvalues of the negative Laplacian	p. 233
The sloshing problem	p. 235
The maximum-minimum principle	p. 236
The Rayleigh-Ritz method	p. 237
Appendices
Bessel functions	p. 243
Multipoles	p. 247
Two dimensions, infinite depth	p. 247
Two dimensions, finite depth	p. 253
Three dimensions, infinite depth	p. 258
Three dimensions, finite depth	p. 261
Oblique waves in infinite depth	p. 264
Oblique waves in finite depth	p. 267
Principal-value and finite-part integrals	p. 269
References	p. 271
Index	p. 295
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781584881322
ISBN-10: 1584881321
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 320
Published: 26th February 2001
Publisher: CRC PR INC
Country of Publication: US
Dimensions (cm): 24.54 x 16.1 x 2.36
Weight (kg): 0.62
Edition Number: 1