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Handbook of Mathematical Techniques for Wave/Structure Interactions - C. M. Linton

Handbook of Mathematical Techniques for Wave/Structure Interactions

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

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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.

The water-wave problemp. 1
Introductionp. 2
The linearized equationsp. 3
Interaction of a wave with a structurep. 5
The radiation conditionp. 7
The scattering problemp. 8
The radiation problemp. 8
Hydrodynamic forces and momentsp. 10
Limitations of the inviscid, linear theoryp. 11
Reciprocity relationsp. 12
Energy of the fluid motionp. 19
Energy radiated to the far fieldp. 19
Potential and kinetic energyp. 20
Eigenfunction expansionsp. 23
Construction of vertical eigenfunctionsp. 24
Two-dimensional problemsp. 27
The wave-maker problemp. 27
Forced oscillations of a rectangular tankp. 28
Three-dimensional problemsp. 30
Sloshing in a rectangular tankp. 30
Oblique wavesp. 31
Scattering by a symmetric obstaclep. 32
Cylindrical polar coordinatesp. 33
Sloshing in a cylindrical tankp. 35
The Helmholtz equationp. 36
Scattering by a vertical circular cylinderp. 37
Matched eigenfunction expansionsp. 39
Scattering by a vertical barrierp. 39
A heaving truncated circular cylinderp. 45
The finite dock problemp. 49
Infinite depthp. 52
Multipole expansionsp. 55
Isolated obstaclesp. 56
A submerged circular cylinderp. 56
A heaving hemispherep. 64
Sloshing in a hemispherep. 67
Multiple bodiesp. 70
Two submerged circular cylindersp. 70
A row of vertical circular cylindersp. 73
Integral equationsp. 79
Source distributionsp. 80
Numerical solutionp. 82
Irregular valuesp. 84
Green's theoremp. 85
Scattering by a vertical cylinderp. 88
Thin obstaclesp. 90
Numerical solutionp. 91
Interior problemsp. 94
Free-surface problemsp. 96
Numerical evaluation of Green's functionsp. 98
Green's functions for three-dimensional water-wave problemsp. 99
Channel Green's functionsp. 104
Diffraction by a breakwaterp. 107
Diffraction by a gap in a breakwaterp. 107
Diffraction by an insular breakwaterp. 112
Embedding formulasp. 114
Numerical solutionsp. 117
Babinet's principlep. 123
The Wiener-Hopf and related techniquesp. 129
The Wiener-Hopf techniquep. 130
The Sommerfeld problemp. 132
High-frequency approximationsp. 136
A submerged horizontal platep. 141
Residue calculus theoryp. 148
Asymptotics of infinite productsp. 148
The finite dock problemp. 151
Periodic coastlinesp. 157
Arraysp. 167
An array of vertical circular cylindersp. 168
A general interaction theoryp. 173
The wide-spacing approximationp. 178
Scattering by equally-spaced identical structuresp. 182
Wave propagation through a periodic arrayp. 183
Diffraction by multiple gratingsp. 187
A single gratingp. 188
Reciprocity relationsp. 190
Multiple gratingsp. 193
Wave interaction with small objectsp. 199
Introductionp. 199
Diffraction by a breakwaterp. 200
Informal solution to the breakwater-gap problemp. 201
A formal matching principlep. 203
Formal solution to the breakwater-gap problemp. 206
The insular breakwaterp. 213
Scattering by a vertical cylinderp. 214
Radiation by a heaving cylinderp. 217
A technique for eigenvalue problemsp. 220
Variational methodsp. 227
Scattering and radiation problemsp. 227
The variational principlep. 228
Numerical implementationp. 229
The Galerkin methodp. 231
Complementary approximationsp. 231
Eigenvalue problemsp. 233
Eigenvalues of the negative Laplacianp. 233
The sloshing problemp. 235
The maximum-minimum principlep. 236
The Rayleigh-Ritz methodp. 237
Bessel functionsp. 243
Multipolesp. 247
Two dimensions, infinite depthp. 247
Two dimensions, finite depthp. 253
Three dimensions, infinite depthp. 258
Three dimensions, finite depthp. 261
Oblique waves in infinite depthp. 264
Oblique waves in finite depthp. 267
Principal-value and finite-part integralsp. 269
Referencesp. 271
Indexp. 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