


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