Handbook of Mathematical Techniques for Wave/Structure Interactions  book cover
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Handbook of Mathematical Techniques for Wave/Structure Interactions




ISBN 9781584881322
Published February 26, 2001 by Chapman and Hall/CRC
316 Pages

 
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Book Description

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.

Table of Contents

INTRODUCTION
The Water-Wave Problem
The Linearised Equations
Interaction of a Wave with a Structure
Reciprocity Relations
Energy of the Fluid Motion
EIGENFUNCTION EXPANSIONS
Introduction
Construction of Vertical Eigenfunction
Two-Dimensional Problems
Three-Dimensional Problems
Matched Eigenfunction Expansions
MULTIPOLE EXPANSIONS
Introduction
Isolated Obstacles
Multiple Bodies
INTEGRAL EQUATIONS
Source Distribution
Green's Theorem
Thin Obstacles
Interior Problems
Free-Surface Problems
Numerical Evaluation of Green's functions
Diffraction by a Gap in a Breakwater
Diffraction by an Insular Breakwater
Embedding Formulae
Numerical Solutions
THE WIENER-HOPF AND RELATED TECHNIQUES
The Weiner-Hopf Technique
Residue Calculus Theory
ARRAYS
The Wide-Spacing Approximation
SMALL OBJECTS
Introduction
Breakwater with a Gap
Vertical Cylinder
Heaving Cylinder
Eigenvalue Problems
VARIATIONAL METHODS
Scattering and Radiation Problems
Eigenvalue Problems
APPENDICES
Bessel Functions
Multipoles
Principle Value and Finite Part Integrals

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