A wide range of mathematical techniques are now available for the solution of problems involving the interaction of waves with structures. Many of these techniques are described in existing textbooks, but often not in the context of wave/structure interactions and often without reference to applications at all. This book draws together some of the most important of these methods into a single text to form a convenient reference work for both applied mathematicians and engineers. All of the techniques are described within the context of wave/structure interactions and are often illustrated by application to research problems. An advantage of describing a number of methods within the same text is that, for particular problems, direct comparisons can be made between them.
The methods described in this book may be applied to a wide variety of problems from many fields of research including water waves, acoustics, electromagnetic waves, waves in elastic media, and solid-state physics. When writing the book it soon became clear that it was impossible to do justice to all of these fields, and so we decided to focus mainly on problems that have interpretations within the linearized theory of water waves. However, we have made extensive reference to applications of the techniques in other areas, both throughout the text and in extensive bibliographical notes that are placed at the end of many of the sections within the book. Our hope is that in this way the book will be a useful reference work for workers from a wide range of research fields.
The reader is assumed to have a knowledge at an undergraduate level of multivariable calculus, including the solution of linear partial differential equations, and complex-variable theory. Detailed explanations are given of the important steps within the mathematical development and, where possible, physical interpretations of mathematical results are
