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PREFACE

Reciprocity relations are among the most interesting and intriguing relations in classical physics. At first acquaintance the relations promise to be a gold mine of useful information. It takes, however, some ingenuity to unearth the nuggets that are not immediately obvious from the formulation. In the theory of elasticity of solid materials the relevant reciprocity theorem emanated from the work of Maxwell, Helmholtz, Lamb, Betti and Rayleigh, towards the end of the nineteenth century, and several applications have appeared in the technical literature since that time. This writer has, however, always believed that more information than generally assumed could be wrested from reciprocity considerations. I was particularly wondering whether reciprocity considerations could be used to actually determine by analytical means the elastodynamic fields for high-rate loading of structural configurations. I explored this question for a number of problems, and obtained the actual fields generated by loading from a reciprocity relation in conjunction with an auxiliary solution, a free wave, which was called a virtual wave. These recent results comprise an important part of the book.
To my knowledge, the topic of reciprocity in elastodynamics has not been discussed in a comprehensive manner in the technical literature. It is hoped that this book will fill that void. Various forms of the reciprocity theorem are presented, with an emphasis on the ones for time-harmonic fields, and numerous applications, general and specific, old and new, are presented.
The book should be of interest to research workers in such fields as ultrasonics of solids, particularly for detection of defects and the determination of elastic constants, seismology, exploratory geophysics, the dynamic response of structures, and structural acoustics.
Parts of the book were read by graduate students in a course on wave propagation in elastic solids. My colleague, John Harris, also read a number of Chapters, as did David Feit. Their comments are gratefully acknowledged.
A special word of thanks goes to Linda Kearfott who typed and retyped the manuscript as the material was arranged, rearranged and revised.
Over the years my work in the area of this book and in related areas has been consistently supported by the Office of Naval Research. The monitor of my research project in recent years was Dr. Y. N. Rajapakse. The ONR funding is gratefully acknowledged.
The constant support of my wife, Marcia, made it possible to complete the book. I can never thank her enough for all she has given me.