Reciprocity relations are among the most interesting and intriguing relations in classical physics. At first acquaintance these relations promise to be a goldmine of useful information. It takes some ingenuity, however, 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 always believed, however, that more information than is generally assumed can be wrested from reciprocity considerations. I have wondered in particular whether reciprocity considerations could be used to actually determine by analytical means the elastodynamic fields for the high-rate loading of structural configurations. I have 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 called the “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 those for time-harmonic fields, together with numerous applications, general and specific, old and new.