Introduction

Fields of classical physics such as electromagnetic wave theory, acoustics and elastodynamics all have their own reciprocity theorems, which for acoustics and elastodynamics have been discussed in the preceding chapters. A comparable discussion of reciprocity in electromagnetic wave theory is outside the scope of this book. Moreover, there are already several books that have dealt in considerable detail with electromagnetic reciprocity; see e.g., Collin (1960), Auld (1973) and de Hoop (1995).

Interesting applications of reciprocity relations for the interactions of electromagnetic and elastodynamic fields to non-destructive evaluation, particularly as it relates to piezoelectricity, have not received the attention that they deserve, with the exception of the work by Auld (1979). In the present chapter we therefore attempt to correct for this lack of exposure by a discussion of reciprocity for piezoelectric systems.

General reciprocity relations involving coupled electromagnetic and elastic waves were first presented by Foldy and Primakoff (1945) and Primakoff and Foldy (1947), who used these relations to demonstrate the interchangeability of source and receiver in electro-acoustic transmission measurements. In the important paper by Auld (1979) these relations were used to analyze elastic wave scattering coefficients from observations at the electrical terminals of the electromechanical transducers employed in performing a non-destructive testing experiment. In Auld's paper, an expression was derived that directly relates the electrical signal received by an ultrasonic transducer to the radiation patterns of the transmitting and receiving transducers and to the modified patterns resulting from scattering from a flaw.