Introduction

The problem of the interaction between the vibration of a finite elastic structure and the associated acoustic field in an unbounded exterior domain occurs in many areas of mathematical physics. In particular, in the field of underwater acoustics it is required to determine the acoustic field either radiated by a submerged vibrating elastic structure or scattered by a submerged elastic structure. Here, the impedance mis-match between the structure and the acoustic medium is less than that between the same structure and air and hence it is often not appropriate to assume that the surface of the structure is perfectly rigid. Examples of this problem range from that of finding the radiated or scattered sound field around entire ships and submarines to that of determining the behaviour of individual sonar transducers. A practical problem considered here is to determine the acoustic field radiated by a piezoelectric ring sonar transducer and the frequency for which the maximum response is obtained.