Vibrations of Coaxially Segmented, Longitudinally Polarized Ferroelectric Tubes

Ferroelectric ceramic materials are often used in underwater sound transducers by stacking a number of identical pieces together. In this paper, the theoretical behavior is derived for a ferroelectric, cylindrical tube consisting of any number of longitudinally polarized coaxial segments. The effects due to lateral dimensions, which may not be negligible, are included. Electromechanical equivalent circuits are developed that greatly simplify and improve the analysis of composite resonators in transducer design. The theoretical parameters are related simply to experimentally measured quantities so that the parameters can be evaluated even though the lateral dimensions are large relative to the length of each individual segment. The dielectric, piezoelectric, and elastic losses are included in the general theory but losses are not considered explicitly.