Method for Computing the Electrical and Acoustical Behavior of Free-Flooding Cylindrical Transducer Arrays

A method is described for computing the electrical and acoustical behavior of arrays of free-flooding, thin, cylindrical transducers. Each of the gaps between transducers is divided into a small number of “water rings,” which are acoustically driven by the vibrations of the transducers and other water rings. Several water rings are also added at each end of the array. Mutual impedance coefficients between transducer rings and water rings can then be determined from expressions for mutual impedance between bands on the inside and outside of an infinite rigid cylinder. Comparisons of theoretical predictions and measured data are made for an actual four-element array. The theoretical and measured admittance plots agreed very well with respect to size, shape, and frequency. For the two trandsucers in the middle of the array, the input conductance (and resistance) were negative over a small band for both theory and measurement. The theoretical and measured transmit voltage responses agreed well over most of the band considered. However, the measured beam patterns had deep nulls on the cylindrical axis that were not reproduced in the theoretical results.