Application of the T-matrix method to the numerical modeling of an array of active acoustic transducers

Abstract

The conventional T-matrix method is a procedure for the computation of the far-field scattering of a plane wave by a compact but otherwise arbitrary collection of scatterers [cf. V. V. Varadan and V. K. Varadan, J. Acoust. Soc. Am. 70, 213–217 (1981)]. Its strength is that the effects of multiple scattering to all orders are rigorously and self-consistently obtained from the single-scattering properties of each scatterer in a free-field environment. For acoustic waves, the T-matrix method has been extended to the case where the source of the scattered radiation is the scatterers themselves, i.e., to the case of an array of active transducers. As an example, the method has been applied to an array of piezoelectric spherical shell sonar transducers. A description of the T-matrix method applied to active acoustic arrays will be given. The use of the finite-element code ATILA [J. N. Decarpigny et al., J. Acoust. Soc. Am. 78, 1499–1507 (1985)] to compute the single-transducer radiation and scattering properties will be described. Results will be compared to Pritchard’s approximation. [Work sponsored in part by the Naval Postgraduate School and the Naval Undersea Warfare Center.]