Application of the T-matrix method to the numerical modeling of a linear active sonar array

Abstract

Classically, the T-matrix method is a procedure to exactly compute the multiple scattering of an incident wave from a “cloud” of objects, given knowledge of the free-field scattering properties of a single object for an arbitrary incident wave. For acoustic waves, Profs. Baker and Scandrett have extended the T-matrix method to the case in which the radiation sources are also the scatterers, that is, to the case of an array of active transducers. This thesis is the first successful practical demonstration of the T-matrix method applied to an active sonar array for which a finite-element model was employed to compute the scattering properties of a single transducer. For validation, a T-matrix model of a linear array of piezoelectric spherical thin-shell transducers was modeled, for which analytical approximate values of the T-matrix element values are known. Subsequently, a T-matrix model of a linear array of piezoelectric class V flextensional “ring-shell” transducers was modeled. Beam patterns of the linear array models computed with the T-matrix method are compared with those of an array of point sources, demonstrating that the T-matrix method produces more realistic beam patterns, especially for end fire arrays.