A generalized network formulation for acoustic scattering

Abstract

The discretized Helmholtz and equivalence integral equations yield the impedance representation of a generalized network formulation for acoustic scattering. Trans- and self-impedances relate the ensonification, the scattered field, and the pressure and velocity on the scatterer’s surface, S; the scatterer’s dry impedance loads S. This formulation suggests applying analysis tools from electrical circuit theory: network element abstraction and change of field-variable basis. The scatterer’s wet admittance (impedance) corresponds to the augmented driving point admittance (impedance) from electrical network theory. The lower-branch modes of the scattering from a submerged spherical shell occur when the reactance looking into the fluid from S negates that looking into the shell. Change of basis on S transforms the impedance representation into the admittance, arbitrary-reference, and network-scattering representations. The impedance, admittance, and arbitrary-reference representations naturally separate hard, soft, and intermediate background scattering, respectively. Scattering from passive objects with limited vibrational degrees of freedom is bounded: the lower-branch modes of the submerged spherical shell approach this bound. No bound exists when the vibrational degrees of freedom are unlimited.