A Thévenin-Inspired Approach to Multiple Scattering in Acoustics

Abstract

We have previously shown how Thévenin's theorem may be used to solve problems in linear acoustic scattering from a mobile body, by forming the solution as a superposition of the field scattered from the body when held immobile and the solution for radiation from the body in a quiescent field (Williams, R. P. and Hall, N. A., 2016, “Thévenin Acoustics” J. Acoust. Soc. Am., 140(6), pp. 4449–4455). For problems involving scattering from multiple mobile bodies, the approach can be extended by using multiport network formalism. The use of network formalism allows for the effects of multiple scattering to be treated using analogous circuit models, facilitating the integration of scattering effects into circuit-based models of acoustic transducers. In this paper, we first review Thévenin's theorem for electrical and linear acoustic systems, and discuss the Thévenin-inspired approach to scattering from one rigid, mobile cylinder. Two-port formalism is introduced as a way to address problems involving two scatterers. The method is illustrated using the problem of scattering from a pair of rigid, mobile cylinders in an ideal plane progressive wave. The velocities of the cylinders and the resultant pressure field in response to the incoming wave are found. Unique features of the method compared to more conventional approaches are discussed.