Plane wave propagation in generalized multiply connected acoustic filters

Abstract

A generalized algorithm is developed for studying the sound wave propagation in a system of interconnected rigid walled acoustic filter elements. The algorithm is based on the transfer matrix approach of analysis. Interconnection between various elements is represented by a connectivity matrix. Equations of mass velocity continuity and pressure equilibrium at the interconnections are generated using this connectivity matrix and are solved to get the overall transfer matrix of the system. The algorithm used for generalized labeling of the network and computation of transmission loss is discussed. The algorithm is applied to investigate multiply connected automobile mufflers as a network of acoustic elements. Results for some configurations have been compared with those from the finite element model analysis and experiments cited in the literature. A parametric study with respect to some geometric variables is carried out. While the results are illustrated here for a few configurations, the approach holds for all kinds of combinations of acoustic elements with any degree of complexity. The acoustical similarity between apparently different networks is discussed. The approach is flexible to incorporate any other acoustic elements, provided the acoustic variables at the junctions of the element can be related by a transfer matrix a priori.