Generalized analysis of a muffler with any number of interacting ducts

The muffler elements that use perforated elements for acoustic attenuation are common in practice. In typical commercial mufflers perforated elements are used involving two, three, four or more interacting ducts. Analysis of such configurations involves writing down the basic governing equations of mass continuity, momentum balance, etc., and then elimination of velocity variables to obtain the coupled ordinary differential equations in terms of acoustic pressure variables. Mathematical modelling and the consequent analytical derivation of the transmission loss for these multi-duct acoustical elements become increasingly tedious, as just not the number of ducts, but also their relative arrangement along with the boundary conditions dictate the analysis considerably. In the present paper, authors have proposed a generalization and thus an algebraic algorithm to directly produce the system matrix, eliminating the tedium of writing the basic governing equations and elimination of velocity variables. Also, a convenient approach for applying the boundary conditions is outlined here.