A method for modeling perforated tube muffler components. I. Theory

TLDR: In this paper, a simple method is presented for modeling perforated muffler components, such as concentric resonators and expansion chambers, with one acoustically long dimension, using a segmentation procedure in which each segment is described by a transmission matrix.

Abstract: A simple method is presented for modeling perforated muffler components such as concentric resonators with perforated flow tube, and expansion chambers and reverse flow chambers with perforated inlet and outlet tubes. The theory includes mean flow, but is confined to those configurations having one acoustically long dimension. It is based on a segmentation procedure in which each segment is described by a transmission matrix. The four‐pole parameters of a component are then found from the product of the transmission matrices. The four‐pole parameters for configurations having through flow, cross flow, and reverse flow are presented. Because the product matrices are dimensionally small and because no inversion is needed, computational time is much lower than other methods such as finite element or finite difference. This allows rapid and economical modeling to be performed where iterative solutions are required because of dominating finite amplitude effects, for example.