Propagation of acoustic waves in two waveguides coupled by perforations. II. Application to periodic lattices of finite length

TL;DR

This paper presents an analytical model for acoustic wave propagation in coupled waveguides with perforations, analyzing effects like finite size, coupling, and dispersion in periodic lattices, applicable to mufflers and silencers.

Contribution

It introduces a comprehensive analytical approach using impedance matrices to study waveguides coupled by perforations, including effects of finite size and series impedance, which was not extensively covered before.

Findings

Coupling coefficient characterizes guide interactions.

Finite lattice size affects insertion loss and dispersion.

Series impedance influences cutoff frequencies and eigenmodes.

Abstract

The paper deals with the generic problem of two waveguides coupled by perforations, which can be perforated tube mufflers without or with partitions, possibly with absorbing materials. Other examples are ducts with branched resonators of honeycomb cavities , which can be coupled or not, and splitter silencers. Assuming low frequencies, only one mode is considered in each guide. The propagation in the two waveguides can be very different, thanks e.g. to the presence of constrictions. The model is a discrete, periodic one, based upon 4th-order impedance matrices and their diagonalization. All the calculation is analytical, thanks to the partition of the matrices in 2nd-order matrices, and allows the treatment of a very wide types of problems. Several aspects are investigated: the local or non-local character of the reaction of one guide to the other; the definition of a coupling coefficient; the effect of finite size when a lattice with n cells in inserted into an infinite guide; the relationship between the Insertion Loss and the dispersion. The assumptions are as follows: linear acoustics, no mean flow, rigid wall. However the effect of the series impedance of the perforations, which is generally ignored, is taken into account, and is dis- cussed. When there are no losses, it is shown that, for symmetry reasons, the cutoff frequencies depend on either the series impedance or the shunt admittance , and are the eigenfrequencies of the cells of the lattice, with zero-pressure or zero-velocity at the ends of the cells.