Propagation of acoustic waves in two waveguides couples by perforations. I. Theory.

International audienceThe problem of propagation in two guides coupled by perforations, important for a perforated tube muffler, is discussed. At low frequencies, if the distance between perforations is sufficiently large, a discrete model can be used. An exact equivalent circuit for a perforation is obtained by using a modal theory and a matrix formalism. A series inductance due to the existence of antisymmetric field in the perforation is proven to exist, completing the perforation shunt impedance concept. This model is directly exploitable for lattice analysis. For homogeneous lattices (i.e. with identical propagation in the two guides), either regular or irregular, two modes exist: a planar mode and a "flute" mode, either propagating or evanescent. Cutoff frequencies of periodic lattices are found to depend on either the shunt inductance or the series inductance (the first cutoff depending on the shunt one). In homogeneous lattices, a new type of evanescent waves can exist, with non-zero energy flux, equal and opposite in sign in each guide. Finally, the effect of mean flow in such a lattice is discussed