Propagation of Acoustic Waves in Two Waveguides Coupled by Perforations. II. Analysis of Periodic Lattices of Finite Length

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 discussed. 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.

Characteristics and mechanism of coupling effects in parallel-cladded acoustic waveguides

“…In 1994, coupled wave propagation in two guides through perforations was discussed theoretically by Kergomard and collaborators [23]. Later, in 2016, they analyzed the coupling between two waveguides consisting of periodic lattices of finite length in 2016 [24]. In 2005, Pennec and collaborators studied the resonant tunneling of acoustic waves in phononic crystal waveguides.…”

Pulsation attenuation in a reciprocating compressor piping system using a volume-perforated pipe-volume suppressor

“…1 Owing to the successful use of filters to reduce noise, scholars have started to apply filters with different internals to suppress gas pulsations. 2,3 Perforated elements, which are widely used in sound attenuation, 4–8 are added into surge tanks to help improve the performance in attenuating pressure pulsations. Brablik 9 suggested the use of a perforated pipe to reduce pressure pulsations and provided a brief analysis to show the operation of the perforated pipe.…”