The transfer matrix method (TMM) is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer. In this work, a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks, acoustic mosaics, or a collection of acoustic elements in parallel. In this method, it is assumed that each parallel element can be modeled by a 2 × 2 transfer matrix, and no diffusion exists between elements. The resulting transfer matrix of the parallel assembly is also a 2 × 2 matrix that can be assembled in series with the classical TMM. The method is validated by comparison with finite element (FE) simulations and acoustical tube measurements on different parallel/series configurations at normal and oblique incidence. The comparisons are in terms of sound absorption coefficient and transmission loss on experimental and simulated data and published data, notably published data on a parallel array of resonators. From these comparisons, the limitations of the method are discussed. Finally, applications to three-dimensional geometries are studied, where the geometries are discretized as in a FE concept. Compared to FE simulations, the extended TMM yields similar results with a trivial computation time.
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December 2013
December 01 2013
Transfer matrix method applied to the parallel assembly of sound absorbing materials
Kévin Verdière;
Kévin Verdière
a)
GAUS, Department of Mechanical Engineering, Université de Sherbrooke (Qc)
, J1K 2R1, Canada
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Raymond Panneton;
Raymond Panneton
GAUS, Department of Mechanical Engineering, Université de Sherbrooke (Qc)
, J1K 2R1, Canada
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Saïd Elkoun;
Saïd Elkoun
GAUS, Department of Mechanical Engineering, Université de Sherbrooke (Qc)
, J1K 2R1, Canada
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Thomas Dupont;
Thomas Dupont
DRIVE, ISAT, Université de Bourgogne
, 49 Rue Mademoiselle Bourgeois, 58027 Nevers Cedex, France
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Philippe Leclaire
Philippe Leclaire
DRIVE, ISAT, Université de Bourgogne
, 49 Rue Mademoiselle Bourgeois, 58027 Nevers Cedex, France
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a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]
J. Acoust. Soc. Am. 134, 4648–4658 (2013)
Article history
Received:
October 24 2012
Accepted:
February 11 2013
Citation
Kévin Verdière, Raymond Panneton, Saïd Elkoun, Thomas Dupont, Philippe Leclaire; Transfer matrix method applied to the parallel assembly of sound absorbing materials. J. Acoust. Soc. Am. 1 December 2013; 134 (6): 4648–4658. https://doi.org/10.1121/1.4824839
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