As standard ASTM E2611 reveals, the normal incidence sound transmission loss measured on a small sample in an acoustic tube is not only a property of the material but also strongly dependent on boundary conditions (generally unknown) and on the way the material is mounted. This article proposes an experimental method to control the effects of the lateral boundary conditions in an acoustic tube. The main objective is to deduce the properties of a “client element” (material sample) from the measured global acoustic properties of a patchwork composed by the “client material” and a known “host support.” Three patchwork configurations have to be distinguished: patchworks with and without an impervious and rigid interface between the elements and patchworks composed by elements that cannot be identified as equivalent fluids. For each of these configurations, the use of a specific method based on the Mixing Rule Method (MRM) or on the Parallel Transfer Matrix Methods (P-TMM or dP-TMM) used in reverse way is proposed. Numerical and experimental validations are proposed in acoustic tubes on a convenient configuration: a material sample surrounded by an air ring. This configuration allows reducing the material elastic-frame behavior to leave a limp-frame behavior. The proposed methods allow removing the effect of the lateral air ring host surrounding the material. For homogeneous materials, the two methods based on MRM and dP-TMM give similar good results. For non-homogeneous materials or for materials that cannot be modeled as equivalent fluids, only the method based on dP-TMM gives good results.

1.
ASTM International, E2611-19 Standard Test Method for Normal Incidence Determination of Porous Material Acoustical Properties Based on the Transfer Matrix Method, West Conshohocken, PA; ASTM International,
2019
, .
2.
ISO 10534-2, Acoustics—Determination of sound absorption coefficient and impedance in impedance tubes. Part 2: Transfer-function method, International Organization for Standardization, Geneva, Switzerland,
1998
.
3.
ASTM International, E1050-19 Standard Test Method for Impedance and Absorption of Acoustical Materials Using a Tube, Two Microphones and a Digital Frequency Analysis System, West Conshohocken, PA, ASTM International,
2019
, .
4.
R. J.
Donato
, “
Model experiments on surface waves
,”
J. Acoust. Soc. Am.
63
,
700
703
(
1978
).
5.
T. E.
Vigran
,
L.
Kelders
,
W.
Lauriks
,
P.
Leclaire
, and
T. F.
Johansen
, “
Prediction and measurements of the influence of boundary conditions in a standing wave tube
,”
Acta Acust.
83
,
419
423
(
1997
).
6.
B. H.
Song
,
J. S.
Bolton
, and
Y. J.
Kang
, “
Effect of circumferential edge constraint on the acoustical properties of glass fiber materials
,”
J. Acoust. Soc. Am.
110
,
2902
2916
(
2001
).
7.
B. H.
Song
and
J. S.
Bolton
, “
Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube
,”
J. Acoust. Soc. Am.
113
,
1833
1849
(
2003
).
8.
D.
Pilon
,
R.
Panneton
, and
F.
Sgard
, “
Behavioral criterion quantifying the edge-constrained effects on foams in the standing wave tube
,”
J. Acoust. Soc. Am.
114
,
1980
1987
(
2003
).
9.
H.-S.
Tsay
and
F.-H.
Yeh
, “
The influence of circumferential edge constraint on the acoustical properties of open-cell polyurethane foam samples
,”
J. Acoust. Soc. Am.
119
,
2804
(
2006
).
10.
M.
Schwartz
and
E. J.
Gohmann
, “
Influence of surface coatings on impedance and absorption of urethane foams
,”
J. Acoust. Soc. Am.
34
,
502
(
1962
).
11.
J.-F.
Allard
and
P.
Delage
, “
Free field measurements of absorption coefficients on square panels of absorbing materials
,”
J. Sound Vib.
101
,
161
170
(
1985
).
12.
A.
Cummings
, “
Impedance tube measurements on porous media: The effects of air-gaps around the sample
,”
J. Sound Vib.
151
(
1
),
63
75
(
1991
).
13.
X.
Olny
and
C.
Boutin
, “
Acoustic wave propagation in double porosity media
,”
J. Acoust. Soc. Am.
114
,
73
89
(
2003
).
14.
D.
Pilon
,
R.
Panneton
, and
F.
Sgard
, “
Behavioral criterion quantifying the effects of circumferential air gaps on porous materials in the standing wave tube
,”
J. Acoust. Soc. Am.
116
(
1
),
344
356
(
2004
).
15.
F. C.
Sgard
,
X.
Olny
,
N.
Atalla
, and
F.
Castel
, “
On the use of perforations to improve the sound absorption of porous materials
,”
Appl. Acoust.
66
,
625
651
(
2005
).
16.
T.
Dupont
,
P.
Leclaire
,
O.
Sicot
,
X. L.
Gong
, and
R.
Panneton
, “
Acoustic properties of air-saturated porous materials containing dead-end porosity
,”
J. Appl. Phys.
110
,
094903
094913
(
2011
).
17.
K.
Verdière
,
R.
Panneton
,
S.
Elkoun
,
T.
Dupont
, and
P.
Leclaire
, “
Transfer matrix method applied to the parallel assembly of sound absorbing materials
,”
J. Acoust. Soc. Am.
134
(
6
),
4648
(
2013
).
18.
K.
Verdière
,
R.
Panneton
,
S.
Elkoun
,
T.
Dupont
, and
P.
Leclaire
, “
Comparison between parallel transfer matrix method and admittance sum method
,”
J. Acoust. Soc. Am.
136
,
EL90
(
2014
).
19.
K.
Verdière
,
R.
Panneton
,
S.
Elkoun
,
T.
Dupont
, and
P.
Leclaire
, “
Recent highlights on the parallel transfer matrix method (PTMM)
,” in
Proceeding of Symposium on the Acoustics of Poro-Elastic Materials (SAPEM)
,
Stockholm
,
16–18 December 2014
.
20.
X.
Olny
, Ph.D. thesis,
Institut National des Sciences Appliquées
,
Lyon, France
,
1999
.
21.
E.
Gourdon
and
M.
Seppi
, “
On the use of porous inclusions to improve the acoustical response of porous materials: Analytical model and experimental verification
,”
Appl. Acoust.
71
(
4
),
283
298
(
2010
).
22.
F.
Chevillotte
,
L.
Jaouen
, and
F. X.
Bécot
, “
On the modeling of visco-thermal dissipations in heterogeneous porous media
,”
J. Acoust. Soc. Am.
138
(
6
),
3922
(
2015
).
23.
T.
Dupont
,
P.
Leclaire
,
K.
Verdière
,
R.
Panneton
, and
S.
Elkoun
, “
A method for measuring the acoustic properties of a porous sample mounted in a rigid ring in acoustic tubes
,” in
Proceeding 21st International Congress on Acoustics (ICA) Montreal
,
2–7 June 2013
.
24.
T.
Dupont
,
K.
Verdière
,
P.
Leclaire
, and
R.
Panneton
, “
A method to control the lateral boundary condition effects in the characterization of acoustic materials in an impedance tube
,” in
Proceeding of Internoise
,
San Francisco
,
9–12 August 2015
.
25.
J. F.
Allard
and
N.
Atalla
,
Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
(
Wiley and Sons, Ltd.
,
Chichester, West Sussex, United Kingdom
,
2009
), p.
358
.
26.
C. J.
Sacristan
,
T.
Dupont
,
O.
Sicot
,
P.
Leclaire
,
K.
Verdière
,
R.
Panneton
, and
X. L.
Gong
, “
A mixture approach to the acoustic properties of a macroscopically inhomogeneous porous aluminum in the equivalent fluid approximation
,”
J. Acoust. Soc. Am.
140
(
4
),
2847
2855
(
2016
).
27.
Y.
Salissou
,
O.
Doutres
, and
R.
Panneton
, “
Complement to standard method for measuring normal incidence with three microphones
,”
J. Acoust. Soc. Am.
131
,
EL216
(
2012
).
28.
N.
Geebelen
,
L.
Boeckx
,
G.
Vermeir
,
W.
Lauriks
,
J.-F.
Allard
, and
O.
Dazel
, “
Measurement of the rigidity coefficients of a melamine foam
,”
Acta Acust. Acust.
93
,
783
788
(
2007
).
29.
R.
Panneton
, “
Comments on the limp frame equivalent fluid model for porous media
,”
J. Acoust. Soc. Am.
122
(
6
),
EL217
EL222
(
2007
).
30.
Joint Committee for Guides in Metrology, Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008, Bureau international des Poids et Mesures, Sèvres,
2008
.
31.
Y.
Salissou
and
R.
Panneton
, “
Quantifying the through-thickness asymmetry of sound absorbing porous materials
,”
J. Acoust. Soc. Am.
124
(
2
),
EL28
(
2008
).
32.
O.
Doutres
,
N.
Atalla
, and
H.
Osman
, “
Transfer matrix modeling and experimental validation of cellular porous material with resonant inclusions
,”
J. Acoust. Soc. Am.
137
(
6
),
3502
3513
(
2015
).
33.
O. C.
Zwikker
and
C. W.
Kosten
,
Sound-Absorbing Materials
(
Elsevier
,
Amsterdam
,
1949
).
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