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Numerical Simulation of the Measurement of the Diffuse Field Absorption Coefficient in Small Reverberation Rooms
Journal Article
2011-01-1641
ISSN: 1946-3995, e-ISSN: 1946-4002
Sector:
Topic:
Citation:
Bertolini, C. and Guj, L., "Numerical Simulation of the Measurement of the Diffuse Field Absorption Coefficient in Small Reverberation Rooms," SAE Int. J. Passeng. Cars – Mech. Syst. 4(2):1168-1194, 2011, https://doi.org/10.4271/2011-01-1641.
Language:
English
Abstract:
The Diffuse Field Absorption Coefficient (DFAC) is a physical
quantity very often used in the automotive industry to assess the
performance of sound absorbing multilayers. From a theoretical
standpoint, such quantity is defined under rather ideal conditions:
the multilayer is assumed to be infinite in extent and the exciting
acoustic field is assumed to be perfectly diffuse. From a practical
standpoint, in the automotive industry the DFAC is generally
measured on samples having a relatively small size (of the order of
1m2) and using relatively small cabins (in the order of 6-7 m₃). It
is well known that both these factors (the finite size of the
sample and the small volume of the cabin) can have an influence on
the results of the measurements, generating deviations from the
theoretical DFAC.
The widely used Transfer Matrix Method (TMM) allows the
evaluation of the theoretical DFAC and can, in some
implementations, approximately take into account the finite size of
the sample by means of a suitable analytical correction. Within
this method, though, the exciting acoustic field is always assumed
to be ideally diffused or, in any case, given by the superposition
of a set of uncorrelated plane waves impinging on the sample with
incident angles within a certain predefined range.
This paper intends to present numerical investigations that
allow going beyond this modeling technique.
In a first part of the paper, this is done using an analytical
model consisting of a rectangular cavity having the dimensions of a
small cabin. The reverberation time of this cavity is evaluated
with and without an absorbing sample placed on its floor and, from
these data, the corresponding DFAC is calculated using Sabine's
law. Results from this model are presented and compared with
results coming from testing. Using this analytical model, it is
already possible not only to evaluate the effect of the finite size
of the sample, but also the effect of its positioning on the
cavity's floor and, more importantly, the effect of the limited
volume of the measurement environment. Both these latter effects
cannot be taken into account in any way by means of the TMM.
In the second part of the paper, a further degree of complexity
is added: the same type of simulations are carried out by means of
a finite element model of the widely used Alpha Cabin (whose volume
is about 6.5 m₃), coupled to a finite element model of the
absorbing sample. Also in this case, simulation results are
compared to results coming from testing. The use of a finite
element model allows taking into account also the effect of the
diffraction around the sample's edges. Also this effect is
known to have, in special cases, some influence on the results of
DFAC measurements and, of course, cannot be taken into account
within the analytical model based on a rectangular cavity.