Prediction of interior trim sound absorption using
Statistical Energy Analysis
L. Egab, X. Wang, M. Fard, R. Jazar
RMIT University, Bundoora, Victoria, Australia
e-mail: laith.egab@student.rmit.edu.au
Abstract
The study and prediction of acoustic performance of interior trim materials have always been of great
interest for acoustic engineers. The aim of this study was to investigate the use of statistical energy
analysis (SEA) to predict the acoustic performance of interior trim materials in term of sound absorption.
To accurately predict the acoustic performance by SEA, it is important to evaluate and calculate the
material physical properties such as porosity, flow resistivity, tortuosity, and viscous/thermal characteristic
length of interior materials. In this study, the material physical parameters were measured and estimated
using standardized test and inverse methods. Alpha cabin and impedance tube were used to measure the
random and normal sound absorption coefficients respectively. The computer model based on SEA
method was then validated with the experiment in order to obtain correlation between simulation and
measurement. The prediction of normal sound absorptions was found to be in acceptable agreement with
its corresponding test data, while prediction of random sound absorptions showed a relatively poor
correlation with the test data. Moreover, poor correlation has been investigated with further analysis of the
parametric data to enhance the correlation.
1
Introduction
Porous materials such as foams and fiber are widely used as passive noise control treatments. The study of
acoustical performance of these materials is essential to reduce the vehicle cabin noise. For the prediction
of the behavior of these materials knowledge of their acoustical and material physical properties are
important. The material physical properties such as flow resistivity, porosity, tortuosity, and two
characteristics lengths can be measured using standardized tests or predicted using inverse methods based
on theoretical modeling.
The acoustic performance of interior trim materials can be measured in term of sound absorption. The
normal sound absorption can be measured using impedance tube method based on ASTM 1050 standards
while the random sound absorption is measured using alpha cabin based on ASTM C423 standards [2, 3].
In this study, AutoSEA2 software package based on statistical energy analysis method is used to predict
the acoustic performance of interior trim materials. The estimated material physical properties in
conjunction with measured physical properties of the materials were used as input into AutoSEA2 to
predict the normal and random sound absorption of each material. The aim of this paper is to deliver a
practicable process which can estimate and optimize the interior trims acoustic performance in the early
design phase. This will allow the NVH engineer to optimize the new interior trim concept and save
development time and cost.
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Methodology
Materials
The SM200L and SM300L nonwoven mats are useful sound absorbers that can be applied in automotive
interiors such as door panels, pillar stuffers, instrument panels and package trays. These mats are
constructed from polyester staple fibers (35%) and polypropylene fibers (65%). The polypropylene fibers
are very fine and produce high-energy absorption while the larger polyester fibers strengthen the fabric.
The actual fabric is shown in Figure (1). A black scrim is attached to one side of the mat and is made of
polypropylene (100%) nonwoven fabric. The mat is hydrophobic and so, does not absorb water. While the
composition of both the mats is the same, their physical and acoustical properties vary slightly [12, 13].
The very fine structure of the fibers in nonwoven mats makes them efficient absorbers of sound
transmitted by air. Nonwoven materials absorb unwanted sound by dissipating the energy of sound waves
when they pass through the material and are directed by its fibers. The energy is further reduced as some
of it is converted to heat. The difference between the original amount of energy and the remaining
unabsorbed energy is the absorption coefficient of the material.
Figure 1: SM200L and SM300L Thinsulate™ Acoustic Insulation mats [12]
2.2
Material Physical properties in Biot theory
Biot theory was developed for sound propagation in granular porous materials and then adapted for sound
propagation in elastic porous materials [5]. It relates the acoustic properties of the materials, typically
measured in term of sound absorption coefficient and transmission loss, to the macroscopic or nonacoustical material physical properties. Porous materials have two phases; the solid phase, which is fibrous
in nature, forms the frame, while the interstitial fluid fills up the pores in the frame. The acoustical energy
is dissipated as the result of the interaction of the fluid and solid phases. In particular, they convert
acoustical energy into heat by thermal, structural and viscous means. For the coupling of the fluid with the
frame, the non-acoustical material physical properties involved in the Biot theory are the flow resistivity,
the porosity, the tortuosity, and thermal and viscous characteristic lengths.
The important material physical parameters of non-woven mats used in the experiment are listed in table1.
The bulk densities of SM200L and SM300L are 18.1Kg/m3 and 16.2 Kg/m3, respectively.
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Parameters
SM200L SM300L
Density (Kg/m3)
18.1
16.2
Thickness (mm)
13
21
Flow resistivity (Ns/m4)
36,000
31,288
Porosity
0.99
0.99
Tortuosity
1.1
1.5
Viscous characteristic length (µm)
109
109
Thermal characteristic length (µm)
218
218
Table 1: Physical parameters of the test samples
Measurements of the flow resistivity were made with the ASTM standards C522 [4]. Measurements of the
tortuosity were made by the SI method, as proposed by Leclaire [6]. Porosity was estimated from Eq. (1)
  1
1
m
(1)
Where:
1 = the density of the porous medium
 m = the density of the raw material
The assumed densities of SM200L and SM300L were 1810 Kg/m3 and 1620 Kg/m3, respectively.
Garai and Pompoli [7] proposed a relational equation (NMR) between the flow resistivity and the diameter
of the polyester fibers.
2
 NMR d NMR
 1.404  28.3  10 9
(2)
Where:
 NMR = the flow resistivity
d NMR = the diameter of polyester fiber predicted by Garai and Pompoli model.
Allard and Champoux [8] showed that sound propagation in rigid-framed fibrous materials depends on the
total length of fibers per unit volume of a material. Equations (3) – (5) show the relationship of the two
characteristic lengths and the total length per unit volume of a material.
4 1
d 2  m
1

2rL
  2
L
Where:
d = the diameter of a fiber (mm),
L = the total length of fibers per unit volume of a material (mm)
 = the viscous characteristic length predicted by Allard model ( m )
  = the thermal characteristic lengths predicted by Allard model ( m )
(3)
(4)
(5)
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Impedance Tube measurements
The acoustic absorption of the sound absorber materials is measured using an impedance tube in
accordance with ASTM E1050 standards. In 1979, Chung and Blazer presented the theory of a transfer
function method of measuring normal incident in duct acoustic properties. It works on the principle of
standing wave interference patterns due to the superposition of forward and backward-traveling waves
inside the tube. The complex transfer function method is used to measure the pressure differences between
two adjacent microphones and then calculate acoustical properties of the sample, namely, the complex
acoustic impedance at normal incidence, the complex reflection coefficient, and the sound absorption
coefficient of the sample. This method is quick and requires only a small size sample of the material.
Figure (1) shows test measurement set up uses an impedance tube with a sound source connected to the
other end. The specimen holder is a detachable extension of the tube and makes an airtight fit with the end
of the tube opposite the sound source. The B&K Front-end hardware in combination with Pulse software
was used to generate a white noise through this speaker into the tube. A white noise was then generated to
incident on the sample placed at the other end. Sound pressure is measured at two fixed locations where
the microphones are placed close to the samples to compute the normal incident sound absorption and
reflection coefficients.
Figure 2: Impedance tube set up
2.3
Alpha Cabin measurements
The Alpha cabin is a small reverberation chamber with non-parallel walls shown in figure (3), which is
used to measure the random sound absorption coefficient of the test sample. The acoustic absorption of the
alpha cabin is very low, and this design ensures a high level of sound insulation so as to maintain the low
levels of background noises at a particular frequency range.
The alpha cabin test required a 1x1m material specimen. The alpha cabin tests employed the B&K PULSE
T60 time decay measurement software program module, which is similar to that for a reverberation room
measurement following the ASTM C423 standards. The Alpha Cabin has three 50-W co-axial speakers for
sound source and three microphones were used to monitor the SPL inside the chamber. Absorption by
Alpha cabin is calculated from the measurement of the reverberation time with and without the test sample
using Sabine’s empirical formula given below:
S    55.3 
Where:
 = correction factor (0.92)
V
1 1
(  )
C T2 T1
(6)
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c = the speed of sound (m/s)
V = the volume of cabin (m3)
S = the surface area (m2)
α = the absorption coefficient
T2 = the reverberation time with a sample (sec)
T1= the reverberation time without a sample (sec)
Figure 3: Alpha Cabin
2.4
Statistical Energy Analysis simulation
Statistical Energy Analysis (SEA) is a noise and vibration prediction method, particularly effective at mid
to high frequencies [1]. SEA is used for acoustic modeling of the interior trim materials as the previous
methods such as Boundary Element Method (BEM) and Finite Element Method (FEM) become less
reliable and time consuming at the mid-high frequencies (>400 Hz). Basically, SEA is based on energy
balance between subsystems and the impact of acoustic treatment is governed by energy absorbed by the
treatment, energy transferred to adjacent structures, and energy transferred to adjacent acoustic spaces
[11].
The foam module in Auto SEA2 (software supplied by ESI Group) is based on the theory of elastic porous
materials (Biot theory) which can be used to predict the structural acoustic of multilayered energy
absorbing noise control treatments. Four different models of foam and fibrous materials are represented in
Auto SEA2: the elastic porous (foam) model, the limp porous (fiber) model, the rigid (fiber) porous model
and the Delany-Bazley (fiber) model. These models predict absorption coefficient, resonance dominated
insertion loss and mass dominated insertion loss using a plane wave propagation model for layered media
treatments.
There are four ways to alter sound absorption and transmission loss characteristics of subsystems available
in AutoSEA2. They are Sound Packages, Treatment-Layup, User-defined Treatment and Multiple NCT.
For example, Noise Control Treatment allows adding special materials to individual faces of subsystems
to modify their vibro-acoustic properties. The Treatment Lay-up allows user to specifically add one or
more layers on each of the subsystem. The layer can be foam, fiber, fluid, isotropic solid and also viscoelastic solid [9]. From measurement data or empirical formulas the material physical properties such as
airflow resistivity, porosity, tortuosity, and the two characteristic lengths are obtained and then substituted
to the SEA model. The model allows for predicting the acoustic properties of the sound absorption
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coefficients and sound transmission loss from these material physical parameters. Inverse method using
the measured acoustic properties can also be used to estimate the non-acoustical material physical
properties in AutoSEA2 using User-defined Treatments.
Figure 4: Simulation of Alpha Cabin and Foam using SEA
3
Results and discussion
Figure (5) and (6) show the differences in normal and random incidence absorption coefficients between
the SM200L and SM300L, respectively. We may be able to explain the results to some degree by
evaluating the physical properties of the test samples as listed in table1. For example, SM300L has better
absorption coefficient in the whole frequency range because it has the higher thickness 21mm in
comparison to SM200L with thickness 13 mm. Although SM200L has higher airflow resistivity but it has
lower absorption coefficients. The non-woven mats with its high airflow resistivity show good absorption
characteristics when tested in the Alpha cabin according to ASTM C423 standards, see figure (6). This is
due to the Alpha Cabin’s ability to take random incidence sound absorption into account.
Correlation between the measured and predicted normal sound absorption associated to samples SM200L
and SM300L are presented in figures (7) and (8), respectively. The measured physical parameters were
substituted into the SEA model. The results showed that predicted normal absorption coefficients of test
samples were in close correlation to measured data. The discrepancy between predicted and measured
value is calculated by
100 
m   p
m
(7)
Where:
 m = is the measured absorption coefficient
 p = is the predicted absorption coefficient
The mean value of the prediction error of sample SM200L was 7 % and that of Sample SM300L was less
than 1%. Based on these results of the normal incidence absorption, the prediction accuracy of SEA model
was superior to that of measured absorption using Impedance tube.
Figure (9) and (10) show the comparison between the measured and predicted diffuse field absorptions
for the SM200L and SM300L, respectively. It can be seen that the predicted absorption coefficients is
somewhat lower than the measured one, in particular in the frequency range between 500 and 4000 Hz.
One possible explanation for this underestimation is that SEA only predict the absorption at one oblique
angle -/+ 78 degree and does not take random diffusivity into account. Also, the diffraction effects of
sound due to the finite dimension of the materials, which might play a role in increasing the measured
absorption coefficients [10].Figure (11) shows the effect of airflow resistivity on sound absorption
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coefficients. It is clear that the variation in the airflow resistivity has a significant effect on sound
absorption of sound porous materials. Also, figure (12) shows that tortuosity determines the high
frequency behavior of sound porous materials. The greater the tortuosity value is, the better is sound
absorption of the material at high frequencies.
Figure 5: Normal sound absorption of SM200L and
SM300L
Figure 6: Random sound absorption of SM200L
and SM300L
Figure 7: Normal sound absorption correlation of
SM200L
Figure 8: Normal sound absorption correlation
of SM300L
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Figure 9: Random sound absorption correlation of
SM200L
Figure 10: Random sound absorption correlation
of SM300L
Figure 11: Effect of flow resistivity on sound
absorption coefficients
Figure 12: Effect of tortuosity on sound
absorption coefficients
Conclusions
This paper discusses the acoustical characterization of interior trim materials using simulation technique
based on Statistical Energy Analysis (SEA). It gives an overview of technique characterization of porous
acoustic materials to simulate acoustic properties from material physical properties. It also discusses the
details about the experimental evaluation of sound absorption of acoustic materials. SEA provides a quick
solution to NVH engineers to optimize the new interior trim concept save development time and cost. The
prediction of normal sound absorptions has been found to be in acceptable agreement with measurements,
while prediction of random sound absorptions has been found to be relatively poor. The material physical
properties such as flow resistivity and tortuosity are identified to have significant effects on characterizing
sound absorption of materials. The results have showed that materials with high porosity, tortuosity and
optimized flow resistivity give better sound absorptions. Further study on characterization of layered trim
materials is needed to be done in order to validate the methodology of acoustic characterization of interior
trims.
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Acknowledgements
The authors would like to thank 3M Australia for their support providing us with the materials that making
this work possible. Also sincere thanks to Mr. Peter Tkatchyk, NVH lab supervisor for his support.
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