PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Prediction of oblique incidence sound absorption coefficient for
microfiber sound absorber
Tatsuhiro KOMITO1; Senji KITAHARA1; Toshimitsu TANAKA2
1
2

Sekiso Co., Ltd., Japan

Kanagawa University, Japan

ABSTRACT
Automotive parts are required to reduce weight and size, and such the task is also necessary for soundabsorbers as well. So the microfiber sound absorber with high performance whose fiber diameter is several
hundreds nanometers or several micrometers is being used widely. On the other hand, it is important todevelop techniques for estimating sound absorbing performance when we design the structure of microfiber
sound absorber.
However, preceding research is not for estimating oblique incidence sound absorbing coefficient but for
estimating normal incidence sound absorbing coefficient. This paper presents numerical calculation andexperiment for the oblique incidence sound absorbing coefficient of the microfiber sound absorber in the freesound field, and refers to some considerations on the structure of microfiber sound absorber.
Keywords: Sound absorbing material, Microfiber, Finite element method

1. INTRODUCTION
The weight reduction and space saving of automobile parts are advancing, and for the soundabsorbing material such the tackling is also becoming indispensable. For this reason, microfiber soundabsorbing materials having a fiber diameter of several hundred nanometer or several micrometers,
which are light-weight, thin, and have high sound absorbing performance, are beginning to be widelyused.
Regarding the prediction method of the normal incidence sound absorption coefficient of the
microfiber sound absorbing material, it has been reported by Kato (1) and Kurosawa (2) et al. that themeasured value and the predicted value do not coincide with each other in the Delany -Bazley modeland the Miki model when the fiber diameter is small, and the limp frame porous model proposed by thePanneton (3) is valid. However, with respect to the flow resistivity, the porosity, the tortuosity, theviscous characteristic length, the thermal characteristic length, etc. of the non-acoustic parameters
required for calculating the limp frame porous models, it has been reported by Kino (5) that theestimated value and the measured value of the sound absorption coefficient almost coincide with eachother when we use non-acoustic parameters identified from the measured sound absorption coefficientby the software Foam-X (manufactured by ESI Corporation) based on the inverse method (4), but thatthe identified value and the measured value of the non-acoustic parameters do not always coincidewith each other.
On the other hand, for the actual application cases of the microfiber sound absorbing material, notonly the normal incident sound absorption coefficient but also the oblique incident sound absorption
coefficient are necessary in many cases, but there is no report of the prediction for the oblique
incidence sound absorption coefficient of microfiber sound absorber.
Therefore, in this paper, for the purpose of predicting the performance of the oblique incidencesound absorption coefficient of the microfiber sound absorbing material, first, the non-acoustic
parameter in the normal incidence sound absorption coefficient prediction was examined. Next, theexperimental value of the oblique incidence sound absorption coefficient was compared with thepredicted value by the finite element analysis, and the knowledge for obtaining the predicted value
1

1984

komito@sekiso.co.jp

with high accuracy was obtained.

2. THEORY
The limp frame porous model, which has been validated in predicting the normal incidence soundabsorption coefficient of the microfiber sound absorbing material, is a model derived from the energy
loss by the flow through the vibrating soft skeleton of a material. The complex elastic modulus of thematerial [ K~ eq ] and the complex density of the material [ ~eq ] are obtained by the following equations(1),(2) and (3).
~K eq 

P0 j 0 B 2 2  
8    11  
1

2
2
16
  j 0 B  

~eq ~eq 

1(1)

~eq M   0 2
M  ~eq  2  0(2)2
 0  
4  
1 j
1  j 2 2 20    0   

 , M     0 ,   1  
s



(3)

~
Where Kis the effective bulk modulus of air in the fiber,  is the air specific heat ratio (=1.4), P0 iseq
the standard atmospheric pressure (=1013 hPa), 𝜂 is the air viscosity (=1.81×10 -5 Ns/m2),   is thethermal characteristic length, B 2 is the air Prandtl number (=0.708),  is the angular frequency,  0 is
 is the effective density of air in the fiber,   is the tortuosity,  is thethe air density (=1.2 kg/m3), ~eq
porosity,  is the flow resistivity,  is the viscous characteristic length,  is the density of thesample,  s is the density of the fiber.

3. PREDICTION OF NORMAL INCIDENCE SOUND ABSORPTION
COEFFICIENTS OF MICROFIBER SOUND ABSORBING MATERIALSAs a preliminary stage of the performance prediction of the oblique incidence sound absorption
coefficient of the microfiber sound absorbing material, the prediction model with high accuracy for thenormal incidence sound absorption coefficient was examined.
3.1 Specimens of Microfiber Sound Absorbing Material
Table 1 shows the average density and porosity of five specimens having different densities used
for the measurement. The material of test pieces were polypropylene fibers, the average fiber diameterwas 3.02 μm, and the thickness of the test pieces was 20 mm.
Table 1 – Sample properties of microfiber absorbers
A

B

C

D

E

Density(kg/m3)

7.89

14.09

20.31

28.30

40.71

Porosity

0.99120.98430.9774

0.9686

0.9548

3.2 Actual Measurement of The Normal Incidence Sound Absorption CoefficientFig. 1 shows the measured values of the normal incidence sound absorption coefficients of thespecimens having different densities shown in Table 1. The impedance Tube, Type4206 (manufactured
by B&K) was used for measuring the normal incidence sound absorption coefficient.

1985

Sound absorption coefficient

100%
80%
60%

A(7.89kg/㎥ )B(14.09kg/㎥ )40%

C(20.31kg/㎥ )20%

D(28.30kg/㎥ )E(40.71kg/㎥ )

0%
0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

Fig.1 – Measured normal incidence sound absorption coefficients of microfiber absorber samples whose
thicknesses are 20mm.
3.3 Predictive Calculation
First, for the four calculation models shown below, the prediction of the sound absorption
coefficient in the case of thickness of 20 mm was calculated.
(i) Delany-Bazley-MIKI model (6)(ii) Limp frame porous model 1(Non-acoustic parameters except for the flow resistivity identified
by Foam-X from the measured results of the sound absorption coefficient in Fig. 1 were used,
but the flow resistivity was measured value.)(iii) Limp frame porous model 2(Non-acoustic parameter identified by Foam-X from the measured
results of the sound absorption coefficient in Fig. 1 were used, and the flow resistivity was also
identified by Foam-X.)(iv) Using the characteristic impedance and complex propagation constant measured by thetwo-microphone method
The value of the flow resistivity were calculated in the approximate equation derived frommeasured data of the flow resistivity shown in Fig.2, in which 65 samples with range of densities from
15.8 kg/m3 to 59.3 kg/m3 were measured by AIR-PERMEABILITY TESTER, KES-F8-AP1(manufactured by Kato Tech Co., Ltd.). The value of the flow resistivity in the model (i) and (ii) was
obtained by substituting the density of the specimen into the approximate equation, and was identified
by using Foam-X in the model (iii).
Flow resistivity(Ns/m4)

7.E+05
6.E+055.E+05
4.E+05
3.E+05

2.E+05
1.E+050.E+0002040Density(kg/m3)

60

80

Fig.2 – Measured flow resistivity
It can be seen from Table 2 that the identified values of flow resistance differ greatly from themeasured values as the density increases. On the other hand, the difference between the case in which
the flow resistance is identified and the case in which the flow resistivity is measured, is small for theviscosity characteristic length and the thermal characteristic length.
Fig. 3 shows the calculated values and the measured value of the normal incidence soundabsorption coefficient of the models (i) to (iv). In these figures, “with FR” means that the measured
flow resistivity was used for the calculation, and “without FR” means that the identified flow
resistivity was used for the calculation.
From Fig.3, it can be confirmed that the MIKI model is not suitable for predicting the performance1986

of the microfiber sound absorbing material because the degree of coincidence decreases against
increasing densities.
Since the limp frame model (iii) has the non-acoustic parameters which have been identified so thatthey coincide with the actual measured sound absorption coefficient, the calculated value of thenormal incident sound absorption coefficient is consistent with experimentally measured value.
However, with respect to the model (ii) in which the measured values o f the flow resistances wereadopted in the identification of the parameters, the consistency decreases as the density becomes larger
than that of the specimen D (28.30 kg/ m3 ), which suggests the necessity of the consideration forhandling non-acoustic parameters to apply the limp frame model of the microfiber sound absorbing
material.
Table 2 shows the non-acoustic parameters of the specimens identified by the Foam-X andmeasured flow resistivities used to calculate the limp frame porous model.
Table 2 – Non-acoustic parameters of the specimens
Usage of
Flow
Density
VCL(a) TCL(b)measured flow
3 Porosity resistivity Tortuosity(kg/m )
(μm)
(μm)
resistivity(Ns/m4)

A

○
×

7.89

0.9912

19614
20128

1
1

41.3
41.5

82.5
82.9

B

○
×

14.09 0.9843

49296
44927

1
1

24.3
24.3

48.7
48.6

C

○
×

20.31 0.9774

88144
63759

1
1

17.6
16.6

35.2
33.3

D

○
×

28.30 0.9686

149356100424

1
1

12.1
11.3

24.1
22.6

E

○
×

40.71 0.9548

266126143680

1
1

6.7
9.4

13.3
18.8

80%
Exp.

(i) MIKI

40%(ii) Limp_with FR

20%(iii) Limp_without FR(iv) Measured Zc,γ

0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

3

Sound absorption coefficient(a) A (Density: 7.89kg/m )

80%

60%

Exp.

(i) MIKI

40%(ii) Limp_with FR

20%(iii) Limp_without FR(iv) Measured Zc,γ

0%

6000

0

1000

2000 3000 4000
Frequency (Hz)(b) B (Density: 14.09kg/m )

100%
80%

60%

Exp.

(i) MIKI

40%(ii) Limp_with FR

20%(iii) Limp_without FR(iv) Measured Zc,γ

0%

0

1000

5000

3

2000 3000 4000
Frequency (Hz)

5000

6000

Sound absorption coefficient

60%

100%

Sound absorption coefficient

100%

Sound absorption coefficientSound absorption coefficient(a): Viscous characteristic length, (b): Thermal characteristic length

6000

100%
80%

60%

Exp.

(i) MIKI

40%(ii) Limp_with FR

20%(iii) Limp_without FR(iv) Measured Zc,γ

0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

3

(c) C (Density: 20.31kg/m )

100%
80%

60%

Exp.

(i) MIKI

40%(ii) Limp_with FR

20%(iii) Limp_without FR(iv) Measured Zc,γ

0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

(d) D (Density: 28.30kg/m3)(e) E (Density: 40.71kg/m3)
Fig.3 – Comparison between measured and predicted normal incidence sound absorption coefficient of
microfiber absorber sample A – E whose thickness is 20mm.
3.4 Predictive Calculations for Different Thicknesses
In order to evaluate the prediction accuracy of the four calculation models ((i) to (iv)) in thepreceding section, the measured values and the predicted calculation values were compared in Fig.4
and Fig.5, where the thickness was different, but the density was same as that shown in Table 1. In thecalculation, previously identified non-acoustic parameters were adopted. Comparisons were made fortwo cases with thicknesses of 10 mm and 40 mm.

1987

80%

60%
40%
20%
0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

6000

0

3

1000

2000 3000 4000
Frequency (Hz)

80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

1000

2000 3000 4000
Frequency (Hz)

5000

100%
80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

6000

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

3

(b) B (Density: 14.09kg/m )

100%

0

5000

3

(a) A (Density: 7.89kg/m )Sound absorption coefficient

100%

Sound absorption coefficientExp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γSound absorption coefficient

100%

Sound absorption coefficientSound absorption coefficient

From Fig.4 and Fig.5, it was found that the consistency between the measured value and thecalculated value of the MIKI model was generally poor for both different thickness. In addition, it wasconsidered that the model (iv) based on the measured characteristic impedance and the complex
propagation constant has poor consistency when the material is thin, because the influence of themeasurement error of the two-microphone method may appear. On the other hand, the limp frame
porous model has more accurate consistency than other models, and the model (iii) was the mostaccurate model in which the value of the flow resistivity was identified by Foam-X the same as othernon-acoustic parameters were identified at the specimen thickness 20mm, although the identified
value of the flow resistivity was different from measured value.

(c) C (Density: 20.31kg/m )

100%
80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

6000

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

20%
0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

3

Sound absorption coefficient(a) A (Density: 7.89kg/m )

6000

80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

0

1000

2000 3000 4000
Frequency (Hz)(b) B (Density: 14.09kg/m )

100%
80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

0

1000

5000

3

2000 3000 4000
Frequency (Hz)

5000

6000

Sound absorption coefficient

40%

100%

6000

Sound absorption coefficient

100%

Sound absorption coefficientSound absorption coefficient(d) D (Density: 28.30kg/m3)(e) E (Density: 40.71kg/m3)
Fig.4 – Comparison between measured and predicted normal incidence sound absorption coefficient of
microfiber absorber sample A – E whose thickness is 10mm.
100%

80%
60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

3

(c) C (Density: 20.31kg/m )

100%
80%

60%
Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR(iv) Measured Zc,γ

40%
20%
0%

0

1000

2000 3000 4000
Frequency (Hz)

5000

6000

(d) D (Density: 28.30kg/m3)(e) E (Density: 40.71kg/m3)
Fig.5 – Comparison between measured and predicted normal incidence sound absorption coefficient of
microfiber absorber sample A – E whose thickness is 40mm.

4. NUMERICAL ANALYSIS OF OBLIQUE INCIDENCE SOUND ABSORPTION
COEFFICIENTIn this chapter, the calculation accuracy of predictive calculation models (i) to (iv ) was investigatedby experiment and numerical analysis for the oblique incidence sound absorption coefficient of the
microfiber sound absorbing material.
4.1 Numerical Solution
For the numerical analysis, a finite element analysis software Actran (product of MSC) was used.

1988

The analysis region of the sound absorbing material is treated as the sound field which has the effective
complex sound wave velocity and the effective complex density to calculate four cases of the model(1) to the model (iv).
4.2 Calculation Model
Fig. 6 shows the numerical analysis model of FEM.
The oblique incidence sound absorption coefficient was derived (7) by computing sound pressure at
the observation point under three conditions of the specimen surface, the specimen reflection
condition, the complete reflection condition and the non-reflection condition in Fig.6.
The oblique incidence sound absorption coefficients of three specimens C (20.31 kg/㎥), D (28.30kg/㎥) and E (40.71 kg/㎥) in Table 1 were calculated and compared with the measured results. The
number of elements was 121807, and the element size was 2.5 mm to 10 mm.
Infinite Elements(on the boundary)
Noise source

1000mm

R=1500mm

1000mmObservation
point

1000mm

1000mmSpecimen
Nonreflective (20mm×1000mm)
Boundaries

YX

Fig.6 – FEM 2D model for numerical analysis
4.3 ExperimentFig. 7 shows an outline of the apparatus used for the measurement of the oblique incidence soundabsorption coefficient.
The sound source speaker and the microphone were arranged at symmetrical positions, and thereference microphone was set in the vicinity of the sound source speaker. The direction of the
speaker was arranged so as to be incident on the test piece at 45 degrees, and the are a of the test
piece was 1 m2 .
Measurements were carried out in the anechoic room. The method for calculating the oblique
incidence sound absorption coefficient was the same as the case in the numerical analysis describedabove.
Speaker
Microphone(Reference)

Microphone
White Noise
Direct wave (2m)

45° 45° Reflectedwave (2.82m)

Anechoicroom

Specimen(1m2)

Speaker
Amp

FFT
AnalyzerPC

Fig.7 – Experimental apparatus for measurement of sound absorption coefficient at 45degree oblique
incidence

19894.4 Comparison between Calculated Results and Measured Results
Fig. 8 shows the comparison between the calculated oblique incidence sound absorption
coefficient, which was derived from the computed sound pressure at the observation point, andexperimental value.
From Fig. 8, it was confirmed that the model (iii) of which the flow resistance was also
identified when the other parameters were identified by using Foam-X and the model (iv) based on
the measured characteristic impedance and complex propagation constant were highly consistent inall cases. But the case of the model (ii), in which the flow resistivity was not identified but measured,shows good consistency for the specimen C(20.31 kg/㎥) and D(28.30 kg/㎥) but shows large
difference between measured value and calculated value for the specimen E(40.71 kg/㎥)
100%

Sound absorption coefficientSound absorption coefficient

100%

80%
60%

Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR

40%
20%

(iv) Measured Zc,γ

0%
0

1000

2000
3000
Frequency (Hz)4000(a) C (Density: 20.31kg/m3)

80%
60%

Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR

40%
20%

(iv) Measured Zc,γ

0%

5000

0

1000

2000
3000
Frequency (Hz)

4000

5000

(b) D (Density: 28.30kg/m3)

Sound absorption coefficient

100%

80%
60%

Exp.
(i) MIKI(ii) Limp_with FR(iii) Limp_without FR

40%
20%

(iv) Measured Zc,γ

0%
0

1000

2000
3000
Frequency (Hz)

4000

5000

(c) E (Density: 40.71kg/m3)
Fig.8 – Comparison between measured and computed sound absorption coefficient of microfiber absorbersample C – E at 45degree oblique incidence

5.

AN EXAMPLE OF AN APPLICATION FOR AN ACTUAL PRODUCTThe optimum structure of the microfiber sound absorbing structure was investigated by using the
calculation model (iii) with the best calculation accuracy. And the performance of the obtained
optimum structure was evaluated by measuring the sound absorption coefficient by reverberation room
method close to the actual sound field.
Fig. 9 shows the comparison between the developed structure of microfiber sound absorbing
material (400 g/m2 ) under the restriction of the whole thickness 19mm and the current structure which
consist of 4mm thick polyester fiber and 15mm back sir space.
The improvement of sound absorption coefficient by 0.3 in the 1 kHz band and the wei ght reduction
were achieved for the developed structure of the microfiber sound absorbing material.

1990

Sound absorption coefficient
by Reverberation room method

1.2

Microfiber
absorbingstructure

1
0.8
0.6

Current structure

0.4

0.2
0
200

400

800
1600
Frequency [Hz]

3150

6300

Fig.9 Comparison of the sound absorption coefficient measured by reverberation room method between
microfiber absorbing structure and current structure

6. CONCLUSIONAs described above, in order to predict the performance of the oblique incidence sound absorption
coefficient of the microfiber sound absorbing material, the following findings were obtained byexamining the non-acoustic parameters in the prediction of the normal incidence sound absorption
coefficient and by comparing between the experimental value of the oblique incidence soundabsorption coefficient and the predicted value derived from the finite element analysis.
(1) Delany-Bazley-MIKI model is inadequate for predicting the performance of microfiber soundabsorbers.
(2) It was confirmed that the performance of the microfiber sound absorbing material could be
predicted with high accuracy by using the limp frame porous model when all the non-acoustic
parameters were identified by the Foam-X.
(3) However, when we adopt the measured flow resistivity and other non-acoustic parameters
identified by Foam-X to analyze the microfiber sound absorbing performance by using the limp
frame porous model, the accuracy of the prediction is not always improved. And attention must
be taken.
(4) In predicting the oblique incidence sound absorption coefficient of the microfiber soundabsorbing material, it was found that the limp frame porous model or the model of the complex
sound velocity and complex density obtained from the measured characteristic impedances andcomplex propagation constants had good agreement with the measurement.
It should be noted that the elucidation of (3) is a future theme.

REFERENCES
1. Katou T. Akasaka S. Matsumoto H. Asai S. Relation of sound absorption coefficient and acoustic
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SDT13003; Japan 2013. pp. 1-4.
2. Kurosawa Y. Development of normal incidence absorption prediction technique for ultrafine fiber (inJapanese). Proc Dynamics and Design Conference 2015 USB of The Japan Society of MechanicalEngineers; 539 (2015)
3. Panneton R. Comments on the limp frame equivalent fluid model for porous media, J. Acoust. Soc. Am.,
122 (6), 2007. EL217 -EL222.
4. Atalla Y. Panneton R. Inverse Acoustical Characterization of Open Cell Porous Media Using Impedance
Tube Measurements, Canadian Acoustics; Vol. 33. No. 1. 2005. pp.11-24.
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model (in Japanese). Proc Architectural Acoustics of Acoustical Society of Japan; AA2015-12. 2015.
6. Miki Y. Acoustical properties of porous materials - Generalizations of empirical models, J.Acoust. Soc.
Jpn. (E). 11. pp.25-p.28. 1990.
7. Yamaguchi Z. Tanaka T. A measuring method of oblique incidence absorption coefficient for a shallow
incidence angle. Proc Inter-Noise 2006; 06-619. CD-ROM. 2006.
8. Komito T. Kitahara S. Takao H. Shinoda K. Tanaka T. Research on improvement of sound absorbing
structure including air space with partition (2nd report) (in Japanese). Proc Spring meeting of Society ofAutomotive Engineers of Japan 2015; S337, 2015.

1991