PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Experimental study on sound absorption characteristics of granularmaterial : Influence of lateral constraints of casing
Takumasa TSURUHA1; Yoshinari YAMADA1; Makoto OTANI2; Yasushi TAKANO2
1

Takenaka R&D Institute, Japan
2

Kyoto University, JapanABSTRACT
The sound absorption characteristics of flowable granular materials may vary owing to lateral constraints. Inorder to clarify the effect of lateral constraints on the sound absorption characteristics of granular materials,
the normal incidence sound absorption coefficients of hollow glass beads filled in cylindrical containers ofdifferent diameters were measured. The measurement results demonstrated that the sound absorption
coefficients varied depending on the diameters of the containers. As the diameter increased while thethickness of the granular material was constant, the first peak frequency of the sound absorption coefficient
shifted towards a lower frequency. The amount of shift due to diameter expansion increased with larger
thickness of the granular material. These results suggest that the sound absorption characteristics of granularmaterials can be controlled by adjusting the distance between the constraining walls without changing thethickness of the granular materials. 
Keywords: Absorption, Granules, Constraint

1. INTRODUCTION
It is well-known that granular materials have sound absorption characteristics [1-4]. Glass beads andvermiculite, whose particle sizes are of the millimeter order, absorb sound energy at high frequencies
in a manner similar to fibrous porous materials such as glass wool [1,2]. On the other hand, silica
powder and fine polymer particles, whose particle sizes are of the micrometer order, show different
sound absorption characteristics having a sharp peak at low frequencies [3,4]. For granular materials
that possess sound absorption characteristics having a sharp peak at low frequencies, it is thought thatvibrations of the particles contribute to sound absorption at the first peak frequencies of normal
incidence sound absorption coefficient because these first peaks correspond to the first modal
frequencies of the vibrating particles [3].
When granular materials are used for sound absorption, it is necessary to take measures to retain
their shapes as a mass because of flowability. One such measure to retain the shape is to constrain thematerials by walls. The sound absorption characteristics of constrained granular materials may bevariable because the vibrations of the particles are suppressed by the walls. A formula has been
proposed in literature to predict the first peak frequency of normal incidence sound absorption
coefficient for a granular material filled in a container, using the apparent dynamic longitudinal elastic
modulus and effective mass [5]. According to the formula [5], the first peak frequency depends on adiameter of cylindrical container. However, experimental verification of the effect of the diameter on
the sound absorption coefficient is insufficient. Therefore, this study aims to experimentally clarify
the effect of lateral constraints on sound absorption characteristics of granular materials.
Measurements of normal incidence sound absorption coefficients are performed with a granularmaterial filled in cylindrical containers of different diameters.

2. THEORETICAL DERIVATION OF FIRST PEAK FREQUENCYThis study assumes that the first peak frequency of the normal incidence sound absorption coefficient1

tsuruha.takumasa@takenaka.co.jp2979

corresponds to the first modal frequency of vibration of granular materials. The first modal frequencyof vibration is expressed as [6]݂଴ ൌͳ݇ඨǤʹߨ ‫ܯ‬ୣ୤୤

(1)

The first peak frequency of the normal incidence sound absorption coefficient is also given by Eq.(1).
Here, k is the apparent dynamic longitudinal elastic modulus, and Meff is the effective mass of granularmaterials.
 The apparent dynamic longitudinal modulus of granular materials filled in a container is describedas [6]ଶ

ିଵଶʹߩ݃ߩ݃ߩ݃ଷ݇ ൌ ߚ‫ܧ‬଴ ൬ െ ܲ଴ ൰ ݄ ൥൜ ൅ ሺܲ଴ െ ሻ݁ ିఉ௛ ൠ െ ܲ଴ ଷ ൩͵
ߚߚ
ߚ

(2)

 ǡ

where ρ is the bulk density; g is the gravitational acceleration; P 0 is the external force applied to thematerial surface; h is the thickness of granular materials; S is the area of the surface on which soundis incident; E 0 is the constant inherent to the material. In this case, P 0 is the effective sound pressure
on the surface. β is called the Janssen coefficient, which is given byߚൌͶ‫ߤܭ‬ௐ ǡ݀

(3)when the shape of the container is cylindrical [7]. Here, K is the ratio of horizontal force to verticalforce in the direction of sound propagation. In this case, the vertical force corresponds to the soundpressure in a granular material in the direction of sound propagation, and the horizontal force
corresponds to the force acting on the walls of a container. μ w is the friction coefficient between thecontainer wall and the granular material; d is the inner diameter of the cylindrical container. If theexternal force applied to material surface in the sound propagation direction is small enough toఘ௚ఘ௚establish thatെ ܲ଴ ൎ ఉ , Eq.(2) is simplified toఉଶଵଷʹߚ݇ ൌ ܵ‫ܧ‬଴ ሺߩ݃ሻଷ ൬൰  Ǥିఉ௛
͵
ͳെ݁

(4)

The effective mass of the granular material filled in a container is given as [5]‫ܯ‬ୣ୤୤ ൌߩܵ൫ͳ െ ݁ ିఉ௛ ൯  Ǥߚ(5)

The first peak frequency of normal incidence sound absorption coefficient is determined fromEq.(1) by substituting Eqs.(4) and (5).

3. MEASUREMENT OF SOUND ABSORPTION COEFFICIENT
3.1

Granular Material
Hollow glass beads were used as the granular material in the measurements. Table 1 shows thebasic properties of the hollow glass beads. These beads were filled in cylindrical containers madeof polylactic acid resin, and no additional force was applied as the material was constrained by thecontainer walls. The surface of the material in the container was leveled smoothly by light tapping
after pouring. Figure 1 shows the material used in the measurements.

Table 1 Basic properties of the specimen.

Granular material
Hollow glass beads
Mean Particle Diameter (μm)
603120Bulk Density (kg/m )3200
True Density (kg/m )Porosity
0.42980

3.2 Measurement Set-up
The sound absorption coefficients of the hollow glass beads were measured by the transfer function
method using acoustic tubes [8]. Figure 2 illustrates the measurement set-up. The measurements wereconducted using two types of cylindrical steel acoustic tubes with inner diameters of 100 and 200mm, respectively. The acoustic tubes were positioned such that the axial direction was perpendicular
to the ground, and the specimens were installed at the bottom. A maximum length sequence pseudorandom noise was used as a sound source. The frame of the container was attached to the wall of theacoustic tube, and the contact gap between the container and the tube was sealed by petrolatum. The
back of the container was attached to a hard steel plate, which can be regarded as rigid. The soundabsorption coefficient with an empty container was approximately 0.01 in the frequency range from40 to 2k Hz. It was confirmed that the effect of the container itself and the contact gap of the soundabsorption coefficients were small. The sound absorption coefficients were measured for material
thicknesses of 40, 80, 160, and 320 mm.AmplifierNoise Generator

LoudspeakerMic. A
100 mm

Mic.
AmplifierMic. B

2ch
FFT

50 mm

Personal
ComputerhGranular material

Figure 1 Hollow glass beads used in themeasurements.

Figure 2 Measurement set-up of normal incidencesound absorption coefficient.

4. RESULTS
The experimental results of the sound absorption coefficients of the hollow glass beads are shown inFig. 3. Furthermore, Fig. 4 shows the experimental results of the first peak frequency of the soundabsorption coefficients based on the material thickness. Figure 3 depicts that the values of the soundabsorption coefficients at first peak frequency are almost similar regardless of the diameter ofcontainer. Figure 4 shows that the first peak frequency shifted towards lower frequency with larger
diameter under a constant material thickness. The larger the thickness, the larger the change in thefirst peak frequency due to the diameter variation.
The first peak frequency is theoretically derived as described in Section 2. The derivations require
constants E 0 K μ w as the physical properties of the material. However, it is difficult to measurethem directly. Therefore, they were estimated by curve-fitting the calculated results to experimental
results by the least-squares method for the case of 100 mm diameter. As a result, they were estimatedas E 0㸻1.4310 5 and Kμ w㸻0.29. Using the estimated values for E 0 and Kμw , the first peak frequencyof the hollow glass beads filled in the container of diameter of 200 mm are obtained. Figure 4 shows
the theoretical values of the first peak frequency for two different diameters. In case of 200 mmdiameter, the theoretical values of the first peak frequency using the estimated E 0 and Kμ w for the caseof 100 mm diameter show good agreement with the experimental results, which validated the theory
described in section 2. Furthermore, theoretical values shown in Fig. 4 suggested that the first peakfrequency of the hollow glass beads filled in the container may converge to a specific value as thematerial thickness increases.
Additionally, the first peak frequency in case of an infinite diameter is shown in Fig. 4 to exclude
the effect of the wall constraints. The first peak frequency in this case can be regarded as a specificvalue inherent to the material, and it is predicted to decrease in proportion to the thickness in this case.
The first peak frequency in case of an infinite diameter is lower than the ones in case of a finite

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diameter.

h = 40 mm

h = 80 mm

h = 160 mm

h = 320 mm

Figure 3 Normal incidence sound absorption coefficients of hollow glass beads using acoustic
tubes with different diameters.
d 䠙 100 mm
200infinite

䠖Theory䠈䕕䠖Measurement
䠖Theory䠈䚽䠖Measurement䠖TheoryFigure 4 First peak frequency of normal incidence sound absorption coefficients of hollow
glass beads for various thickness.

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5. CONCLUSION
By measuring the normal incidence sound absorption coefficients of the hollow glass beads filled incontainers of different diameters, the effect of constraints by the walls on the sound absorption
coefficient of granular material was verified. The results reveal that, for the hollow glass beads, thefirst peak frequency varies depending on the distance between the constraining walls; the variationsof coefficients due to the variation of the distance are larger as the material thickness increases. Theseresults suggest that the sound absorption characteristics of granular materials can be controlled byadjusting the distance between the constraining walls without changing the material thickness. The
lower limit of the first peak frequency can be determined from the physical properties of the material
according to the material thickness.

REFERENCES
1. K.V. Horoshenkov, M.J. Swift, The acoustic properties of granular materials with pore size distribution
close to log-normal, Journal of the Acoustical Society of America 110(5) (2001) 2371-2378.
2. V.V. Voronina, K.V. Horoshenkov, Acoustic properties of unconsolidated granular mixes, AppliedAcoustics 65 (2004) 673-691.
3. Y. Okudaira, Y. Kurihara, H. Ando, M. Satoh, K. Miyanami, Sound absorption measurements forevaluating dynamic physical properties of a powder bed, Powder Technology 77 (1993) 39-48.
4. Z. Hong, L. Bo, H. Guangsu, Sound absorption behavior of multiparous hollow polymer micro-spheres,Materials Letters 60 (2006) 3451-3456.
5. T. Tsuruha, Sound absorbing characteristics of granular material multi-divided by membranes supported
by rigid frame, Proc. Euronoise (2018) 65-70.
6. A.J. Matchett, T. Yanagida, Elastic modulus of powder beds-the effects of wall friction:a model compared
to experimental date, Powder Technology 137 (2003) 148-158.
7. J. Duran, Sands, Powders, and Grains, Springer, 2000.
8. ISO10534-2:1998, Acoustics - Determination of sound absorption coefficient and impedance inimpedance tubes, Part 2: Transfer-function method.

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