PORTABLE INSTRUMENTS PRODUCING HIGHLY DIRECTIVE ACOUSTICAL BEAMS FOR THE CHARACTERISATION OF SOUND ABSORBING MATERIALS

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CHARACTERISATION OF SOUND ABSORBING MATERIALS

B. Castagnède¹, A. Moussatov¹, D. Lafarge¹, V. Tournat¹, V. Gusev², M. Saeid¹

1Laboratoire d'Acoustique de l'Université du Maine, UMR 6613, Le Mans, France

2Laboratoire de Physique de l’État Condensé, l'Université du Maine, UMR 6087, Le Mans, France

ABSTRACT

This presentation reviews some recent work dealing with the audio application of ultrasonic parametric arrays for the characterisation of air-saturated porous materials.

Parametric arrays were originally designed 50 years ago for the field of underwater non-linear acoustics [1,2]. They are based on the powerful emission of two ultrasonic frequencies ω₁ and ω₂ which are sufficiently close such that Ω = ω₂ − ω₁ << ω_1,2. The amplitude modulated ultrasonic carrier waves will initially propagate in air, then the high-frequency components ω_1,2will be damped out by attenuation after some distance. Accordingly, the demodulated low frequency component Ω will be created, during propagation in air, in the form of a highly directive audio-range acoustical beam [3], which could be used for metrology purposes, in the present case for the characterisation of poroelastic absorbing materials [4].

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1 INTRODUCTION

At normal incidence, both reflection and transmission configurations could be used, enabling to access to absorption versus frequency or alternatively to dispersion, i.e. to phase (or group) velocities [4,5,6]. Numerous results, obtained with several parametric arrays working at various ultrasonic frequencies (e.g. between 40 and 50 kHz) will be shown allowing to determine acoustical properties over the 100 Hz – 10 kHz bandwidth, depending on the used instrument and configuration [5,6]. The obtained data will be systematically compared to the numerical predictions based on the so-called “equivalent-fluid model” [7]. The link between absorption and dispersion will also be further discussed in view of the causality Kramers-Krönig relationships. Finally, a special emphasis will be given for the description of portable instruments based on conventional audio instrumentation, covering in most cases the 100 Hz – 5 kHz range. This patented design might prove in the future to be of crucial use for

“in-situ” and “on-line” characterisation of sound absorbing materials, i.e. when measuring the materials as mounted in-use, or during their manufacturing. This portable instrument, because of its simplicity and easiness will prove to be very efficient in various situations, including the characterisation of sustainable materials (for example porous materials made from natural or recycled fibres).

Some preliminary work performed with a portable system and with specialised software was briefly outlined at several conferences at the end of 2005 [8, 9]. Moreover, a very recent Ph.D thesis was summarising most of the achieved results obtained so far with a dedicated laboratory (e.g. not portable) system during the last two years, and provided a comprehensive introduction to the use and implementation of parametric arrays for the characterisation of the acoustical properties of air-filled poroelastic materials [10], in the frame of the “equivalent fluid model”.

2 THE PORTABLE INSTRUMENT: HIGHLY DIRECTIVE SOUND BEAM PROJECTOR

Figure 1 provides a schematic view of the experimental set-up. The audio projector is mounted vertically approximately 1 m above the tested porous plate, in order to produce powerful plane wave orthogonal to the surface of the material. An audio microphone is mounted a few cm above the sample. During a preliminary calibration procedure, which should be done from time to time, the sample holder (in the shape of an “wheel-table”) is firstly removed in order to capture the incident wave field. Next, the table is mounted back in its prior location with a rigid reflector mounted on it. In that second step one records simultaneously the incident and the reflected field, both having the same amplitude. After the calibration two steps procedure is done, one can perform real absorption measurements just by mounting the porous plate above the table. The detected signals are recorded onto a portable computer connected a low- cost audio card working at a 92 kHz sampling frequency. This is amply sufficient to cover the audio range, let say between a few 100 Hz and 10 kHz. The processing of the signals in order

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to compute the acoustical coefficient of reflection is done by using the LabVIEW version 7.1 software.

Figure 1 : Schematic of the used set-up. 1: Audio sound projector ; 2 Mounting frame ; 3 : Audio microphone ; 4 : Poroelastic plate ; 5 : Removable wheel-table ; 6 : Connection towards audio acquisition card and portable computer.

3 EXPERIMENTAL RESULTS AND COMMENTS

Some measurements of the coefficient of absorption versus frequency are described in this section. They are generally provided over the 500 Hz – 6.5 kHz bandwidth. The lowest frequency which is available is somehow related to the size of the sample compared to the wavelength, because the measurements are done in the free field configuration. Accordingly, at 500 Hz, one should use 1 m square sample, or at least 80 cm x 80 cm plates, as the wavelength at such frequency is 68 cm. Another limitation concerning low frequency is related to the distance between the plane were the sample is mounted (i.e. the top of the supporting table) and the ground. For instance, with a regular 1m high table, the lowest frequency is 200 Hz, because otherwise the direct and reflected wave-packets are mixing up each other even when using ultra-short signals (one single wavelength duration). After proper calibration procedure which consists in measuring individual contributions of the incident wave, the reflected wave onto a perfectly rigid reflector, and the same reflected wave after interaction with the tested porous material, one can obtain the coefficient of absorption A(ω) just by writing the energy conservation balance law in the form : A(ω) = 1 – |R(ω)|², where R(ω) is the coefficient of reflection versus frequency. Some significant examples are provided below. One start with a fibrous mat made of glass fibers (glass wool), as shown on Figure 2. The 4 drawings

1 2

3 4

5

6

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pictures between the direct measurements performed with the audio projector (fine frequency measurements in red continuous lines) and the measurements obtained with a Bruel & Kjaer kundt tube (discrete one third octave data, seen as blue squares). The agreement is generally very good, in some cases being simply fair. These data clearly show the loss in absorption when decreasing the thickness of the fibrous mat plates.

Figure 2 : Coefficient of absorption of some glass wool materials versus frequency for different thickness h of the plates. a) h = 25 mm ; b) h = 20 mm ; c) h = 15 mm ; d) h = 5 mm.

As shown on Figure 3, we have compared the measurements of the coefficient of absorption performed with a Kundt tube to data obtained with our free-field system on a felt material. In fact, the green triangles data are really the one to be compared, because the other Kundt tube measurements (shown with black crosses) were obtained on a different plate (i.e. such comparison is a reproducibility test). The red line and green data are also plotted versus some numerical simulation predictions based on the “fluid equivalent model” (as shown with blue squares) [7]. The agreement is fair, being acceptable at high frequency. One should note that

Red line : audio projector measurements

Blue squares : Kundt tube measurements

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000 7000

Absorption coefficient

Frequency (Hz)

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000 7000

Frequency (Hz)

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000 7000

Frequency (Hz)

0 0.1 0.2 0.3 0.4 0.5 0.6

0 1000 2000 3000 4000 5000 6000 7000

Frequency (Hz)

Blue squares : Kundt tube measurements Red line : audio projector measurements

a) b)

c) d)

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the physical parameters of the model were not really measured, and that the numerical fit was not done in great detail, the porosity φ , the resistivity σ , the tortuosity α∞, the viscous characteristic length Λ , and the thermal characteristic length Λ’ being roughly adjusted.

Figure 3 : Coefficient of absorption of a 25 mm thick felt material measured in the free-field and with a Kundt tube as compared with a numerical simulation. The physical parameters were the following φ = 0.90 ; σ = 46 000 Nsm-⁴ ; α∞ = 1.06 ; Λ = 43 µm ; Λ’= 129 µm.

4 DISCUSSION AND CONCLUSIONS

In the present work, we have presented some preliminary measurements of the acoustical coefficient of absorption in a free-field configuration. The set-up is built with some simple modules including a so-called parametric sound projector, an ordinary audio microphone and a standard portable computer connected to a low-cost acquisition audio card. The obtained results performed on various porous absorbing materials clearly show good agreement with Kundt tube measurements, as well as with numerical simulations done in the frame of the “equivalent fluid”

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption coefficient

Frequency (Hz)

Red line : Audio projector measurements

Blue squares : Numerical simulation

Black crosses : Kundt tube measurements

Green triangles : Kundt tube measurements

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model. The main advantage of the technique is to be working in the free-field. This enables to obtain absorption coefficient data for “in-situ” configurations as well as “on-line” directly on the production lines. Additionally, the measurements are also available for laboratory use, with sustainable porous materials which are made with natural or recycled fibres.

REFERENCES

[1] V.A. Zverev, Acous. Phys., 45, 611-618 (1999), and references therein.

[2] B.K. Novikov, O.V. Rudenko, V.I. Timoshenko, Nonlinear underwater acoustics, ASA, New York (1989).

[3] D.T. Blackstock, J. Acous. Soc. Am., 102, 3106 (1997) ; F.J. Pompei, J. Audio Eng. Soc., 47, 726-731 (1999).

[4] B. Castagnède, V. Tournat, A. Moussatov, V. Gusev, French patent submitted to INPI (n°

0303913) on 28th march 2003. PCT International extension pending.

[5] M. Saeid, B. Castagnède, A. Moussatov, V. Tournat, V. Gusev, C. R. Mécanique , 332, 849-858 (2004). Also see B. Castagnède et al, Forum Acusticum 2005, Budapest.

[6] B. Castagnède, M. Saeid, A. Moussatov, V. Gusev, V. Tournat, Ultrasonics 44, 221-229 (2006).

[7] J.F. Allard, “ Propagation of sound in porous media : modelling sound absorbing materials ”, Elsevier Applied Science, London (1993).

[8] A. Moussatov, B. Castagnède, Audio beams generated by ultrasonic parametric arrays in air for acoustic NDT of poroelastic materials, WCU/UI’05 (World Congress on Ultrasonics merged with Ultrasonics International), Beijing, China, 28^th august – 1^st september 2005.

[9] A. Moussatov, B. Castagnède, Technology of sound projection applied to the characterization of acoustical parameters of poroelastic materials, Symposium on the Acoustics of Poro-Elastic Materials, Vaulx-en-Velin, Dec. 7-9, 2006.

[10] M. Saeid, Antennes paramétriques pour l'étude de la propagation acoustique dans les matériaux poroélastiques, Ph.D thesis defended on feb. 9th 2006, Université du Maine (France).