acoustic properties of porous materials used in …706746/fulltext01.pdf · acoustic properties of...

Acoustic properties

of porous materials

used in silencers

Jesper Kristoffersson

Master of Science Thesis

Stockholm, Sweden 2013

Acoustic properties of porous materials

used in silencers

Jesper Kristoffersson ISSN 1651‐7660

TRITA‐AVE 2013:35

Stockholm 2013

Master of Science Thesis Royal Institute of Technology School of Engineering Sciences Department of Aeronautical and Vehicle Engineering The Marcus Wallenberg Laboratory for Sound and Vibration Research

III

Abstract

The aim of this master thesis is an experimental investigation of the acoustic characteristics of absorbing materials used in mufflers for trucks and cars. The difference in the composition between different wool type materials consists of difference in material, fibre diameter, length, density and fibre orientation. It is also possible to construct mufflers using micro perforated plates (MPP), either solely or in combination with wool type materials. When a specific material is selected the characteristics of the performance can be altered by compressing the material to different bulk densities.

It was investigated how some of these properties change the airflow resistivity of the material. When the airflow resistivity of the material is known this parameter can be used in FEM software to describe how a specific material will react, behave and perform as an absorbent.

Two different methods were used to extract the airflow resistivity. The fastest method is from the ISO standard ISO 9053 were the airflow resistivity is measured over a sample with a flow speed down to 0.5 mm/s. The second method is the Transfer Matrix Method (TMM) with which the airflow resistivity is extracted from the acoustic transfer matrix of the sample. Both methods are fully described in the report. The TMM was used within a frequency range of 0‐1600 Hz at no flow conditions. Measurements using both methods were performed at room temperature .

Ten different wool type materials and two different kinds of MPP were studied. For the wool type materials, the airflow resistivity was measured with the fibres parallel and perpendicular to the direction of sound and airflow. The material samples had bulk

densities of 80‐210 g/l. For the MPP the specific airflow resistance was measured with the static flow perpendicular to the plates. The results from the two methods were compared and the transmission loss, absorption coefficient, reflection coefficient and the complex speed of sound were calculated using the transfer matrix from the TMM. Regarding the TMM these data were also compared to the results that can be calculated when using the measured airflow resistivity together with the empirical expressions from Delany‐Bazley & Miki. Repacking of some materials were done in order to study the differences introduced by the packing process.

IV

The conclusions after the measurements were:

• The agreement between the two methods was very good. • The value of the resistivity was doubled for measurements with the fibres

perpendicular to the direction of sound. • When the materials with a high degree of micro strands were oriented with the

fibres perpendicular to the direction of sound there was a resonant behaviour in the sample. The onset frequency of this resonance increased with increasing bulk density. This resonance leads to difficulties in predicting the behaviour of real life exhaust systems.

• In order to get reliable results, further studies on the micro perforated plates must be made, with even lower flow velocities and sound pressure levels and maybe with other methods.

V

Sammanfattning

Målet med detta examensarbete är en experimentell undersökning av akustiska egenskaper för absorbenter i ljuddämpare hos lastbilar och personbilar. Skillnaden i sammansättningen mellan olika ullmaterial består i materialtyp, fiberdiameter, fiberlängd, densitet och fiberriktning. Det är även möjligt att konstruera ljuddämpare genom att använda mikroperforerade plåtar, antingen ensamma eller i kombination med ullmaterial. För ett specifikt material kan egenskaperna ändras genom att packningsdensiteten i ljuddämparen varieras.

Det undersöktes hur vissa av de olika egenskaperna ändrade materialets strömningsmotstånd. Med kännedom om materialets strömningsmotstånd kan finita elementprogram användas för att beskriva hur ett specifikt material kommer att fungera som absorbent.

Två olika metoder användes för att få fram materialens strömningsmotstånd. Den enklaste och snabbaste metoden är den som beskrivs i standarden ISO 9053 i vilken strömningsmotståndet mäts över ett materialprov med en strömningshastighet ner till 0.5 mm/s. I den andra metoden beräknas strömningsmotståndet ur överföringsmatrisen till materialprovets uppmätta akustiska 4‐pol. 4‐polen uppmättes med två‐mikrofonsmetoden. Båda metoderna finns beskrivna i rapporten. Två‐mikrofonsmetoden användes i frekvensomfånget 0‐1600 Hz utan strömning. Utförandet av båda metoderna gjordes i 20 °C.

10 olika ullmaterial och två mikroperforerade plåtar ingick i undersökningen. Strömningsmotståndet för ullmaterialen uppmättes med fiberriktningen parallell samt vinkelrät mot luftflödet och ljudets riktning. Materialen uppmättes med packningsdensiteterna 80‐210 g/l. För de mikroperforerade plåtarna uppmättes det specifika strömningsmotståndet Pa s/m, med luftflödet vinkelrätt mot plåtarna. Resultaten från de två metoderna jämfördes och från den uppmätta 4‐polens överföringsmatris beräknades transmissionsisoleringen, absorptionskoefficienten, reflektionskoefficienten och den komplexa ljudhastigheten. Resultaten från två‐ mikrofonsmetoden och det uppmätta strömningsmotståndet jämfördes med de resultat som kan fås genom att använda de empiriska uttryck Delany‐Bazley & Miki tagit fram. Ompackning gjordes av vissa material för att kunna studera packningsprocessens påverkan på resultaten.

VI

Efter mätningarna drogs följande slutsatser:

• Överensstämmelsen mellan de två metoderna var mycket bra. • Värdet på strömningsmotståndet fördubblades då fiberriktningen var vinkelrät

mot luftflödet och ljudets riktning. • När material med en stor andel av mikrofiber orienterades med fibrerna

vinkelrätt mot ljudets riktning antydde resultaten närvaron av resonanser i materialet. Då packningsdensiteten ökade, steg frekvensen för resonansen. Denna resonans skulle kunna leda till bekymmer vid användande av dessa material.

• Mer utförliga mätningar måste göras på de mikro‐perforerade plåtarna för att få tillförlitliga resultat. Både med lägre ljudtrycksnivåer och lägre flödeshastigheter men kanske även med andra metoder.

VII

Preface

This report is a Master of Science dissertation, as a part of the mechanical engineering education at the Royal Institute of Technology (KTH), Stockholm, Sweden. The special interest during the education has been the field of Sound and Vibration.

The work has been performed at Scania CV AB, RTRN, Acoustics department, Södertälje, Sweden, and at the department of Aeronautical and Vehicle Engineering, MWL, KTH Royal Institute of Technology, Stockholm, Sweden. At Scania under the supervision of Tony Karlsson, Development Engineer, and Adjunct Professor Ragnar Glav, Dr. Tech. Head of Acoustics, Truck Chassi Development. At KTH the work has been done under the supervision of Professor Hans Bodén, with support from Professor Mats Åbom, Dr., Nils‐Erik Hörlin and Christophe Van Der Kelen.

I would like to thank Scania CV AB for the facilities, financing and material supplied.

A special thank you to Tony, P.O., Petra and P.G., at Scania RTRN for their support and help during this journey.

IX

Sist, men absolut viktigast!

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Utan dig och vår älskade lilla Selma skulle jag inte klarat det! Så är det!

Ni har varit min omedvetna sporre som jag kunnat glädjas åt, tänka på och längta efter alla de tidiga morgnar, långa dagar, sena nätter och tråkiga helger vi varit ifrån varandra.

Men nu ska vi vara tillsammans för alltid!

Det bästa av det bästa är ni!

Bis?

XI

List of symbols

Hii Transfer functions between signals Hpi, Hqi Transfer function between volume velocity and pressure and the reference

signal at position i. H1, H2 Transfer function for different states indicating: (1) means speaker

upstream active and (2) means speaker downstream active. M Mach number R Reflection coefficient S Cross‐sectional area of the duct, m2

T The transfer matrix of an empty duct TL Transmission loss, dB Ts The transfer matrix of the sample Ttot The total transfer matrix, ducts and sample included T´tot The dimensionless total transfer matrix, ducts and sample included TMM Transfer Matrix Method Z The impedance of a rigid backed layer, Pa s/m Zc Characteristic impedance, Pa s/m Z0 Characteristic impedance of air in the duct, Pa s/m an Absorption coefficient at normal incidence c Speed of sound, m/s ca Complex speed of sound, m/s c0 Speed of sound in air, 344 m/s e Reference signal, V f Frequency, Hz h Sample thickness, m j Imaginary unit k0 Wave number of air, 1/m ka Complex wave number l The distance of the reference section until the surface of the sample pi Pressure at microphone position i, Pa qi Volume velocity at microphone position i, Pa r Airflow resistivity MKS Rayl/m s Microphone distance

Mean air velocity, m/s Pressure drop across sample Sample length, m Density of air, ~1.21 kg/m3 Normalized flow resistance Normalized characteristic impedance Normalized input impedance

XIII

Contents 1 Introduction ......................................................................................................................................................1

1.1 Aims of this mater thesis ...............................................................................................................1

2 Theory..................................................................................................................................................................2

2.1 The Delany and Bazley method .......................................................................................................2

2.1.1 Calculation of acoustical properties.....................................................................................5

2.2. The 4‐pole transfer matrix method ..............................................................................................7

2.2.1 Calculation of acoustic properties...................................................................................... 10

3 The measurement set ups ........................................................................................................................ 18

3.1 Static Air Flow resistivity measurements ................................................................................ 18

3.1.1 Measurement procedure........................................................................................................ 18

3.1.2 Measurement details ............................................................................................................... 19

3.1.3 Deviations from International Standard ISO 9053..................................................... 20

3.2 Transfer Matrix Method rig............................................................................................................ 22

3.2.1 Measurement procedure........................................................................................................ 22

3.2.2 Measurement details ............................................................................................................... 24

3.2.3 Deviations from the Standard E2611 – 09 ..................................................................... 26

3.3 Data handling........................................................................................................................................ 26

4 Results & Discussion................................................................................................................................... 28

4.1 Sample holder ...................................................................................................................................... 28

4.2 Results for wool type materials.................................................................................................... 32

4.2.1 General comments .................................................................................................................... 32

4.2.2 Comments regarding yarn type materials...................................................................... 44

4.2.3 Comparison for Parallel vs. Perpendicular and Repacking..................................... 53

4.2.4 Comparison with Delany & Bazley‐Miki.......................................................................... 55

4.3 Micro Perforated Plates results .................................................................................................... 59

5 Conclusions..................................................................................................................................................... 64

6 References....................................................................................................................................................... 66

1

1 Introduction

Acoustic absorptive fibre materials are used in automobile silencer systems. Historically, wool type materials from basalt has been the acoustic absorbing material but since new legislations demand less emission in the form of degraded fibre parts, new materials are of great interest. This is also important for the truck and car manufacturers since mechanical and chemical degrading, of the fibre materials means a decreasing performance of the muffler system. The performance of the muffler is the best when the truck or car leaves the factory but decreases during the life span of the vehicle. Since performance, weight and economy constantly are under consideration regarding the choice of material, new materials are always of great interest if they can improve the performance.

To be able to use them in simulation programs their acoustic properties need to be known and therefore they need to be tested. Different materials can exhibit similar acoustic properties by changing their bulk densities.

In fibre materials as for instance glass wool, the attenuation capabilities are mainly determined by the static airflow resistivity. This is known from the work of Delany and Bazley [1]. This means that if the airflow resistivity of the material is known many acoustical properties, i.e., transmission loss, characteristic impedance, speed of sound, absorption and reflection coefficient can be predicted with a great accuracy.

If the speed of sound and the characteristic impedance are known, then a complete description of the material can be made using the equivalent fluid model of Mechel, 1976 [2]. This model characterizes the fibrous or porous material as a homogenous fluid but with a complex valued speed of sound (amplitude and phase) and characteristic impedance.

One important effect neglected by Mechel in his model is the fibre movement caused by the acoustic waves when the direction of the fibres is perpendicular to the direction of sound.

1.1 Aims of this mater thesis

The aims of the project was to compare the results from the Transfer Matrix Method and the Static Airflow Resistivity method in terms of the extraction of resistivity for various materials, bulk densities, and fibre directions, and to develop the MATLAB codes necessary to calculate the different quantities from the measured data.

2

2 Theory

2.1 The Delany and Bazley method

To be able to measure the resistivity of a material, a sample is placed inside a tube with a known cross section area. The sample is exposed to a static airflow and the pressure drop, the mean air velocity across the sample, and the sample length, are measured. Since the sample diameter is affecting the mean air velocity care must be taken to calculate the correct mean air velocity across the sample. The airflow resistivity is defined as the pressure drop per sample length divided by the mean airflow velocity, ISO 9053[3]

(1)

For the method to be valid, the sample under test should be homogenous, the fibres should be small compared to the wavelength and the sample should be isotropic. This last limitation is not fulfilled when tests are performed on glass or mineral wools but for practical purposes this is normally negligible. To obtain more precise results it is possible to measure the material in all three spatial directions. Some of the materials were measured with the flow both parallel and perpendicular to the direction of the fibres in the materials.

When the airflow resistivity of the material is known, several acoustic properties can be calculated using the empirical derived formulas of Delany and Bazley.

There are two sets of formulas, one for porous materials and one for fibrous materials.

These are the formulas for fibrous materials,

(2)

3

(3)

Frequency boundaries proposed by Delany and Bazley for these expressions and for homogenous materials with porosity close to one are:

(4)

For comparison the by Miki Y. [4] (1990) revised Delany and Bazley models will be used as well:

(5)

(6)

The same boundaries as for the original Delany and Bazley models will be used here although Miki had observed that his revised expressions behaved well in a larger

frequency range especially for

In 1992, Mechel F.P. [5] presented another set of formulas for the characteristic impedance and wave number for glass fibre.

(7)

(8)

(9)

For the results of using these expressions certain characteristics about the measured material can be concluded. As the airflow resistivity approaches zero, the wave number and the characteristic impedance approach the values that these parameters have in air. The negative imaginary part of the wave number determines the dissipation of sound.

4

When the real part is larger than one there is an indication that the speed of sound through the absorbing material is lower than in air.

5

2.1.1 Calculation of acoustical properties

When these parameters are known, the absorption coefficient, the reflection coefficient and the transmission loss can be estimated using:

(10)

(11)

(12)

Where:

By calculating the 4‐pole matrix (T), defined in 2.2, of the sample it is also possible to estimate the transmission loss (TL) of the sample.

(13)

(14)

But since in this case, , this can be simplified to,

(15)

The expressions for the absorption coefficient, reflection coefficient and the transmission loss will be used together with the wave number and characteristic impedance calculated with the air flow resistivity results from the 4‐pole transfer matrix measurements. These results will be compared to the results gained directly from the 4‐pole transfer matrix.

7

2.2. The 4-pole transfer matrix method

By measuring the input and the output of a system, a transfer matrix that describes the system can be derived.

(16)

In this expression and are acoustic state vectors that describe the input and the output of the system. is the 2 x 2 matrix that describes the system. Since the matrix contains four unknowns, four equations are needed in order to solve the system of equations. This means that two pairs of state vectors are needed and this can be accomplished either by changing the termination of the duct or by changing the sound source, from speaker A to speaker B. The first method is called “the two‐load method” and the second method is called “the two‐source method”. Since it has been shown by Åbom, 1990 [6] that better results are gained with “the two‐source method”, this is the method used in this report.

Considering a test set up as in Figure 1, the task is to determine the acoustic two‐port across the sample. The choice of variables that the two‐port consists of can vary but here the acoustic pressure (p) and the volume velocity (q) will be used. This means that we have:

(17)

, characterizes the complete system between microphone 3 and 4, and can be obtained by measuring p3, p4, q3 and q4 for two different states. A and B will denote the two different states and we will get the system of equations:

(18)

From this equation can be derived if the two different states are linearly independent. Two obtain q3 and q4 two microphones on each side are used. The test setup is shown in Figure 1. For the high frequency range microphone number 2, 3, 4 and 5 are being used, and for the low frequency range microphone number 1, 3, 4 and 6 are being used.

8

• 16 are the microphone positions. • Sl is the microphone distance for the low frequency measurements. • Sh is the microphone distance for the high frequency measurements. • l is the distance from the sample to the closest microphone. • h is the sample thickness. • The speakers are labelled A (upstream) and B (downstream).

To be able to obtain q for the low frequency range, the following equations are used:

(19)

(20)

(21)

(22)

Here the expressions for the volume velocity are normalized with Z0 in order to later get the normalized transfer matrix T’.

For the high frequency range these expressions become,

(23)

(24)

(25)

(26)

Microphones Microphones

sl

sh

l hSpeaker A Speaker B Anechoic termination

Wind tunnel outlet

1 2 3 4 5 6

Sample

Sample

Figure 1 Transfer Matrix Method measurement rig at Scania, Södertälje.

9

where Z0 is the characteristic impedance of the air in the duct, k0 is the wave number, sl the low frequency range microphone separation distance and sh the high frequency range microphone separation distance.

These expressions are rewritten in terms of frequency responses. This is done by dividing the measured quantities with a reference signal e, which is the voltage taken from the loudspeakers in the duct. For the high frequency range these expressions become,

(27)

(28)

Where and

The final system of equations that need to be solved is

(29)

T’tot means that the transfer matrix is normalized with Z0, since Hqi are normalized with Z0.

The normalized transfer matrix can finally be determined by a matrix inversion.

(30)

This normalized transfer matrix now represents the total system between the two microphones 3 and 4. Theoretically without flow the determinant of this matrix should be equal to one, Munjal, 1987 [7]. This calculation will be done to control the set‐up of the test rig and the measurement quality.

In order to obtain the transfer matrix for the sample only, T’tot must be multiplied from left and right with the inverse of the corresponding normalized empty duct matrix representing the duct piece upstream (u) and downstream (d) the sample.

(31)

(32)

10

(33)

T’u =normalized transfer matrix for the empty duct section upstream of the sample

T’d = normalized transfer matrix for the empty duct section downstream of the sample

2.2.1 Calculation of acoustic properties

If the acoustic impedance can be derived from the sample transfer matrix, a couple of acoustical properties can be calculated.

The transfer matrix equation is,

(34)

For a rigid backed sample, q4=0, and this implies that

. (35)

The input impedance can now be calculated as:

(36) This can be used to calculate the reflection coefficient and the absorption coefficient.

37

38

11

Finally the air flow resistivity needs to be calculated from the normalized transfer

matrix.

The definition of the air flow resistivity at steady flow i.e. at zero frequency is:

39

where S is the tube cross‐sectional area.

For a propagating wave in the positive x‐direction,

, 40

12

where is the pressure amplitude. When the definition of the characteristic impedance

is used, then q can be written,

41

If equation 41 and 40 are inserted in 39 , then r can be calculated from,

42

If we assume that the equivalent fluid model can describe the sample, and that the

sample is homogenous along the centre of the sample, then T´s must have the form of,

. 43

13

This is the straight duct transfer matrix, where , the complex wave number, with

ca complex speed of sound, h sample thickness m and is the normalized

characteristic impedance.

One way to determine the complex speed of sound is to form the complex exponential

from the elements of T´s.

44

From this it is possible to derive the complex wave number as,

14

.

45

Observing T’s , it can be noticed that,

, 46

where , and for this can be simplified into,

47

15

If finally equation 47 is inserted into 42 , then r, according to Åbom, 1999 8 can be

calculated from,

48

16

In practice this is done by plotting r for the frequency range of interest, see Figure 2, and

zooming in on the lower frequency range were the curve behaves linearly, see Figure 3.

Finally a straight line fit is calculated and the airflow resistivity for static flow is

extracted.

0 500 1000 1500-4

-2

0

2

4x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity - M12 170

(g/l)

Figure 2 Airflow resistivity plotted.

17

0 50 100 150 200-1

0

1

2

3

4x 10

4

Frequency (Hz)Ai

rflow

Res

istiv

ity P

a s/

m2

Airflow Resistivity - , with line fitM12 170

(g/l)

← Resistivity 27303.3059

Figure 3 Airflow resistivity, zoom.

The final property that can be calculated from the normalized transfer matrix is the

transmission loss with the expression,

(49)

18

3 The measurement set ups

3.1 Static Air Flow resistivity measurements

3.1.1 Measurement procedure

The procedure is explained using Figure 4. The valve at (8) is closed (down position) and the tare buttons on the Swema 3000 (6) and differential pressure transmitter (7) are pressed in order to calibrate the equipment. A sample is put inside the small sample holder (2), see Figure 5, and the lids with nets are attached. The small sample holder is slid into the larger sample holder (1), which is inserted into the measurement compartment. The valve (8) is opened. The desired pressure drop across the laminar flow element (4) is regulated by turning the air valve regulator (5). The pressure drop across the laminar flow element (4), as displayed on the Swema 3000 (6), is used together with the sample cross section area, to calculate the mean air flow velocity across the sample. The pressure drop across the sample in test is displayed on the differential pressure transmitter (7).

1. Sample holder (cylindrical) 2. Small sample holder (cylindrical) with detachable end nets 3. Sample 4. Calibrated laminar flow element 5. Air valve regulator 6. Pressure drop measurement instrument Swema 3000

3 2

1

4

5

6

7

Compressor

8

Figure 4 Static air flow measurement rig MWL, KTH, Stockholm.

19

7. Differential pressure transmitter 8. Valve

3.1.2 Measurement details

The wool type materials studied had bulk densities 80‐210 g/l. The increase in bulk density was made in steps of 10 g.

Each bulk density of the wool type materials was measured at four different flow velocities 8.8, 17.6, 26.3 and 35.1 mm/s.

For the materials M2‐M6, measurements were made with the fibres parallel to the flow direction, see Figure 13. For material M2 and M6, measurements were also done with the fibres perpendicular to the flow direction, see Figure 14. Materials M7‐M10 and M12 were materials with fibre direction randomly distributed. Material M10 was measured a second time, trying to measure with the fibres perpendicular to the direction of sound.

The micro perforated plate materials were measured with the flow velocities 4.4, 8.8, 17.6 and 35.1 mm/s.

Dry air at 70 F (21.1° C) was assumed i.e., no adjustments were made for temperature and humidity dependence of the viscosity, but the temperature, atmospheric pressure and humidity were measured and recorded for reference.

All of the materials except material 12 were cut with scissors and packed inside the holder manually since they were composed of individual strands. Material 12 was cut out in a circle shape by a sharp duct piece, slightly bigger than the holder tube, to make sure that the fit was tight with no leakage. The micro perforated plates were cut into a circle shape with a diameter slightly larger than the holder tube and held in place by a putty, after which the plate was held tight between the holder tube end and the lid.

Figure 5 Sample holder and small sample holder with lids.

20

3.1.3 Deviations from International Standard ISO 9053

According to the standard, measurements should be made for air flow velocities across the sample down to 0.5 x 10‐3 m/s. For these low air flow velocities and for materials with low flow resistivity, the accuracy of the differential pressure transmitter started to affect the results of the pressure drop across the sample by introducing an error in the order of 30 %. In order to reduce the error introduced by the equipment the measurements were made with the flow velocities 8.8, 17.6, 26.3 and 35.1 mm/s. This reduced the error from the readings of the differential pressure transmitter to less than 3%. To make sure that the higher than recommended flow velocities did not introduce non‐linearities in the results, the resistivity measurements for the different flow velocities were compared.

Due to the immense number of materials and bulk densities only some materials were repacked and measured to control the difference in the results introduced by the packing procedure.

Although the standard states that the measurement section diameter should be 95 mm, the diameter was 34 mm. The empty sample holder with the small sample holder inside was measured and there was no registered pressure drop.

22

3.2 Transfer Matrix Method rig

3.2.1 Measurement procedure

The measurement of the transfer matrix was made according to the standard E2611 – 09 [9], with one microphone that was moved to the different microphone positions in the test rig. All measurements were made under no flow conditions.

The sample was placed inside the sample holder, see Figure 7and Figure 8, and the sample holder was clamped together and attached to the measurement rig, see Figure 9. All openings were sealed.

The microphone was placed in the microphone calibrator (Brüel & Kjær, type 4231) and amplitude calibrated with LMS Test.Lab, which was the program used to acquire the transfer functions between the microphone and the speaker signal. The microphone was placed in position 1, Figure 6, and the complex transfer function between the microphone and the signal exiting the loudspeaker A was measured. This same procedure was repeated for all microphone positions and for both speakers.

The sample holder depicted in Figure 7 and Figure 8 was used for the wool type materials. The wool samples were slid into the holder, see Figure 7 , part (II) and were held in place by the rigid copper wiring nets attached to the “lids”, depicted in, part (I & III).

The measurements started with the lowest bulk density, and for each increment in bulk density, part (II) was dismounted and the correct amount of material was carefully added to the material already inside the holder. Care was taken to make sure that the material could move freely inside the holder to ensure evenly distributed bulk density in the sample.

Figure 6 Transfer Matrix Method measurement rig at Scania, Södertälje.

Mic positions Mic positions

sl

sh

l hSpeaker A Speaker B Anechoic termination

Wind tunnel outlet

1 2 3 4 5 6

Sample

Sample

23

For the micro perforated plates, the sample holder shown in Figure 10 – Figure 12 was used. The lid, part I in Figure 10, was only used to mount the holder in the rig.

The micro perforated plates were held in place by a putty, to the right in part II in Figure 10 and in Figure 11, and care was taken to make sure that there were no leaks between the edges of the plates and the duct.

Figure 11 Sample holder for micro perforated plates.

Figure 12 Sample holder mounted in the test rig.

Figure 8 Actual sample holder, wool type materials.

Figure 9 Sample holder mounted in the test rig.

I II

Figure 10 Sample holder for micro perforated plates (II) and adherent “lid” (I).

I II III

Figure 7 Sample holder for wool type materials, holder (II), "lids" (I & III)

24

3.2.2 Measurement details

The wool type materials studied had bulk densities 100‐200 g/l. The bulk density was increased in steps of 20 g.

For the materials M2‐M6, measurements were made with the fibres parallel to the direction of sound, see Figure 13. For material M2 and M6, measurements were also done with the fibres perpendicular to the direction of sound, see Figure 14. Materials M7‐M10 and M12 were materials with fibre direction randomly distributed. Material M10 was measured a second time, trying orientate the fibres perpendicular to the direction of sound.

Figure 13 Fibre direction is parallel to the upstreamdownstream direction.

Figure 14 Fibre direction is perpendicular to the upstreamdownstream direction.

25

The micro perforated plate materials were measured with three different sound pressure levels since the results indicated that they did not behave according to the theory.

The temperature and the atmospheric pressure were recorded for each bulk density and the results were included in the calculations. For reference the average temperature and atmospheric pressure was 21° C and 100 kPa.

The humidity was not measured and thus not included in the calculations.

The valid frequency range for the four‐pole measurement depends on the distance between the microphones

, (Åbom & Bodén, 1986[10]) (50)

For the test rig the frequency limits were:

Low frequency limits: 35.3‐282 Hz

High frequency limits: 288‐2304 Hz

Since it is under most circumstances better to extend the frequency range downwards the high frequency range was chosen to be:

Extended high frequency limit: 282.8‐2304 Hz

The cut on frequency for the measurement rig, H. Bodén et al [11], under which plane wave decomposition is a correct assumption, is:

(51)

From this, the .

The final frequency range was 0‐1600 Hz with a frequency resolution of 0.78125 Hz. The excitation signal was random noise and for each measurement 50 averages were made. The data acquisition time was 1.28 s.

26

All of the materials except material 12 were cut with scissors and packed inside the holder manually since they were composed of individual strands. Material 12 was cut out in a circle shape by a sharp duct piece, slightly bigger than the holder tube, to make sure that the fit was tight with no leakage. The micro perforated plates were cut into a circle shape slightly smaller than the holder tube and held in place by a putty.

3.2.3 Deviations from the Standard E2611 – 09

Due to the immense number of materials and bulk densities only some materials were repacked and measured to control the difference in the results introduced by the packing procedure

3.3 Data handling

Several extensive MATLAB codes were written by the author to take care of and be able to analyze the large amount of measurement data from the Transfer Matrix Measurements.

28

4 Results & Discussion

In this section combined results from the static airflow measurements and the transfer matrix measurements are presented.

4.1 Sample holder

Comments regarding the results displayed in Table 1Table 3

To be able to check in what way the measurements were affected by the sample holder, the two different holders were measured in the rig without any material. For reference, the empty holder without any nets attached, was measured. The results can be seen in Table 1‐Table 3.

To be able to check the validity of the developed MATLAB code, the theoretical results for the normalized T’s11 and T’s12 were plotted as a comparison. The agreement between the theoretical results and the results from the test rig were very good and this was used as a confirmation of a correctly developed and functional MATLAB‐code.

The determinant of the transfer matrix was calculated and plotted. This was used as a confirmation of the quality of the measurements. This should be 1 for good quality measurements.

The inspection of Table 1‐Table 3 displayed a very small influence of the holders on the transmission loss compared to the measurement of the empty duct, and the spikes in all the plots were believed to origin from the fine frequency resolution.

As another reference the complex speed of sound was plotted.

Around 1600 Hz all the results start to be affected by the cut on frequency for the duct, which can clearly be seen in the plot of the determinant.

The results in the low frequency range are restricted by the limitation of the speakers. This limit is normally 20 Hz for this type of speakers

29

Table 1 Results for the empty holder with no nets attached.

0 500 1000 15000

0.5

1

1.5

2

2.5

3

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

Transmission Loss - Empty Holder no nets

Empty Holder no netsTheoretical

0 500 1000 1500

-1

-0.5

0

0.5

1

Frequency (Hz)

Normalized transfer matrix element T´11Empty Holder no nets

T´11 real partT´11 imag partT´11 real theoT´11 imag theo

0 500 1000 1500-0.5

0

0.5

1

1.5

2

Frequency (Hz)

Normalized transfer matrix element T´12Empty Holder no nets

T´12 real partT´12 imag partT´12 real theoret.T´12 imag theoret.

0 500 1000 1500

-2

-1

0

1

2

3

Frequency (Hz)

Determinant check of Two-Port - Empty Holder no nets

real partimaginary part

0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficientEmpty Holder no nets

0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficientEmpty Holder no nets

0 200 400 600 800 1000 1200 1400 1600

-100

0

100

200

300

400

500

600

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound Empty Holder no nets

realimag

0 500 1000 1500

-3

-2

-1

0

1

2

3

Frequency (Hz)

Nor

mal

ized

cha

ract

eris

ticin

put i

mpe

danc

e

Normalized characteristic input impedanceEmpty Holder no nets


30

Table 2 Results for the empty holder with one net, setup for the MPP measurements.

0 500 1000 15000

0.5

1

1.5

2

2.5

3

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)Transmission Loss -

Empty holder with one net for MPP setup

Empty holder with one net for MPP setupTheoretical

0 500 1000 1500

-1

-0.5

0

0.5

1

Frequency (Hz)

Normalized transfer matrix element T´11Empty holder with one net for MPP setup


0 500 1000 1500-0.5

0

0.5

1

1.5

2

Frequency (Hz)

Normalized transfer matrix element T´12Empty holder with one net for MPP setup


0 500 1000 1500

-2

-1

0

1

2

3

Frequency (Hz)

Determinant check of Two-Port - Empty holder with one net for MPP setup


0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficientEmpty holder with one net for MPP setup

0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficientEmpty holder with one net for MPP setup

0 200 400 600 800 1000 1200 1400 1600

-100

0

100

200

300

400

500

600

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound Empty holder with one net for MPP setup

realimag

0 500 1000 1500

-3

-2

-1

0

1

2

3

Frequency (Hz)

Nor

mal

ized

cha

ract

eris

ticin

put i

mpe

danc

e

Normalized characteristic input impedanceEmpty holder with one net for MPP setup


31

Table 3 Results for the empty holder with two nets, setup for the wool type material measurements.

0 500 1000 15000

0.5

1

1.5

2

2.5

3

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

Transmission Loss - Empty Holder with nets

Empty Holder with netsTheoretical

0 500 1000 1500

-1

-0.5

0

0.5

1

Frequency (Hz)

Normalized transfer matrix element T´11Empty Holder with nets


0 500 1000 1500-0.5

0

0.5

1

1.5

2

Frequency (Hz)

Normalized transfer matrix element T´12Empty Holder with nets


0 500 1000 1500

-2

-1

0

1

2

3

Frequency (Hz)

Determinant check of Two-Port - Empty Holder with nets


0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficientEmpty Holder with nets

0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficientEmpty Holder with nets

0 200 400 600 800 1000 1200 1400 1600

-100

0

100

200

300

400

500

600

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound Empty Holder with nets

realimag

0 500 1000 1500

-3

-2

-1

0

1

2

3

Frequency (Hz)

Nor

mal

ized

cha

ract

eris

ticin

put i

mpe

danc

e

Normalized characteristic input impedanceEmpty Holder with nets


32

4.2 Results for wool type materials

4.2.1 General comments

Initially there were 2 more materials, material 1 and material 11, but the amount of available material was not enough to complete the two measurements methods. This is why there are no results presented for these materials.

Since the fibres of material 4 did not fill the sample holder enough to stay in place in the TMM, there are only results for bulk density 171, 190 and 212 (g/l) for material 4. This implies that the results for bulk density 106, 127 and 149 for the static airflow measurement are unreliable, see Table 7.

The plot “Resistivity Control Static airflow measurements for different velocities” displays how the resistivity measured in the static airflow rig was affected by the change of flow velocity. This was done to make sure that the results within the measured velocities were accurate and that there were no changes and non‐linearities in the resistivity results. There was a very good, almost exact agreement for the results between the different velocities for all the wool type materials.

The “Airflow Resistivity Method Comparison” plot displays the comparison between the results from the Transfer Matrix Method and the Static Airflow Method. Regarding material 2‐6, Table 4‐Table 10, the agreement between the two methods is really good, especially for the lower bulk densities. One reason that the agreement between the two methods is not perfect for some of the higher bulk densities could be that as the bulk density increased it was harder to keep the strands in parallel and thus the length of the packed sample increased and this led to a decrease of the resistivity, since the sample length in the calculations was kept constant. On the other hand it is possible that the difficulty to keep the strands parallel led to more fibres positioned perpendicular to the direction of sound and thus an increased resistivity.

Regarding the transmission loss and resistivity plots there are some similarities regarding the properties of the materials. For materials with strands that do not contain a high degree of micro strands, think straws of spaghetti in parallel, the airflow resistivity is relative low and thus the transmission loss low. For example material 3‐4, see Table 6‐Table 7 and material 8, see Table 12 display this behaviour. A higher degree of micro strands drastically increase the resistivity and transmission loss.

An interesting phenomena is the increase of both resistivity and transmission loss when the direction of the fibres change from parallel to perpendicular compared to the direction of sound. The trend for the transmission loss behaviour is that it increases until somewhere between 400‐700 Hz, depending on the material and bulk density, where there is a sudden increase followed by a drastic drop and again an increase back to where the original linear curve increase should have been. This behaviour repeats

33

itself for increasing bulk densities but the effect of the variations in transmission loss is heavily increased and the start and stop frequency for the dip in the transmission loss curve increase with increasing bulk density.

A theory regarding this behaviour is that when the bulk density increases, the connection between the individual fibres become stronger, and therefore, the dip in the transmission loss increases too. But for increasing bulk densities there is a gradual increase of the frequency for the resonant behaviour. This behaviour is only present when the fibres are oriented perpendicular to the direction of sound and an indication of anisotropic behaviour of the material. This was observed already in 1989 by (Dahl et al [12], where this effect was attributed to motions of the fibres as the fibres were perpendicular to the direction of the sound.

There seem to be a connection between the speed of sound in the material and the transmission loss. At the frequency where there is a sudden increase in the speed of sound there is a sudden change in the transmission loss as well. This behaviour is displayed by material 2, 6, 7, 9 and 12. By inspecting the materials it is visible that they have a high degree of micro fibres. On the other material 8 and 10 that are composed by non inter‐connecting strands with a small (material 8) or no amount of (material 10) micro fibres do not display this behaviour, even though many of the fibres in the sample are oriented perpendicular to the direction of the sound.

This behaviour is seen in the absorption and the reflection coefficient as well. Just before the resonance in the material, for example material 6, 212 (g/l), Table 10 with the fibres perpendicular to the direction of the sound, the transmission loss and the absorption coefficient increases and thereafter they drastically decreases. This is probably where the resonance of the material is positioned.

For materials with a small amount of micro strands there is a lesser degree of difference in the transmission loss, absorption coefficient and the reflection coefficient between different bulk densities.

34

Table 4 Results for material 2, parallel measurements.

Figure 15 Material 2, separate (left), piece of matt

(right). 50 100 150 200 2500

0.5

1

1.5

2

2.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )

Resistivity control-static airflowmeasurement for different velocities

M2

velocity 1velocity 2velocity 3velocity 4

50 100 150 200 2500

0.5

1

1.5

2

2.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity Method Comparison M2

Transfer Matrix MethodStatic Flow Res. Meas.

0 500 1000 1500

-2

-1

0

1

2

3

4

5x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity-Transfer Matrix Method M2

different bulk densities (g/l)

106127149170191212

0 500 1000 15000

10

20

30

40

Transmission Loss M2


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficient M2


106127149170191212

35

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

ntReflection coefficient

M2 different bulk densities (g/l)

106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M2


106 real106 imag127149170191212

Table 5 Results for material 2, perpendicular measurements.

80 100 120 140 160 180 200 2200

1

2

3

4

5

6x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M2 Perpendicular


80 100 120 140 160 180 200 2200

1

2

3

4

5

6

7x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity Method Comparison M2 Perpendicular


0 500 1000 1500-1

-0.5

0

0.5

1

1.5x 10

5

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity-Transfer Matrix Method M2 Perpendicular


106127149170191212

0 500 1000 1500

0

10

20

30

40

Transmission Loss M2 Perpendicular


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficient M2 Perpendicular


106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficient M2 Perpendicular


106127149170191212

36

0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M2 Perpendicular


106 real106 imag127149170191212



(right). 50 100 150 200 2500

2000

4000

6000

8000

10000

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M3


50 100 150 200 2500

2000

4000

6000

8000

10000

12000

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

37

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212

38


Figure 17 Material 4, separate . 50 100 150 200 250

0

500

1000

1500

2000

2500

3000

3500

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M4


50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

4000

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-4000

-2000

0

2000

4000

6000

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



170191212

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



170191212

39

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie



170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

350

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



170 real170 imag191212



(right). 50 100 150 200 2500

0.5

1

1.5

2x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M5


50 100 150 200 2502000

4000

6000

8000

10000

12000

14000

16000

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-1

-0.5

0

0.5

1

1.5

2x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

40

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficient M5


106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212

41



(right). 50 100 150 200 2500

0.5

1

1.5

2

2.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M6


50 100 150 200 2500

0.5

1

1.5

2

2.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-2

-1

0

1

2

3

4x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212

42

Table 10 Results for material 6, perpendicular measurements.

80 100 120 140 160 180 200 2200

1

2

3

4

5

6x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )Resistivity control-static airflow

measurement for different velocitiesM6 Perpendicular


80 100 120 140 160 180 200 2200

1

2

3

4

5

6

7x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity Method Comparison M6 Perpendicular


0 500 1000 1500

-5

0

5

10

15x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity-Transfer Matrix Method M6 Perpendicular


106127149170191212

0 500 1000 1500

0

10

20

30

40

Transmission Loss M6 Perpendicular


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficient M6 Perpendicular


106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficient M6 Perpendicular


106127149170191212

0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M6 Perpendicular


106 real106 imag127149170191212

44

4.2.2 Comments regarding yarn type materials

Regarding the yarn type materials a general comment is that due to the randomness of the distribution of the fibres, the difference in airflow resistivity between the two methods can be explained by the way the yarn was packed in the sample holders. A higher degree of fibres perpendicular to the direction of sound means a greater resistivity and transmission loss.

Even though it was not done on purpose it was much easier to pack the fibres in a parallel direction in the bigger holder that was used for the TMM, since the threads were relatively big, compared to the small sample holder used for the static airflow resistivity measurements. This was observed for Mat7 and Mat9 where the strands were relatively fluffy and thick, and therefore harder to evenly distribute in a small sample holder.

It is clearly visible how different material 8 and 9 react in terms of absorption coefficient. For material 8 which has a very small amount of micro fibres and thus a smaller degree of interconnection between the strands there are no sudden increases and decreases of the transmission loss and absorption coefficient, and the absorption coefficient increases with increased bulk density, especially in the frequencies below 500 Hz. For frequencies above 500 Hz the differences between different bulk densities are smaller. For material 9 there is a higher transmission loss but the absorption coefficient decreases with increased bulk density. This is a well known behaviour for compression of fibre material that on the other hand does not fully apply to material 8.

45

Table 11 Results for material 7.

Figure 20 Material 7, yarn type. 50 100 150 200 250

0

0.5

1

1.5

2

2.5

3x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M7


50 100 150 200 2500

1

2

3

4

5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-6

-4

-2

0

2

4

6

8x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

46

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212


Figure 21 Material 8, yarn type.

50 100 150 200 2500

2000

4000

6000

8000

10000

12000

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M8


50 100 150 200 2500

2000

4000

6000

8000

10000

12000

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-1

-0.5

0

0.5

1

1.5x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

47

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

350

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212



0

1

2

3

4

5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M9


50 100 150 200 2500

1

2

3

4

5

6

7

8x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

5

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

48

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212



2000

4000

6000

8000

10000

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M10


80 100 120 140 160 180 200 2200

0.5

1

1.5

2x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-1.5

-1

-0.5

0

0.5

1

1.5

2

x 104

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

49

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212

Table 15 Results for material 10, repacking measurements.

80 100 120 140 160 180 200 2200

0.5

1

1.5

2x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M10 Repack


80 100 120 140 160 180 200 220

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity Method Comparison M10 Repack


50

0 500 1000 1500-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2Airflow Resistivity-Transfer Matrix Method

M10 Repack different bulk densities (g/l)

106127149170191212

0 500 1000 1500

0

10

20

30

40

Transmission Loss M10 Repack


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficient M10 Repack


106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficient M10 Repack


106127149170191212

0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M10 Repack


106 real106 imag127149170191212

51


Figure 24 Material 12. 80 100 120 140 160 180 200 220

0

1

2

3

4

5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

(Pa

s/m

2 )


M12


80 100 120 140 160 180 200 2200.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2



0 500 1000 1500

-5

0

5x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2



106127149170191212

0 500 1000 15000

10

20

30

40



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt



106127149170191212

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



106 real106 imag127149170191212

52

Table 17 Results for material 12, repacking measurements.

The repacking of this material was only measured with the Transfer Matrix Method.

100 120 140 160 180 200 2201

1.5

2

2.5

3

3.5

4x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity-Transfer Matrix Method M12 Repack

0 500 1000 1500-5

0

5x 10

4

Frequency (Hz)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity-Transfer Matrix Method M12 Repack


106127149170191212

0 500 1000 1500

0

10

20

30

40

Transmission Loss M12 Repack


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106127149170191212

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficient M12 Repack


106127149170191212

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficient M12 Repack


106127149170191212

0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

300

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M12 Repack


106 real106 imag127149170191212

53

4.2.3 Comparison for Parallel vs. Perpendicular and Repacking

As studied by Tarnow (2002) [13], and Allard (1987) [14], the resistivity for a material with the fibres oriented parallel to the direction of the sound is somewhere between 0.5‐0.667 of the resistivity for the same material and bulk density but with the fibres oriented perpendicular to the direction of sound. The results in this report show a very good agreement with these previous results. Due to the properties of most of the materials in this report it was very easy to pack the material in the desired direction.

In the plots for the transmission loss the difference in behaviour between the parallel and the perpendicular direction is very obvious.

For material 10 there were altogether 4 measurements made, two for each method. Due to the properties of this material it was very hard to force the material with the fibres in a predictable parallel or perpendicular direction. This made the outcome of the measurements unpredictable. This can be seen in table 20 and the comparison for material 10. But the agreement with the results from Tarnow and Allard still applies. The highest resistivity for a given bulk density is twice the value of the lowest. The 1st measurement in the static airflow resistivity rig shows the lowest resistivity values for this material. Here the material was randomly packed in the holder. For the other three measurements the intention was to try to pack the material in a perpendicular direction to the sound to get a better agreement between the two methods.

For material 12 there is a sudden increase in the airflow resistivity for the static airflow results at bulk density 115 (g/l). This is likely the cause of a bias error made by the author when weighing the samples.

54

Table 18 Comparisons for different materials and measurements cases.

50 100 150 200 2500

1

2

3

4

5

6

7x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity M2 Parallel vs Perpendicular

TMM-ParallelStat. A.flow-ParallelTMM-PerpStat. A.flow-Perp

0 500 1000 1500

0

10

20

30

40

Transmission Loss M2 Parallel vs Perpendicular different bulk densities (g/l)

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106-Pa170-Pa212-Pa106-Pe170-Pe212-Pe

50 100 150 200 2500

1

2

3

4

5

6

7x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity M6 Parallel vs Perpendicular

TMM-ParallelStat. A.flow-ParallelTMM-PerpStat. A.flow-Perp

0 500 1000 1500

0

10

20

30

40

Transmission Loss M6 Parallel vs Perpendicular different bulk densities (g/l)

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106-Pa170-Pa212-Pa106-Pe170-Pe212-Pe

80 100 120 140 160 180 200 2200

0.5

1

1.5

2x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity M10 vs M10 Repack

TMM-1stStat. A.flow-1stTMM-2ndStat. A.flow-2nd

0 500 1000 1500

0

10

20

30

40

Transmission Loss M10 vs M10 Repack


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106170212106-Repack170-Repack212-Repack

80 100 120 140 160 180 200 2200.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

4

Bulk density (g/l)

Airfl

ow R

esis

tivity

Pa

s/m

2

Airflow Resistivity M12 vs M12 Repack

TMM 1stStat. A.flowTMM 2nd

0 500 1000 1500

0

10

20

30

40

Transmission Loss M12 vs M12 Repack


Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

106170212106-Repack170-Repack212-Repack

55

4.2.4 Comparison with Delany & Bazley-Miki

The results from the TMM of the transmission loss, complex speed of sound, absorption coefficient and the reflection coefficient were compared to the models from Delany & Bazley that were revised by Miki in 1990; see Table 19 and Table 20. The coloured vertical line to the left in the plots defines the low frequency validity limit for the models. There is a high frequency limit but for these materials and bulk densities the limit is well above the investigated range. There were also the models from Delany‐Bazley and Mechel but the results for these two formulas gave similar results.

For all the compared materials, the transmission loss calculated from DB‐Miki, were lower than the measured but the trend was similar above the low frequency limit. The models do not account for the drastic decrease in transmission loss around the resonances of the material with the fibres perpendicular to the direction of sound. The same applies for the calculations of the absorption coefficient and reflections coefficient. This is not surprising since all these calculations depend on the same parameters.

In general the agreement of the results between the models and the measurements were better in the higher bulk density regions even for frequencies below the low frequency limit for the model, even for the real part of the speed of sound. This was a general trend in the results.

56

Table 19 Comparisons between measured results and results calculated with the DelanyBazley and Miki method, material 2, bulk density 127 g/l.

0 500 1000 15000

10

20

30

40

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

Transmission Loss - M2 127

(g/l)

M2 127TiL DB-MikiLow.val.freq.-DB & MikiHigh.val.freq.-DB & Miki

0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

350

400

450

Frequency (Hz)

Spee

d of

sou

nd (m

/s)

Complex speed of sound M2 127

(g/l)

real M2 127imag M2 127real DB-Mimag DB-MLow.val.freq.-DB & MikiHighVal.freq.-DB & Miki

0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient

Absorption coefficientM2 127

(g/l)

M2 127DB-MikiLow.val.freq.-DB & MikiHighVal.freq.-DB & Miki

0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt

Reflection coefficientM2 127

(g/l)


0 500 1000 15000

10

20

30

40

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

Frequency (Hz)

Spee

d of

sou

nd (m

/s)


(g/l)


0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt


(g/l)


57

Table 20 Comparisons between measured results and results calculated with the DelanyBazley and Miki method, material 2, bulk density 149 g/l.

0 500 1000 15000

10

20

30

40

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

Frequency (Hz)

Spee

d of

sou

nd (m

/s)


(g/l)


0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt


(g/l)


0 500 1000 15000

10

20

30

40

Frequency (Hz)

Tran

smis

sion

Los

s (d

B)


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

50

100

150

200

250

300

350

400

Frequency (Hz)

Spee

d of

sou

nd (m

/s)


(g/l)


0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Abso

rptio

n co

effic

ient


(g/l)


0 200 400 600 800 1000 1200 1400 1600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (Hz)

Ref

lect

ion

coef

ficie

nt


(g/l)


59

4.3 Micro Perforated Plates results

The results from the micro perforated plate measurements are presented in terms of specific airflow resistance (Rayl or Pa s/m).

From the manufacturer of these micro perforated plates the specific airflow resistance was specified. Material 13 was a 0.1 aluminium plate with 900 (Pa s/m) and material 14 was a 0.5 mm stainless steel plate with 756 (Pa s/m). As can be seen on the picture of the materials there was a tiny hole in the middle of the plates. This was carefully covered with a small metal sheet to make sure that it should not affect the results.

For the measurements made with the static airflow resistance rig there were several measurements made for each plate. The results were thereafter averaged. For material 13 these measurements varied heavily, something that cannot be explained, by the author. The measurements were performed with great care. The same sample was mounted in the sample holder without removing it for all of the measurements which implies that something could have been wrong with the measurement equipment.

For material 14 there were no variations in the results for the different measurement cases.

For the results of these measurements to be correct, changes in the airflow velocity should not affect the airflow resistance results. Since this was not the case a 2nd degree polynomial curve fit was made with the averaged results and the airflow resistance was approximated with the constant in this polynomial. The unexpected outcome of these measurements could be the result of insufficiently low air flow velocity, since there probably is an acceleration of the air through the micro sized perforations of the plates.

The results from the measurements with the Transfer Matrix Method display a similar trend in that the results varies with varying sound pressure level (relative speaker voltage in the graphs). Also here, a 2nd degree polynomial curve fit was made with the results in order to try to extract some kind of results.

The decision of a 2nd degree polynomial curve fit was made after comparison of the results with polynomials of different degrees and this was the one with the best fit.

Since there is a clear distinction between the results from the two methods and the fact that the flow resistance varies with varying sound pressure level and varying flow velocity none of these results seem plausible, even though some of the results are in the same range as the results supplied from the manufacturer.

Even the results for the transmission loss are not the same for different sound pressure levels.

60

Unfortunately, this makes all of the results from the measurements of the micro perforated plates very unreliable, but something that needs to be further investigated.

Table 21 Results for material 13, Micro Perforated Plate 1.

Figure 25 Material 13, MPP1, mounted in holder. 0 0.01 0.02 0.03 0.04

800

900

1000

1100

1200

1300

1400

Velocity (m/s)

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)

Specific Airflow Resistance - M13different measurement cases

1st meas2nd meas3rd meas4th meas5th measaverage2nd deg. line fit

850.9481 (Pa s/m)

0 0.1 0.2 0.3 0.4 0.5 0.6500

550

600

650

700

750

800

Relative Speaker Voltage

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)

Specific Airflow Resistance-Transfer Matrix Method M13

← 515.6717 (Pa s/m)

Measured values2nd deg. line fit

0 500 1000 1500

-500

0

500

1000

Frequency (Hz)

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)


for Relative Speaker Voltages

0.050.250.55

0 500 1000 15000

2

4

6

8

10



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

0.050.250.55

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



0.050.250.55

61

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie


M13 for Relative Speaker Voltages

0.050.250.55

0 200 400 600 800 1000 1200 1400 1600

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



0.05 real0.05 imag0.250.55

Table 22 Results for material 14, Micro Perforated Plate 2.

Figure 26 Material 14, MPP2, mounted in holder. 0 0.01 0.02 0.03 0.04

250

300

350

400

450

Velocity (m/s)

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)

Specific Airflow Resistance - M14different measurement cases

1st meas2nd meas3rd measaverage2nd deg. line fit

266.3825 (Pa s/m)

0 0.1 0.2 0.3 0.4 0.5 0.620

30

40

50

60

70

80

90

100

Relative Speaker Voltage

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)


← 28.1142 (Pa s/m)

Measured values2nd deg. line fit

0 500 1000 1500

-150

-100

-50

0

50

100

150

Frequency (Hz)

Spec

ific

Airfl

ow R

esis

tanc

e (P

a s/

m)



0.050.250.55

0 500 1000 15000

2

4

6

8

10



Frequency (Hz)

Tran

smis

sion

Los

s (d

B)

0.050.250.55

0 500 1000 1500

0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Abso

rptio

n co

effic

ient



0.050.250.55

62

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ref

lect

ion

coef

ficie


M14 for Relative Speaker Voltages

0.050.250.55

0 200 400 600 800 1000 1200 1400 1600

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Frequency (Hz)

Spee

d of

sou

nd (m

/s)



0.05 real0.05 imag0.250.55

64

5 Conclusions

The purpose of this master thesis project was to measure the airflow resistivity for various sound absorbing materials used in exhaust systems and to compare the results from measurements with the Transfer Matrix Method and the Static Airflow method.

The conclusions after the measurements were:

• The agreement between the two methods was very good. • The value of the resistivity was doubled for measurements with the fibres

perpendicular to the direction of sound. • When the materials with a high degree of micro strands were oriented with the

fibres perpendicular to the direction of sound there was a resonant behaviour in the sample. The onset frequency of this resonance increased with increasing bulk density. This resonance leads to difficulties in predicting the behaviour of real life exhaust systems.

• Further studies on the micro perforated plates must be made with even lower flow velocities and sound pressure levels and maybe with other methods.

66

6 References

1. Delany M. E. and Bazley E. N., Acoustical properties of fibrous absorbent materials, Applied Acoustics 3, 1970, pp. 105‐116.

2. Mechel, F P, Extending the Absorption Formulae of Delaney and Bazley to Low Frequencies, Acustica [0001‐7884], 1976, vol:35, 210‐213.

3. International Standard ISO 9053, Acoustics – Materials for acoustical applications – Determination of airflow resistance, 1991.

4. Miki Y., Acoustical properties of porous materials ‐ Modifications of Delany‐Bazley models, J. Acoust. Soc. Jpn (E). 11(1), 1990, pp. 19‐24.

5. Mechel, F. P., Chapter 8 sound‐absorbing materials and sound absorbers,. Noise and Vibration Control Engineering, Edited by Beranek, L. L. and Vér, I. L., John Wiley and Sons, INC. 1992.

6. Åbom M. Measurement of the scattering‐matrix of acoustical two‐ports in Mechanical Systems and Signal processing 5(2), 1990 pp. 89‐104.

7. Munjal, M. L. Acoustics of ducts and mufflers, New York, 1987, Wiley interscience 8. M Åbom, Determination of porous material data via two‐port measurements,

INTER‐NOISE 1999. 9. Designation: E2611 – 09, Standard Test Method for Measurement of Normal

Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method.

10. Åbom M., Bodén H Influence of errors on the two‐microphonemethod for measuring acoustic properties in ducts in J. Acoust. Soc. Am. 79(2), 1986, pp. 541‐549.

11. H Bodén, U Karlsson, R Glav, H.P. Wallin, M Åbom. (2001) Ljud och Vibrationer, (2nd Ed.) Stockholm: Norstedts Tryckeri AB, ISBN 91‐7170‐434‐5.

12. M. D. Dahl, E. J. Rice, and D. E. Groesbeck, ‘‘Effects of fiber motion on the acoustic behavior of an anisotropic, flexible fibrous material,’’ J. Acoust. Soc. Am. 87, 54–66, 1990.

13. Viggo Tarnow, “Measured anisotropic air flow resistivity and sound attenuation of glass wool”, J. Acoust. Soc. Am. 111 (6), June 2002, Viggo Tarnow.

14. J. F. Allard, R. Bourdier, and A. L’Esperance, ‘‘Anisotropic effect in glass wool on normal impedance in oblique incidence,’’ J. Sound Vib. 114, 233–238, 1987.

15. B. Castagnéde, A. Aknide, B. Brouard, V. Tarnow, “Effects of compression on the sound absorption of fibrous materials”, Applied Acoustics, 61, 173‐182, 2000.

16. H. Geyssel, M. Åbom, Development of an acoustic four‐pole test rig for porous materials and mufflers, technical report, 1998.

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