4th International Conference on Emerging Technologies in Non-Destructive Testing

4th International Conference on Emerging Technologies in Non-Destructive Testing

Bernard CASTAGNÈDE, Alexei MOUSSATOV, Denis LAFARGE, Vincent TOURNAT, Vitalyi GUSEV

USE OF STATE OF THE ART PARAMETRIC

ARRAYS FOR LOW FREQUENCY MEASUREMENTS IN SOUND ABSORBING MATERIALS

- April 2 ^nd – 4 ^th , 2007, Stuttgart, Germany -

Laboratoire d’Acoustique de l’Université

du Maine, UMR C.N.R.S. 6613, France

Impedance tube for measuring

absorption coefficient

Technical specifications

of a parametric array in air

Temporal signals and Amplitude spectra

0.80

-0.80 -0.60 -0.40 -0.20 -0.00 0.20 0.40 0.60

5.0E-4

0.0E+0 2.5E-4

Temporal signal

-10

-90 -80 -70 -60 -50 -40 -30 -20

200000

0 50000 100000 150000

0.03

-0.02 -0.01 0.00 0.01 0.02

5.0E-4

0.0E+0 2.5E-4

Temporal signal

-35

-80 -75 -70 -65 -60 -55 -50 -45 -40

200000

0 50000 100000 150000

freq(pump) = 159 kHz ; freq(modulation) = 4 kHz

0.20

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

2.0E-4 0.0E+0 5.0E-5 1.0E-4 1.5E-4

Temporal signal

-20

-90 -80 -70 -60 -50 -40 -30

200000

0 50000 100000 150000

0.04

-0.01 0.00 0.01 0.02 0.03

2.0E-4 0.0E+0 5.0E-5 1.0E-4 1.5E-4

Temporal signal

-40

-85 -80 -75 -70 -65 -60 -55 -50 -45

200000

0 50000 100000 150000

freq(pump) = 159 kHz ; freq(modulation) = 8 kHz

Temporal signals and

Amplitude spectra

0.20

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

1.0E-4 0.0E+0 2.5E-5 5.0E-5 7.5E-5

Temporal signal

-20

-90 -80 -70 -60 -50 -40 -30

200000

0 50000 100000 150000

0.05

-0.02 -0.01 0.00 0.01 0.02 0.03 0.04

2.0E-4 0.0E+0 5.0E-5 1.0E-4 1.5E-4

Temporal signal

-40

-85 -80 -75 -70 -65 -60 -55 -50 -45

200000

0 50000 100000 150000

freq(pump) = 159 kHz ; freq(modulation) = 16 kHz

Temporal signals and

Amplitude spectra

Dedicated laboratory system

K ( ω ^{) =} γ ^P ₀ ^{/ [} γ ^{– (} γ ^{– 1 ){ 1 +} σ ^' φ

j Pr ω ρ ₀ α _∞ ^{G J}

' (Pr ω ) } ^{– 1} ] ρ ⁽ ω ^{) =} α _∞ ρ ₀ ^{[ 1 +} σ φ

j ω ρ ₀ α _∞ ^{G J (} ω ) ]

z _mat = K ( ω ⁾ ρ ( ω )

k _mat = ω ρ ( ω ) K( ω ⁾ Wave number

Acoustic impedance

Phase wavespeed

c( ω ) = K( ω ) ρ(ω ) "Fluid equivalent"

theoretical modelling

G

( ω ) = 1 + 4 j α

η ρ

ω

σ

Λ

φ

^G

' (Pr ω ) = 1 + 4 j α

η ρ

ω ^Pr

σ ^'

Λ ^'

φ

σ ^{' = 8} α _∞ η Λ ^{' 2} φ

List of the physical parameters of the model

ω = 2 π f : the angular frequency

γ  : the specific heat ratio

P

: the atmospheric pressure Pr : the Prandtl number

ρ

: the air density at rest η : the air viscosity

φ : the porosity

α

: the tortuosity

σ : the air flow resistivity

Λ ^, Λ ' : the viscous, and thermal characteristic lengths

"Fluid equivalent"

theoretical modelling

Dispersion curves measurements

5

-5 -2 0 2

2.0E-4 0.0E+0 5.0E-5 1.0E-4 1.5E-4

référence échantillon

signaux

1.2E-4

0.0E+0 2.0E-5 4.0E-5 6.0E-5 8.0E-5 1.0E-4

2.4E+1 1.2E+1 1.5E+1 2.0E+1

spectres d'amplitude

2

-8 -6 -4 -2 0

24

12 14 16 18 20 22

spectres de phase

315

295 300 305 310

2.4E+1 1.2E+1 1.5E+1 2.0E+1

vitesse de phase (m/s)

freq(pump) = 170 kHz ; freq(modulation) = 16 kHz

H = 20 mm

Dispersion curves measurements

freq(pump) = 40 kHz ; freq(modulation) = 1.5 kHz

2000

-1500 -1000 -500 0 500 1000 1500

2.0E-4 0.0E+0 5.0E-5 1.0E-4 1.5E-4

signals

3.0E-2

0.0E+0 5.0E-3 1.0E-2 1.5E-2 2.0E-2 2.5E-2

2.5

0.5 1.0 1.5 2.0

amplitude spectrum

3

-3 -2 -1 0 1 2

3.0

0.5 1.0 1.5 2.0 2.5

phase spectrum

120

0 20 40 60 80 100

2.5 0.2 0.5 1.0 1.5 2.0

phase wavespeeds (m/s)

H = 5 mm

Dispersion curves

freq(pump) = 40 kHz ; freq(modulation) = 1.5 kHz

Numerical results Experimental results

B. Castagnede et al, Ultrasonics, 44, 221-229 (2006)

Dispersion curves measurements

Red crosses : Experimental data Blue triangles : Numerical

predictions

Black crosses &

other symbols : Experimental data

0 50 100 150 200 250

0 500 1000 1500 2000 2500

Wavespeed (m/s)

Frequency (Hz)

φ = 0.96 ; σ = 16 000 Nsm

 ; α

= 1.08 ; Λ = 180 µm ; Λ’ = 360 µm

30 mm thick plastic foam

Dispersion curves measurements

φ = 0.92 ; σ = 24 000 Nsm

 ; α

= 1.04 ;

Λ = 200 µm ; Λ’ = 400 µm φ = 0.90 ; σ = 35 000 Nsm

 ; α

= 1.06 ; Λ = 150 µm ; Λ’ = 300 µm

20 mm thick felt material 15 mm thick felt material

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

Wavespeed (m/s)

frequency (Hz)

Red crosses : Experimental data Blue triangles : Numerical

predictions

Black crosses : Experimental data

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

Wavespeed (m/s)

Frequency (Hz)

Red crosses : Experimental data

Black crosses &

other symbols : Experimental data Blue triangles : Numerical

predictions

Dispersion curves measurements

φ = 0.88 ; σ = 56 000 Nsm

 ; α

= 1.18 ;

Λ = 100 µm ; Λ’ = 200 µm φ = 0.80 ; σ = 140 000 Nsm

 ; α

= 1.30 ; Λ = 50 µm ; Λ’ = 100 µm

10 mm thick felt material 5 mm thick felt material

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

Wavespeed (m/s)

Frequency (Hz)

Red crosses : Experimental data Black crosses : Experimental data Blue triangles : Numerical

predictions

Red crosses : Experimental data

Blue triangles : Numerical predictions

Black crosses &

other symbols : Experimental data

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

Wavespeed (m/s)

Frequency (Hz)

Dispersion curves of some RIETER automotive felts

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

B CD E

wavespeed (m/s)

Frequency (Hz)

5 mm thickness 10 mm thickness 15 mm thickness 20 mm thickness

Summary experimental results

Dispersion curves of some RIETER automotive felts

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000

B C D E

Wavespeed (m/s)

Frequency (Hz)

5 mm thickness 10 mm thickness 15 mm thickness 20 mm thickness

Summary numerical results

Dispersion curves of some RIETER automotive felts

Physical parameters change

Thickness (mm)

Porosity Resistivity (N m-4 s)

Tortuosity Viscous length ( µ m)

Thermal length ( µ m)

20 0.92 24 000 1.04 200 400

15 0.90 35 000 1.06 150 300

10 0.88 56 000 1.18 100 200

5 0.80 140 000 1.30 50 100

B. Castagnede et al, Applied Acoustics, 61, 173-182 (2000)

Reflexion configuration

Basic sketch and numerical treatment

IEEE 488 interface 1

2

5 4

6

I

8 7

I R

d

d

h

x = 0

3 ^x

R

Reflection coefficient

Reflection coefficient

Frequency (kHz)

H = 20 mm

H = 10 mm

M.Saeid et al, C.R. Mecanique, 332, 849-858 (2004)

Reflected acoustical signals

0.02

-0.02 -0.01 0.00 0.01

5.0E-4 0.0E+0 1.0E-4 2.0E-4 3.0E-4 4.0E-4

Incident Réfléchi

signaux

1.0E-3

0.0E+0 2.0E-4 4.0E-4 6.0E-4 8.0E-4

2.4E+4 1.0E+4 1.2E+4 1.4E+4 1.6E+4 1.8E+4 2.0E+4 2.2E+4

Incident Réfléchi

spectres d'amplitude

0.500

0.200 0.220 0.240 0.260 0.280 0.300 0.320 0.340 0.360 0.380 0.400 0.420 0.440 0.460 0.480

19000 14000 15000 16000 17000 18000

coefficient de rétrodiffusion

H = 10 mm

freq(pump) = 162 kHz ; freq(modulation) = 16 kHz

Reflected acoustical signals

0.02

-0.02 -0.01 0.00 0.01

5.0E-4 0.0E+0 1.0E-4 2.0E-4 3.0E-4 4.0E-4

Incident Réfléchi

signaux

6.0E-4

0.0E+0 1.0E-4 2.0E-4 3.0E-4 4.0E-4 5.0E-4

2.4E+4 1.0E+4 1.2E+4 1.4E+4 1.6E+4 1.8E+4 2.0E+4 2.2E+4

Incident Réfléchi

spectres d'amplitude

0.500

0.200 0.220 0.240 0.260 0.280 0.300 0.320 0.340 0.360 0.380 0.400 0.420 0.440 0.460 0.480

19000 14000 15000 16000 17000 18000

coefficient de rétrodiffusion

H = 10 mm

freq(pump) = 162 kHz ; freq(modulation) = 16 kHz

Reflected acoustical signals

0.02

-0.01 0.00 0.01

5.0E-4 0.0E+0 1.0E-4 2.0E-4 3.0E-4 4.0E-4

Incident Réfléchi

signaux

3.5E-4

5.0E-5 1.0E-4 1.5E-4 2.0E-4 2.5E-4 3.0E-4

2.4E+4 1.0E+4 1.2E+4 1.4E+4 1.6E+4 1.8E+4 2.0E+4 2.2E+4

Incident Réfléchi

spectres d'amplitude

freq(pump) = 162 kHz ; freq(modulation) = 16 kHz

0.500

0.200 0.220 0.240 0.260 0.280 0.300 0.320 0.340 0.360 0.380 0.400 0.420 0.440 0.460 0.480

24000 10000 12500 15000 17500 20000

coefficient de rétrodiffusion

H = 10 mm

"Fluid equivalent"

theoretical modelling

R( ω ^{) = z mat cos k mat h – j} φ ^{sin k} mat h z _mat cos k _mat h + j φ ^{sin k} _mat ^h

R( ω ^{) = z mat –} φ z _mat + φ

Porous layer surrounded by air

Porous layer on a rigid screen

Porous material half-space

R( ω ^{) = j} φ ^{2 – z 2} _mat ^{sin k} _mat ^h

2 φ ^z _mat ^{cos k} _mat ^{h + j} φ ^{2 + z} _mat ^{2 sin k} _mat ^h

Absorption coefficient of a cellular porous material

φ = 0.96 ; σ = 6 000 Nsm

 ; α

= 1.12 ; Λ = 80 µm ; Λ’ = 240 µm

30 mm thick plastic foam

α(ω) = 1 – R (ω) ²

Signals (incident and reflected) versus average number N

N = 1 average

0.10

-0.10 -0.05 0.00 0.05

5

0 1 2 3 4

ms V

2 kHz

0.04

-0.06 -0.04 -0.02 0.00 0.02

5

0 1 2 3 4

ms V

2 kHz

0.04

-0.06 -0.04 -0.02 0.00 0.02

5

0 1 2 3 4

ms V

2 kHz

N = 10 averages

N = 100

averages

Signals (incident and reflected) versus modulation frequency

0.02

-0.03 -0.02 -0.01 0.00 0.01

5

0 1 2 3 4

ms V

1 kHz

0.04

-0.04 -0.02 0.00 0.02

5

0 1 2 3 4

ms V

1.5 kHz

0.04

-0.06 -0.04 -0.02 0.00 0.02

5

0 1 2 3 4

ms V

2 kHz

0.05

-0.10 -0.05 0.00

5

0 1 2 3 4

ms V

3 kHz

Signal processing in order to obtain the absorption coefficient

0.04

-0.06 -0.04 -0.02 0.00 0.02

2.0E-3 0.0E+0 5.0E-4 1.0E-3 1.5E-3

référence échantillon

signaux

4.0E-4

0.0E+0 1.0E-4 2.0E-4 3.0E-4

3.0E+0 0.0E+0 1.0E+0 2.0E+0

référence échantillon

spectres d'amplitude

1.000

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

3.0 0.0 0.5 1.0 1.5 2.0 2.5

coefficient d'absorption

Fmod =1.5 kHz

Absorption Coefficient measurements with an audio parametric projector

Mesures au tube du Kundt Simulation “fluide équivalent”

Mesures pour fmodul = 1 kHz Mesures pour fmodul = 2 kHz Mesures pour fmodul = 3 kHz Mesures pour fmodul = 4 kHz Mesures pour fmodul = 1,5 kHz

0 0.2 0.4 0.6 0.8 1

0 500 1000 1500 2000 2500 3000 3500 4000

Kundt&mesures fines.dat

BD F H JL N

Coefficient d'absorption

Fréquence (Hz)

30 mm thick plastic foam

0 0.2 0.4 0.6 0.8 1

0 500 1000 1500 2000 2500 3000

Kundt+Senn/micdyn40c(MV).bis

B D F J

Coefficient d'absorption

Fréquence (Hz)

Mesures tube de Kundt Simulations numériques Manip Senn modul 1,5 kHz Manip Senn modul 3 kHz

30 mm thick plastic foam

Absorption Coefficient measurements

with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 500 1000 1500 2000 2500 3000

Kundt+Senn/MD40cm/cor.dat

B D F H

Coefficient d'absorption

Fréquence (Hz)

Mesures tube de Kundt Simulation numérique

Manip Senn modul 1.5 kHz Manip Senn modul 3 kHz

30 mm thick plastic foam

Absorption Coefficient measurements

with an audio parametric projector

Portable processing

and monitoring system

15 mm thick automotive felt material

Incident and reflected signals and audio spectra

Central frequency

of the pulse = 2 kHz

15 mm thick automotive felt material Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements

Blue triangles : Numerical simulation predictions

φ = 0.90 ; σ = 70 000 Nsm

 ; α

= 1.06 ;

Λ = 30 µm ; Λ’ = 60 µm

15 mm thick automotive felt material Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements Blue triangles : Numerical simulation predictions

φ = 0.90 ; σ = 70 000 Nsm

 ; α

= 1.06 ;

Λ = 50 µm ; Λ’ = 100 µm

30 mm thick cellular material

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 500 1000 1500 2000 2500 3000

Absorption

Frequency (Hz)

Continuous red line : Audio

projector measurements

Blue triangles : Numerical

simulations predictions

5 mm thick automotive insulating panel Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 500 1000 1500 2000 2500 3000 3500 4000

Absorption coefficient

Frequency (Hz)

Continuous red line : Audio

projector measurements

Big black squares : Kundt

tube measurements

10 mm thick glass wool material

Incident and reflected signals and audio spectra

20 mm thick glass wool material

25 mm thick glass wool

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements

Big black squares : Kundt tube measurements

Blue triangles : Numerical simulations predictions

φ = 0.98 ; σ = 40 000 Nsm

 ; α

= 1.05 ;

Λ = 100 µm ; Λ’ = 200 µm

20 mm thick glass wool

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements

Big black squares : Kundt tube measurements

Blue triangles : Numerical simulations predictions

φ = 0.97 ; σ = 50 000 Nsm

 ; α

= 1.06 ;

Λ = 80 µm ; Λ’ = 160 µm

15 mm thick glass wool

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements

Big black squares : Kundt tube measurements

Blue triangles : Numerical simulations predictions

φ = 0.97 ; σ = 67 000 Nsm

 ; α

= 1.08 ;

Λ = 60 µm ; Λ’ = 120 µm

10 mm thick glass wool

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements Big black squares : Kundt tube measurements

Blue triangles : Numerical simulations predictions

φ = 0.95 ; σ = 100 000 Nsm

 ; α

= 1.12 ;

Λ = 40 µm ; Λ’ = 80 µm

5 mm thick glass wool

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

Absorption

Frequency (Hz)

Continuous red line : Audio projector measurements

Big black squares : Kundt tube measurements

Blue triangles : Numerical simulations predictions

φ = 0.90 ; σ = 200 000 Nsm

 ; α

= 1.25 ;

Λ = 20 µm ; Λ’ = 40 µm

Various thicknesses glass wool materials

Absorption Coefficient measurements with an audio parametric projector

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

BD E F C

Absorption

Frequency (Hz)

25 mm 20 mm 15 mm 10 mm 5 mm

Summary experimental results

Various thicknesses glass wool materials

Absorption Coefficient measurements with an audio parametric projector

Summary numerical results

0 0.2 0.4 0.6 0.8 1

0 1000 2000 3000 4000 5000 6000

B D E FC

25 mm 20 mm 15 mm 10 mm 5 mm

Frequency (Hz)

Various thicknesses glass wool materials Absorption Coefficient measurements with an audio parametric projector

Physical parameters changes

Thickness (mm)

Porosity Resistivity (N m-4 s)

Tortuosity Viscous length ( µ m)

Thermal length ( µ m)

25 0.98 40 000 1.05 100 200

20 0.975 50 000 1.06 80 160

15 0.97 67 000 1.08 60 120

10 0.95 100 000 1.12 40 80

5 0.90 200 000 1.25 20 40

B. Castagnede et al, Applied Acoustics, 61, 173-182 (2000)

Conclusions & perspectives

* The parametric audio projector is a new tool to characterize the physical properties of absorbing poroelastic materials

There is a strong potential which allows :

• Parameters measurements (tortuosity, porosity, etc)

• Possibility of quasi-ponctual measurements

• «in-situ» and «on-line» measurements available

• Tunable frequencies ( 100 Hz to 10 kHz in audio range)

• Portable instruments already available

* Several potential applications in the field of «on line» production quality control of poroelastic materials

* Methods for the «in situ» measurements in various fields of

industry (automotive, aerospace, etc).