A review of experimental methods for the elastic and damping characterizations of acoustical porous material Mickael Deverge, Luc Jaouen, and Sohbi Sahraoui
Acoustic Laboratory, University of Maine, France Internoise, 22-25 August 2004
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Plan
• What’s a porous acoustical material ? • Theoritical description • Some existing methods • Two non-resonant, quasistatic methods ◦ compression ◦ torsion
• Two resonant recent methods ◦ beam bending ◦ plate bending
• Conclusions • Perspectives
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
What’s a porous acoustical material ? 2 phases: • a solid phase, the skeleton, • a fluid phase, the air.
Electron microscope pictures of a melamine foam on the left and of a polyurethane foam on the right. The solid phases appear in white.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
What’s a porous acoustical material ?
• 2 distinguished cases for the modelizations: ◦ Motionless skeleton: “equivalent fluid”. ◦ Skeleton in motion: generalized Biot-Allard theory (Biot 56, Johnson et al. 87, Allard et al. 91, Allard 93)
• Usual assumptions: linear elasticity, isotropy, long wave-length.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Theoritical description
• Generalized Biot-Allard theory: σij,j −φp,i
= ρ11 u¨i + ρ12 U¨i + b(ω)(u˙i − U˙ i ) = ρ12 u¨i + ρ22 U¨i + b(ω)(U˙ i − u˙i )
• Stress-strain relations: σijs
= [(P − 2N)ui,j + QUi,j ] δi,j + 2Nui,j
σijf
= −φpδij = (Qui,j + RUi,j )δi,j
E , ν, G and η are related to coefficients P, Q, N, R.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Some existing methods A
4 3
4
2
2
3
1
1 B 4
LASER
D
3
2
1 C
1: shaker or rotor 2: sample M. Deverge, L. Jaouen & S. Sahraoui
1
4 2
3
3 and 4: accelerometer or force/torque transducer. Elastic and damping characterization of porous materials
Quasistatic compression test • Frequency range ∼ 5 − 100 Hz. • Fluid-structure interactions neglected. • Cubic sample.
4 LASER
3
2
1 C (1: shaker, 2: sample, 3: accelerometer and 4: force transducer)
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Quasistatic compression test 6
10
Evolutions of Ei (N.m−2)
Real part of E i: Ei’
5
10
Imaginary part of E i: Ei’’
Side 1 Side 2 Side 3
4
10
1
10
2
Frequency (Hz)
10
Estimations of a melamine foam complex Young’s moduli at 18o C. ◦: side 1, 4: side 2, : side 3.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Quasistatic torsion test • Frequency range ∼ 0.01 − 10 Hz. • Fluid-structure interactions neglected. • Cylindrical sample.
A
2
1
4
3
(1: rotor, 2: sample, 3: torque transducer and 4: accelerometer)
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Quasistatic torsion test
−2
Real part of shear modulus: G13’ (N.m )
2e+04
0°C 10°C 24°C 40°C
1e+04 9e+03 8e+03 7e+03
1e+05 9e+04
6e+03
8e+04
5e+03
7e+04
4e+03
6e+04 5e+04 −2 10
−2
0°C 10°C 24°C 40°C
Imaginary part of shear modulus: G13’’ (N.m )
2e+05
−1
10
0
10 Frequency (Hz)
1
10
3e+03 −2 10
−1
10
0
10 Frequency (Hz)
1
10
Variations of the shear modulus G13 real and imaginary parts with temperature and frequency for a melamine foam. +: 0o C, o: 10o C, ?: 24o C, : 40o C
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Resonant methods • • • •
Frequency range ∼ 10 − 1000 Hz Fluid-structure interactions no more neglected. Beam- or plate-like samples. Acoustic radiation neglected.
Rod ( Line of imposed displacement )
Porous layer
Base metal beam
Metal plate
Porous layer
Shaker
Ponctual force
LASER
(1: rotor, 2: sample, 3: torque transducer and 4: accelerometer)
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Resonant methods 6
−1
Plate meas. (23°C) Beam meas. (25°C)
10
Estimations of η1
Estimations of E’1 (N.m−2)
10
5
10 2 10
Plate meas. (23°C) Beam meas. (25°C)
−2
3
Frequency (Hz)
10
10
2
10
3
Frequency (Hz)
10
Comparisons of estimation results for the real Young’s modulus E10 and the structural damping coefficient η1 of the melamine foam. : beam bending - three layers configuration (25o C), o: plate bending (23o C).
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Some comparison points
Compression Torsion
freq. range
+
−
5−100 Hz
study of anisotropy
fluid−struct. neglected
0.01−10 Hz com. apparatuses constant volume
fluid−struct. neglected isotropy assumed
Beam bending 10−1000 Hz fluid−struct. interact.
heavy computing isotropy assumed
Plate bending
radiation neglected isotropy assumed
10−1000 Hz fluid−struct. interact. configuration of use simplyfied comput.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Conclusion-Perspectives
Conclusion: No ideal method. Need of a combination of different methods for the complete elastic and damping characterization. Perspectives: • Systematic study of anistropy. • Influence of the acoustic radiation for plate-like sample.
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
Thanks for your attention
[email protected] [email protected] Laboratoire d’Acoustique de l’Universit´e du Maine UMR CNRS 6613 avenue Olivier Messiaen 72085 Le Mans Cedex 9 France Tel : +33 2 43 83 32 50
M. Deverge, L. Jaouen & S. Sahraoui
Elastic and damping characterization of porous materials
