Indirect acoustical characterization of sound absorbing materials Intro by Raymond Panneton Yacoubou Salissou Les présentateurs doivent souvent transmettre des informations techniques à des auditeurs qui connaissent moins bien le sujet et le vocabulaire spécifique. Les informations peuvent être multiples ou complexes. Pour présenter des informations techniques efficacement, utilisez les conseils suivants de Dale Carnegie Training®.   Tenez compte du temps dont vous disposez et préparez la classification de vos informations. Délimitez votre sujet et découpez votre présentation en séquences claires. Suivez une progression logique et ne vous dispersez pas. Terminez la présentation par un résumé, un rappel des étapes clés ou une conclusion logique. Montrez l’intérêt que vous portez à votre assistance. Par exemple, utilisez toujours des données claires et pertinentes. Choisissez un niveau de détail et un vocabulaire adaptés à l'assistance. Utilisez des aides visuelles pour étayer vos points et étapes clés. Les auditeurs seront plus réceptifs si vous êtes à l'écoute de leurs besoins.

Sound absorbers Intro µ-Structure Types Granular, fiber, foam Material Types Polymer, metal, textile, … Frame Types Elastic Acoustically rigid or limp Intro Modeling theories Biot theory (if frame is elastic) Equivalent fluid theory (else)

Equivalent fluid modeling Rigid frame Helmholtz equation with equivalent density and bulk modulus Intro Limp frame Helmholtz equation with equivalent density and bulk modulus Total apparent mass of the bulk volume

Equivalent fluid modeling Equivalent dynamic density Takes into account viscous and inertial effects Some recent models: Johnson et al. (1987) - , , ,  Pride et al. (1993) - , , , , 0 JL model JCA model Intro Equivalent dynamic bulk modulus Takes into account thermal effects Some recent models: Champoux and Allard (1991) - ,  Lafarge I (1993,1997) - , , k0 Lafarge II (1993) - , , k0, 0 Macroscopic parameters  - Open porosity  - Tortuosity  - Static airflow resistivity - Viscous characteristic length 0 - Static viscous tortuosity k0 - Static thermal permeability  - Thermal characteristic length 0 - Static thermal tortuosity

Equivalent fluid modeling Equivalent dynamic density Intro Equivalent dynamic bulk modulus

Macroscopic parameters Characterization Methods Direct Inversion Time Frequency Ultrasound Audio (impedance tube) Iterative Intro T.C.L. Tortuosity Resistivity Porosity Tortuosity Resistivity Porosity V.C.L. T.C.L. Tortuosity V.C.L. T.C.L. Tortuosity Resistivity Porosity V.C.L. T.C.L. Tortuosity Resistivity Porosity V.C.L. T.C.L. Ther. Perm. Number of searched parameters Number of searched parameters Accuracy Accuracy

Macroscopic parameters Characterization Methods Direct Inversion Time Frequency Ultrasound Audio (impedance tube) Iterative Intro Porosity Tortuosity Resistivity V.C.L. T.C.L. Ther. Perm. Direct inversion

Direct inversion method Main assumptions to verify Linear acoustics Sample is saturated by air at rest The open porosity of the sample is assumed known Sample is homogeneous (~symmetric) The frame of the sample is acoustically rigid or limp Sample has an Equivalent Fluid behavior which can be modeled accurately by the JCA model or the JL model Dynamic properties (eq, Keq) can be measured accurately Method

Direct inversion method Analytical expressions for VISCOUS parameters From the Johnson et al. viscous model Method  f , Expected behaviors if sample follows model 9

Direct inversion method Analytical expressions for THERMAL parameters From the Champoux-Allard thermal model From the Lafarge thermal model Method ’, ko’ f Expected behaviors if sample follows model 10

Measurements of eq and Keq Some commonly used impedance tube methods Two-microphone/Two-cavity method by Utsono et al. Method Three-microphone method by Iwase et al. Four-microphone Transfer matrix by Song and Bolton. Modified three-microphone method Compared to 2-mic method: Not only surface meas. Compared to 3-mic Iwase method: no probe and standard Compared to 4-mic method: Uses less mics and transfer functions

Measurements of eq and Keq L d Method ISO 10534-2 or ASTM E1050 for R and Zs

44.5 mm diameter impedance or transmission tube Comparisons Melamine foam 44.5 mm diameter impedance or transmission tube Method

Description of sample Results Main properties Optional properties Material: Polyurethane foam Diameter: 44.5-mm (=tube diameter) Thickness: 50-mm Bulk density: 60 kg/m³ Open porosity: 0.960  0.005 Results Optional properties Static airflow resistivity: 2 300  250 Young’s modulus: ~300 000 Pa

What we actually measure Test 1 ok Frame Acoustical Excitability (FAE) What is done What we want to measure What we actually measure Acoustical measurements in the Standing Wave Tube (SWT) or Results or or Should reduce thickness! [see JASA 114(4) and JASA 116(1)]

Test 2 ok Through thickness symmetry (indication on homogeneity) Results 16 [see JASA 124(2)]

If limp then convert to rigid Test 3 Rigid Observe eq and decide ! Rigid or limp? Rigid Results If limp then convert to rigid 17 [see JASA 122(6)]

Observe constancy of parameters ! Test 4 ok Equivalent fluid behavior following models Observe constancy of parameters !  f () Results 18

Results Results      =hf k0 =lf/8 lf Direct Inversion Iterative Inversion Direct  - 0.960  0.005  2 609  387 2 400  125 2 300  250  1.28  0.01 1.29  0.01  202  14 211  20  =hf 376  28 360  36 k0 =lf/8 167  39 lf 373  38 Results 19

Results Results 20

Results Results 21

Concluding Remarks Conclusion

Thank you! Questions?