Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials

Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials

Volumn , Issue , 2009, Pages 1-358

  Allard, Jean F ^a   Atalla, Noureddine ^b  

^a UNIVERSITÉ DU MAINE   (France)

^b UNIVERSITÉ DE SHERBROOKE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84890254825     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470747339     Document Type: Book

References (252)

1. Achenbach, J.D. (1973) Wave Propagation in Elastic Solids. North Holland Publishing Co., New York.
2. Brekhovskikh, L.M. (1960) Waves in Layered Media. Academic Press, New York.
3. Cagniard, L. (1962) Reflection and Refraction of Progressive Waves, translated and revised by E.A. Flinn and C.H. Dix. McGraw-Hill, New York.
4. Ewing, W.M., Jardetzky, W.S. and Press, F. (1957) Elastic Waves in Layered Media. McGraw-Hill, New York.
5. Miklowitz, J. (1966) ElasticWave Propagation. In AppliedMechanics Surveys, eds H.N. Abramson, H. Liebowitz, J.N. Crowley and R.S. Juhasz, Spartan Books, Washington, pp. 809-39.
6. Morse, P.M. and Ingard, K.U. (1968) Theoretical Acoustics. McGraw-Hill, New York.
7. Allard, J. F., Bourdier, R. and L'Espérance, A. (1987) Anisotropy effect in glass wool on normal impedance at oblique incidence. J. Sound Vib., 114, 233-8.
8. Attenborough, K. (1971) The prediction of oblique-incidence behaviour of fibrous absorbents. J. Sound Vib., 14, 183-91.
9. Bies, D. A. and Hansen, C.H. (1980) Flow resistance information for acoustical design. Applied Acoustics, 13, 357-91.
10. Burke, S. (1983) The absorption of sound by anisotropic porous layers. Paper presented at 106th Meeting of the ASA, San Diego, CA.
11. Champoux, Y, Stinson, M. R. and Daigle, G. A. (1991) Air-based system for the measurement of porosity, J. Acoust. Soc. Amer., 89, 910-6.
12. Delany, M. E. and Bazley, E. N. (1970) Acoustical properties of fibrous materials. Applied Acoustics, 3, 105-16.
13. Dunn, I. P. and Davern, W. A. (1986) Calculation of acoustic impedance of multilayer absorbers. Applied Acoustics, 19, 321-34.
14. Gray, D. E., ed., (1957) American Institute of Physics Handbook. McGraw-Hill, New York.
15. ISO 9053: (1991) Acoustics-Materials for acoustical applications-Determination of airflow resistance.
16. Mechel, F. P. (1976) Ausweitung der Absorberformel von Delany and Bazley zu tiefen Frequenzen. Acustica, 35, 210-13.
17. Miki, Y. (1990) Acoustical properties of porous materials-Modifications of Delany-Bazley models. J. Acoust. Soc. Japan, 11, 19-24.
18. Morse, M. K., and Ingard K. U. (1986) Theoretical Acoustics. Princeton University Press, Princeton.
19. Nicolas, J. and Berry, J. L. (1984) Propagation du son et effet de sol. Revue d'Acoustique, 71, 191-200.
20. Papoulis, A. (1984) Signal Analysis. McGraw-Hill, Singapore.
21. Pierce, A. D. (1981) Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill, New York.
22. Stinson, M. R. and Daigle, G. A. (1988) Electronic system for the measurement of flow resistance. J. Acoust. Soc. Amer. 83, 2422-2428
23. Tarnow, V. (2005) Dynamic measurement of the elastic constants of glass wool. J. Acoust. Soc. Amer. 118, 3672-3678.
24. Zwikker, C. and Kosten, C. W. (1949) Sound Absorbing Materials. Elsevier, New York.
25. Biot, M.A., (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range, II. Higher frequency range. J. Acoust. Soc. Amer., 28, 168-91.
26. Brown, R.J.S., (1980) Connection between formation factor for electrical resistivity and fluid-solid coupling factor in Biot's equations for acoustic waves in fluid-filled porous media. Geophysics, 45, 1269-75.
27. Carman, P.C., (1956) Flow of Gases Through Porous Media. Butterworths, London, 1956.
28. Craggs, A. and Hildebrandt, J.G. (1984) Effective densities and resistivities for acoustic propagation in narrow tubes. J. Sound Vib., 92, 321-31.
29. Craggs, A. and Hildebrandt, J.G. (1986) The normal incidence absorption coefficient of a matrix of narrow tubes with constant cross-section. J. Sound Vib., 105, 101-7.
30. Gray, D.E., ed., (1957) American Institute of Physics Handbook, McGraw-Hill, New York.
31. Hubner, K.H., (1974) The Finite Element Method for Engineers. Wiley-Interscience, New York.
32. Kergomard, J., (1981) Champ interne et champ externe des instruments `a vent, Thèse Université de Paris VI.
33. Kirchhoff, G., (1868) Uber der Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung. Annalen der Physik and Chemie, 134, 177-93.
34. Stinson, M.R., (1991) The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape. J. Acoust. Soc. Amer., 89, 550-8.
35. Tijdeman, H., (1975) On the propagation of sound waves in cylindrical tubes. J. Sound Vib., 39, 1-33.
36. Zienkiewicz, O.C., (1971) The Finite Element Method in Engineering Science. McGraw-Hill, London.
37. Zwikker, C. & Kosten, C.W. (1949) Sound Absorbing Materials. Elsevier, New York.
38. Atalla N., Sgard, F., Olny, X. and Panneton, R. (2001) Acoustic absorption of macro-perforated porous materials. J. Sound Vib. 243(4), 659-678.
39. Attenborough, K. (1982) Acoustical characteristics of porous materials. Phys. Rep., 82, 179-227.
40. Auriault, J. L. (1980) Dynamic behaviour of a porous medium saturated by a newtonian fluid, Int. J. Engn. Sci. 18, 775-785.
41. Auriault, J. L. (1983) Effective macroscopic decription for heat conduction in periodic composites. J. Heat Mass Transfer. 26, 861-869.
42. Auriault, J. L., Borne, L., and Chambon R. (1985) Dynamics of porous saturated media, checking of the generalized law of Darcy. J. Acoust. Soc. Amer. 77, 1641-1650.
43. Auriault, J. L. (1986) Mecanique des milieux poreux saturés déformables. Université P. Fourier, Grenoble, (France).
44. Auriault, J. L. (1991). Heterogeneous medium. Is an equivalent macroscopic description possible?. Int. J. Eng. Sci. 29, 785-795.
45. Auriault, J. L. & Boutin, C. (1994) Deformable media with double porosity-III: Acoustics. Transp. Porous Media 14, 143-162.
46. Auriault, J. L. (2005) Transport in Porous media: Upscaling by Multiscale Asymptotic Expansions. In CISM Lecture 480 Applied micromechanics of porous materials Udine 19-23 July 2004, Dormieux L. and Ulm F. J. eds, pp 3-56, Springer.
47. Ayrault, C., Moussatov, A., Castagnede, B. and Lafarge, D. (1999) Ultrasonic characterization of plastic foams via measurements with static pressure variations. Appl. Phys. Letters 74, 2009-2012.
48. Bensoussan, A., Lions, J. L. and Papanicolaou G. (1978) Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam.
49. Bies, D. A. and Hansen, C. H. (1980) Flow resistance information for acoustical design. Applied Acoustics, 13, 357-91.
50. Boutin, C., Royer, P. and Auriault, J. L. (1998) Acoustic absorption of porous surfacing with dual porosity. Int. J. Solids Struct. 35, 4709-4733.
51. Carcione J. M. and Quiroga-Goode, G. (1996) Full frequency-range transient solution for compressional waves in a fluid-saturated viscoelastic porous medium. Geophysical Prospecting, 44, 99-129.
52. Champoux, Y. and Allard, J. F. (1991) Dynamic tortuosity and bulk modulus in air-saturated porous media. J. Appl. Physics, 70, 1975-9.
53. Cortis, A., Smeulders, D. M. J., Guermond, J. L. and Lafarge, D. (2003) Influence of pore roughness on high-frequency permeability. Phys. Fluids 15, 1766-1775.
54. Debray, A., Allard, J. F., Lauriks, W. and Kelders, L. (1997) Acoustical measurement of the trapping constant of porous materials. Rev. Scient. Inst. 68, 4462-4465. There is a typographical error in the paper, Equationn 14 should be replaced by Z = i/φωlC0C1 [1-1/3/iφ/σω C0C1ω2l2].
55. Fellah, Z. E. A., Depollier, C., Berger, Lauriks, W., Trompette, P. and Chapelon, J. Y. (2003). Determination of transport parameters in air saturated porous media via ultrasonic reflected waves. J. Acoust. Soc. Amer., 114 (2003) 2561-2569.
56. Iwase, T., Yzumi, Y. and Kawabata, R. (1998) A new measuring method for sound propagation constant by using sound tube without any air space back of a test material. Internoise 98, Christchurch, New Zealand.
57. Johnson, D. L., Koplik, J. and Schwartz, L. M. (1986) New pore size parameter characterizing transport in porous media. Phys. Rev. Lett., 57, 2564-2567.
58. Johnson, D. L., Koplik, J. and Dashen, R. (1987) Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mechanics, 176, 379-402.
59. Joos, G. (1950) Theoretical Physics. Hafner Publishing Company, New York.
60. Keith-Wilson, D., Ostashev, V. D. and Collier S. L. (2004) Time-domain equations for sound propagation in rigid-frame porous media. J. Acoust. Soc. Amer., 116, 1889-1892.
61. Keller, J. B. (1977) Effective behaviour of heterogeneous media. In Landman U., ed., Statistical Mechanics and Statistical Methods in Theory and Application, Plenum, New York, pp 631-644.
62. Lafarge, D. (1993) Propagation du son dans les matériaux poreux `a structure rigide saturés par un fluide viscothermique: Définition de paramètres géométriques, analogie electromagnétique, temps de relaxation. Ph. D. Thesis, Université du Maine, Le Mans, France.
63. Lafarge, D., Lemarinier, P., Allard, J. F. and Tarnow, V. (1997) Dynamic compressibility of air in porous structures at audible frequencies. J. Acoust. Soc. Amer., 102, 1995-2006.
64. Lafarge, D. (2002), in Poromechanics II, Proceedings of the Second Biot Conference on Poromechanics, J. L. Auriault ed. (Swets & Zeilinger, Grenoble), pp 703-708.
65. Lafarge D. (2006) in Matériaux et Acoustique, I Propagation des Ondes Acoustiques, Bruneau M., Potel C. (ed.), Lavoisier, Paris.
66. Leclaire, Ph., Kelders, L., Lauriks, W., Melon, M., Brown, N. and Castagnède, B. (1996) Determination of the viscous and thermal characteristic lengths of plastic foams by ultrasonic measurements in helium and air. J. Appl. Phys. 80, 2009-2012.
67. Levy, T. (1979) Propagation of waves in a fluid saturated porous elastic solid. Int. J. Engn. Sci. 17, 1005-1014.
68. Norris, A. N. (1986) On the viscodynamic operator in Biot's equations of poroelasticity. J. Wave-Material Interaction 1, 365-380.
69. Olny, X. (1999) Acoustic absorption of porous media with single and double porosity-modelling and experimental solution. Ph.D. Thesis, ENTPE-INSA Lyon, 281 pp.
70. Olny, X., and Boutin, C. (2003) Acoustic wave propagation in double porosity media. J. Acoust. Soc. Amer. 114, 73-89.
71. Olny, X. and Panneton, R. (2008) Acoustical determination of the parameters governing thermal dissipation in porous media. J. Acoust. Soc. Amer. 123, 814-824.
72. Panneton, R. and Olny, X. (2006) Acoustical determination of the parameters governing viscous dissipation in porous media. J. Acoust. Soc. Amer. 119, 2027-2040.
73. Perrot, C. (2006) Microstructure et Macro-Comportement Acoustique: Approche par Reconstruction d'une Cellule Elementaire Representative. Ph. D. Thesis, Université de Sherbrooke (Canada) and INSA de Lyon (France).
74. Perrot, C., Panneton, R. and Olny X. (2007) Computation of the dynamic thermal dissipation properties of porous media by Brownian motion simulation: Application to an open-cell aluminum foam. J. of Applied Physics 102, 0749171-13.
75. Pride, S. R., Morgan, F. D.and Gangi, F. A. (1993) Drag forces of porous media acoustics. Physical Review B 47, 4964-4975.
76. Sanchez-Palencia, E. (1974). Comportement local et macroscopique d'un type de milieux physiques hétérogènes. Int. J. Eng. Sci., 12, 331-351.
77. Sanchez-Palencia, E. (1980). Nonhomogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer, Berlin.
78. Sgard, F., Olny, X., Atalla, N. and Castel F. (2005) On the use of perforations to improve the sound absorption of porous materials. Applied acoustics 66, 625-651.
79. Straley, C., Matteson, A., Feng S., Schwartz, L. M., Kenyon, W. E. and Banavar J. R. (1987) Magnetic resonance, digital image analysis, and permeability of porous media. Appl. Phys. Lett. 51, 1146-1148.
80. Tarnow, V. (1996) Airflow resistivity of models of fibrous acoustic materials. J. Acoust. Soc. Amer. 100(6), 3706-3713.
81. Tizianel, J., Allard, J. F., Castagnéde, B., Ayrault, C., Henry, M. and Gedeon, A. (1999) Transport parameters and sound propagation in an air-saturated sand. J. Appl. Phys. 86, 5829-5833.
82. Torquato, S. (1990) Relationship between permeability and diffusion-controlled trapping constant of porous media. Phys. Rev. Lett. 64, 2644-2646.
83. Utsuno, H., Tanaka T. and Fujikawa, T. (1989) Transfer function method for mesuring characteristic impedance and propagation constat of porous materials. J. Acoust. Soc. Amer. 86, 637-643.
84. Wilson, D. K. (1993) Relaxation-matched modeling of propagation through porous media, including fractal pore structure. J. Acoust. Soc. Amer. 94, 1136-1145.
85. Allard, J.F., Depollier, C., Guignouard, P. and Rebillard, P. (1991) Effect of a resonance of the frame on the surface impedance of glass wool of high density and stiffness. J. Acoust. Soc. Amer., 89, 999-1001.
86. Atalla N., Panneton, R. and Debergue, P. (1998) A mixed displacement pressure formulation for poroelastic materials. J. Acoust. Soc. Amer., 104, 1444-1452.
87. Beranek, L. (1947) Acoustical properties of homogeneous isotropic rigid tiles and flexible blankets. J. Acoust. Soc. Amer., 19, 556-68.
88. Biot, M.A. (1956) The theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. II. Higher frequency range. J. Acoust. Soc. Amer., 28, 168-91.
89. Biot, M.A. and Willis, D.G. (1957) The elastic coefficients of the theory of consolidation. J. Appl. Mechanics, 24, 594-601.
90. Biot, M.A. (1962) Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Amer., 34, 1254-1264.
91. Brown, R.J.S. and Korringa, J. (1975), On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics, 40, 608-16.
92. Cheng, A.H.D. (1997) Material coefficients of anisotropic poroelasticity. Int. J. Rock Mech. Min. Sci. 34, 199-205.
93. Dahl, M.D., Rice, E.J. and Groesbeck, D.E. (1990) Effects of fiber motion on the acoustical behaviour of an anisotropic, flexible fibrous material. J. Acoust. Soc. Amer., 87, 54-66.
94. Dazel, O., Brouard, B., Depollier., C. and Griffiths. S. (2007) An alternative Biot's displacement formulation for porous materials. J. Acoust. Soc. Amer., 121, 3509-3516.
95. Depollier, C., Allard, J.F. and Lauriks, W. (1988) Biot theory and stress-strain equations in porous sound absorbing materials. J. Acoust. Soc. Amer., 84, 2277-9.
96. Gorog S., Panneton, R. and Atalla, N. (1997) Mixed displacement-pressure formulation for acoustic anisotropic open porous media. J. Applied Physics, 82(9), 4192-4196.
97. Johnson, D.L. (1986) Recent developments in the acoustic properties of porous media. In Proc. Int. School of Physics Enrico Fermi, Course XCIII, ed. D. Sette. North Holland Publishing Co., Amsterdam, pp. 255-90.
98. Kanfoud, J., Hamdi, M.A., Becot F.-X. and Jaouen L. (2009) Development of an analytical solution of modified Biot's equations for the optimization of lightweight acoustic protection. J. Acoust. Soc. Amer., 125, 863-872
99. Kawasima, Y. (1960) Sound propagation in a fibre block as a composite medium. Acustica, 10, 208-17.
100. Korringa, J. (1981), On the Biot Gassmann equations for the elastic moduli of porous rocks. J. Acoust. Soc. Amer., 70, 1752-3.
101. Lambert, R.F. (1983) Propagation of sound in highly porous open-cell elastic foams. J. Acoust. Soc. Amer., 73, 1131-8.
102. Landau, L.D. and Lifshitz, E.M. (1959) Fluid Mechanics. Pergamon, New York.
103. Pilon, D., Panneton, R. and Sgard, F. (2003) Behavioral criterion quantifying the edge-constrained effects on foams in the standing wave tube. J. Acoust. Soc. Amer., 114(4), 1980-1987.
104. Pride, S.R., Berryman J.G. (1998) Connecting theory to experiment in poroelasticity. J. Mech. Phys. Solids, 46, 19-747.
105. Sides, D.J., Attenborough, K. and Mulholland, K.A. (1971) Application of a generalized acoustic propagation theory to fibrous absorbants. J. Sound Vib., 19, 49-64.
106. Zwikker, C. and Kosten, C.W. (1949) Sound Absorbing Materials. Elsevier, New York.
107. Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions. National Bureau of Standards, Washington D. C.
108. Allard, J.F. and Lauriks, W. (1997) Poles and zeros of the plane wave reflection coefficient for porous surfaces. Acta Acustica 83, 1045-1052.
109. Allard, J.F., Henry, M., Tizianel, J., Nicolas, J. and Miki, Y. (2002) Pole contribution to the field reflected by sand layers. J. Acoust. Soc. Amer. 111, 685-689.
110. Allard, J.F., Henry, M., Jansens, G. and Lauriks, W. (2003a) Impedance measurement around grazing incidence for nonlocally reacting thin porous layers, J. Acoust. Soc. Amer. 113, 1210-1215.
111. Allard, J.F., Gareton, V., Henry, M., Jansens, G. and Lauriks, W. (2003b) Impedance evaluation from pressure measurements near grazing incidence for nonlocally reacting porous layers. Acta Acustica 89, 595-603.
112. Allard, J.F., Henry, M. and Gareton V. (2004) Pseudo-surface waves above thin porous layers. J. Acoust. Soc. Amer. 116, 1345-1347.
113. Allard, J.F. and Henry, M. (2006) Fluid-fluid interface and equivalent impedance plane. Wave Motion 43, 232-240.
114. Baños, A. (1966) Dipole Radiation in the Presence of a Conducting Haf-Space. Pergamon Press, New York.
115. Brekhovskikh, L.M. (1960) Waves in Layered Media. Academic, New York.
116. Brekhovskikh, L.M. and Godin, O.A. (1992) Acoustic of Layered Media II, Point Source and Bounded Beams. Springer Series on Waves Phenomena, Springer, New York.
117. Brouard, B. (1994) Validation par holographie acoustique de nouveaux modèles pour la propagation des ondes dans les materiaux poreux stratifiés. Ph.D. Thesis, Université du Maine, Le Mans.
118. Brouard, B., Lafarge, D., Allard, J.F. and Tamura, M. (1996) Measurement and prediction of the reflection coefficient of porous layers at oblique incidence and for inhomogeneous waves. J. Acoust. Soc. Amer. 99, 100-107.
119. Chien, C.F. and Soroka, W.W. (1975) Sound propagation along an impedance plane. J. Sound Vib. 43, 9-20.
120. Collin, R.E. (1960) Field Theory of Guided Waves. McGraw-Hill, New York.
121. Hickey, C., Leary, D. and Allard, J.F. (2005) Impedance and Brewster angle measurement for thick porous layers, J. Acoust. Soc. Amer. 118, 1503-509.
122. Lauriks, W., Kelders, L. and Allard, J.F. (1998) Poles and zeros of the reflection coefficient of a porous layer having a motionless frame in contact with air. Wave Motion 28, 59-67.
123. Li, K.M., Waters-Fuller, T. and Attenborough, K. (1998) Sound propagation from a point source over extended reaction ground. J. Acoust. Soc. Amer. 104, 679-685.
124. Nicolas, J., Berry, J.F. and Daigle, G. (1985) Propagation of sound above a layer of snow. J. Acoust. Soc. Am. 77, 67-73.
125. Tamura, M. (1990) Spatial Fourier transform method of measuring reflection coefficient at oblique incidence. J. Acoust. Soc. Amer. 88, 2259-2264.
126. Wait, J.R. (1970) Electromagnetic Waves in Stratified Media. Pergamon Press, New York.
127. Abramowitz, M. and Stegun, I.A. (1972) Handbook of Mathematical Functions. National Bureau of Standards, Washington D. C.
128. Allard, J.F., Jansens, G., Vermeir, G. and Lauriks, W. (2002) Frame-borne surface wave in air-saturated porous media. J. Acoust. Soc. Amer. 111, 690-696.
129. Allard, J.F., Henry, M., Glorieux, C., Lauriks, W. and Petillon, S. (2004) Laser induced surface modes at water-elastic and poroelastic solid interfaces, J. Appl. Phys. 95, 528-535.
130. Allard, J.F., Brouard, B., Atalla, N. and Ginet, S. (2007) Excitation of soft porous frame resonances and evaluation of rigidity coefficients. J. Acoust. Soc. Amer. 121, 78-84.
131. Boeckx, L., Leclaire, P., Khurana, P., Glorieux, C., Lauriks,W. and Allard, J.F. (2005) Investigation of the phase velocity of guided acoustic waves in soft porous layers. J. Acoust. Soc. Amer. 117, 545-554.
132. Feng, S. and Johnson, D.L. (1983) High-frequency acoustic properties of a fluid/porous solid interface. I. New surface mode. II. The 2D Green's function. J. Acoust. Soc. Amer. 74, 906-924.
133. Geebelen., N., Boeckx, L., Vermeir, G., Lauriks, W., Allard, J.F. and Dazel, O. (2007) Measurement of the rigidity coefficients of a melamine foam. Acta Acustica 93, 783-788.
134. Geebelen N., Boeckx, L., Vermeir, G., Lauriks, W., Allard, J.F. and Dazel, O. (2008), Near field Rayleigh wave on soft porous layers. J. Acoust. Soc. Amer. 123, 1241-1247.
135. Langlois, C., Panneton, R. and Atalla, N. (2001) Polynomial relations for quasi-static mechanical characterization of poroelastic materials. J. Acoust. Soc. Amer., 109(6), 3032-3040.
136. Melon, M., Mariez, M., Ayrault, C. and Sahraoui, S. (1998) Acoustical and mechanical characterization of anisotropic open-cell foams. J. Acoust. Soc. Amer. 104, 2622-2627.
137. Park, J. (2005) Measurement of the frame acoustic properties of porous and granular materials. J. Acoust. Soc. Amer. 118, 3483-3490.
138. Pritz, T. (1986) Frequency dependence of frame dynamic characteristics of mineral and glass wool materials. J. Sound Vib. 106, 161-169.
139. Pritz, T. (1994) Dynamic Young's modulus and loss factor of plastic foams for impact sound isolation. J. Sound Vib. 178, 315-322.
140. Sfaoui, A. (1995a) On the viscosity of the polyurethane foam. J. Acoust. Soc. Amer. 97, 1046-1052.
141. Sfaoui, A. (1995b), Erratum: On the viscosity of the polyurethane foam. J. Acoust. Soc. Amer. 98, 665.
142. Tarnow, V. (2005) Dynamic measurements of the elastic constants of glass wool. J. Acoust. Soc. Amer. 118, 3672-3678.
143. Victorov, I.A. (1967) Rayleigh and Lamb Waves. Plenum, New York.
144. Bolt, R.H. (1947) On the design of perforated facings for acoustic materials. J. Acoust. Soc. Amer., 19, 917-21.
145. Brillouin, J. (1949) Théorie de l'absorption du son par les structures `a panneaux perforés. Cahiers du Centre Scientifique et Technique du B̂atiment, 31, 1-15.
146. Byrne, K.P. (1980) Calculation of the specific normal impedance of perforated facing-porous backing constructions. Applied Acoustics, 13, 43-55.
147. Callaway, D.B. and Ramer, L.G. (1952) The use of perforated facings in designing low frequency resonant absorbers. J. Acoust. Soc. Amer., 24, 309-12.
148. Collin, B. (1960) Field Theory of Guided Waves, McGraw-Hill, New York
149. Davern, W.A. (1977) Perforated facings backed with porous materials as sound absorbers-An experimental study. Applied Acoustics, 10, 85-112.
150. Guignouard, P., Meisser, M., Allard, J.F., Rebillard, P. and Depollier, C. (1991) Prediction and measurement of the acoustical impedance and absorption coefficient at oblique incidence of porous layers with perforated facings. Noise Control Eng. J., 36, 129-35.
151. Ingard, U. (1953) On the theory and design of acoustic resonators. J. Acoust. Soc. Amer., 25, 1037-61.
152. Ingard, U. (1954) Perforated facing and sound absorption. J. Acoust. Soc. Amer., 26, 151-4.
153. Ingard, U. (1968) Absorption characteristics of non linear acoustic resonators. J. Acoust. Soc. Amer., 44, 1155-6.
154. Ingard, U. (1970) Non linear distorsion of sound transmitted through an orifice. J. Acoust. Soc. Amer., 48, 32-3.
155. Ingard, U. and Bolt, R.H. (1951) Absorption characteristics of acoustic material with perforated facing. J. Acoust. Soc. Amer., 23, 533-40.
156. Ingard, U. and Ising, H. (1967) Acoustic nonlinearity of an orifice. J. Acoust. Soc. Amer., 42, 6-17.
157. Ingard, U. and Labate, S. (1950) Acoustic circulation effects and the non linear impedance of orifices. J. Acoust. Soc. Amer., 22, 211-18.
158. Nielsen, A.K. (1949) Trans Danish Acad. Tech. Sci. No. 10.
159. Norris, A.N. and Sheng, I.C. (1989) Acoustic radiation from a circular pipe with infinite flange. J. Sound Vib., 135, 85-93.
160. Rayleigh, J.W.S. (1940) Theory of Sound. MacMillan, London, Vol. II, p. 318.
161. Velizhanina, K.A. (1968) Design calculation of sound absorbers comprising a porous material with a perforated facing. Soviet Physics-Acoustics, 14, 37-41.
162. Zwikker, C. and Kosten, C.W. (1949) Sound Absorbing Materials. Elsevier, New York.
163. Biot, M. A. (1962) Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Amer. 34, 1254-1264.
164. Castagnede, B., Aknine, A., Melon, M. and Depollier, C. (1998) Ultrasonic characterization of the anisotropic behavior of air-saturated porous materials. Ultrasonics 36, 323-343.
165. Cheng, A. H. D. (1997) Material coefficients of anisotropic poroelasticity. Int. J. Rock Mech. Min. Sci. 34, 199-205.
166. Khurana, P., Boeckx L., Lauriks, W., Leclaire, P., Dazel, O. and Allard, J. F. (2009) A description of transversely isotropic sound absorbing porous materials by transfer matrices J. Acoust. Soc. Amer. 125, 915-921.
167. Liu, K. and Liu, Y. (2004) Propagation characteristic of Rayleigh waves in orthotropic fluidsaturated porous media. J. Sound Vib. 271, 1-13.
168. Melon, M., Mariez, E., Ayrault, C. and Sahraoui, S. (1998) Acoustical and mechanical characterization of anisotropic open-cell foams. J. Acoust. Soc. Amer 104, 2622-2627.
169. Royer, D. and Dieulesaint, E. (1996) Ondes Elastiques dans les Solides, Tome 1, Masson, Paris.
170. Sanchez-Palencia, E. (1980) Non-homogeneous Media and Vibration Theory. Springer-Verlag (1980) p.151.
171. Sharma, M. D. and Gogna, M. L. (1991) Wave propagation in anisotropic liquid-saturated porous solids. J. Acoust. Soc. Amer 90, 1068-1073.
172. Tarnow, V. (2005) Dynamic measurements of the elastic constants of glass wool. J. Acoust. Soc. Amer 118, 3672-3678.
173. Vashishth, A., K. and Khurana, P. (2004) Waves in stratified anisotropic poroelastic media: a transfer matrix approach. J. Sound Vib. 277, 239-275.
174. Allard, J.F., Champoux, Y. and Depollier, C. (1987) Modelization of layered sound absorbing materials with transfer matrices. J. Acoust. Soc. Amer. 82, 1792-6.
175. Allard, J.F. (1993) Propagation of sound in Porous media. Modeling sound absorbing materials. Chapter 11, Elsevier Applied Science, London.
176. Atalla, N. and Sgard, F. (2007) Modeling of perforated plates and screens using rigid frame porous models. J. Sound Vib. 303(1-2), 195-208.
177. Beranek, L.L. (1947) Acoustical properties of homogeneous isotropic rigid tiles and flexible blankets. J. Acoust. Soc. Amer. 19, 556-68.
178. Bolton, J.S. (1987) Optimal use of noise control foams. J. Acoust. Soc. Amer. 82, suppl. 1, 10.
179. Brekhovskikh, L.M. (1960) Waves in Layered Media. Academic Press, New York.
180. Brouard B., Lafarge, D. and Allard, J.F. (1994) Measurement and prediction of the surface impedance of a resonant sound absorbing structure. Acta Acustica 2, 301-306.
181. Brouard, B., Lafarge, D. and Allard, J.F. (1995) A general method of modeling sound propagation in layered media. J. Sound Vib. 183 (1), 129-142
182. Depollier, C. (1989) Théorie de Biot et prédiction des propriétés acoustiques des matériaux poreux. Propagation dans les milieux acoustiques désordonnés. Thesis, Université du Maine, France.
183. Doutres O., Dauchez, N., Geneveaux, J.M. and Dazel, O. (2007) Validity of the limp model for porous materials: A creterion based on Biot theory. J. Acoust. Soc. Amer. 122(4), 2038-2048.
184. Folds, D. and Loggins, C.D. (1977) Transmission and reflection of ultrasonic waves in layered media. J. Acoust. Soc. Amer. 62, 1102-9.
185. Ingard K.U. (1994) Notes on Sound Absorption Technology. Noise Control Foundation. Arlington Branch Poughkeepsie, NY
186. Katragadda, S., Lai, H.Y. and Bolton, J.S. (1995) A model for sound absorption by and sound transmission through limp fibrous layers. J. Acoust. Soc. Amer. 98, 2977.
187. Lauriks, W. (1989) Onderzoek van de akoestische eigenschappen van gelaagde poreuze materialen. Thesis, Katholieke Universiteit Leuven, Belgium.
188. Lauriks, W., Cops, A., Allard, J.F., Depollier, C. and Rebillard, P. (1990) Modelization at oblique incidence of layered porous materials with impervious screens. J. Acoust. Soc. Amer. 87, 1200-6.
189. Mulholland, K.A., Parbroo, H.D., and Cummings, A. (1967) The transmission loss of double panels, J. Sound Vib., 6, 324-34.
190. Panneton, R. (2007) Comments on the limp frame equivalent fluid model for porous media, J. Acoust. Soc. Amer. 122(6), EL217-222.
191. Roland, J. and Guilbert, G. (1990) L'amélioration acoustique d'un produit du b̂atiment. CSTB Magazine 33, 11-12.
192. Rebillard, P. et al., (1992) The effect of a porous facing on the impedance and the absorption coefficient of a layer of porous material. J. Sound Vib. 156, 541-55.
193. Shiau, J.M., Bolton, J.S. and Ufford, D.A. (1988) Random incidence sound transmission through foam-lined panels. J. Acoust. Soc. Amer 84, suppl. 1, 96
194. Scharnhorst, K.P. (1983) Properties of acoustic and electromagnetic transmission coefficients and transfer matrices of multilayered plates. J. Acoust. Soc. Amer., 74, 1883-6.
195. Utsuno H., Tanaka T. and Fujikawa T. (1989) Transfer function method for measuring characteristic impedance and propagation constant of porous materials. J. Acoust. Soc. Amer. 86, 637-643.
196. Zwikker, C. and Kosten, C.W. (1949) Sound Absorbing Materials. Elsevier, New York.
197. Atalla, N., Ghinet, S. and Haisam, O. (2004) Transmission loss of curved sandwich composite panels. 18th ICA, Kyoto.
198. Duval, A., Dejaeger, L., Baratier, J. and Rondeau, J-F (2008) Structureborne and airborne Insertion Loss simulation of trimmed curved and flat panels using Rayon-VTM-TL: implications for the 3D design of insulators. Automobile and Railroad Comfort-November 19-20, Le Mans, France.
199. Ghinet, S. and Atalla, N. (2002) Vibro-acoustic behaviour of multi-layer orthotropic panels. Canadian Acoustics 30(3) 72-73.
200. Ghinet, S. and Atalla, N. (2006) Vibro-acoustic behaviours of flat sandwich composite panels. Transactions of Canadian Soc. Mech. Eng J. 30(4).
201. Leppington, F.G., Broadbent, E.G., & Heron, K.H. (1982) The acoustic radiation efficiency from rectangular panels. Proc. R. Soc. London. 382, 245.
202. Leppington, F. G, Heron, K. H. & Broadbent, E. G. (2002) Resonant and non-resonant noise through complex plates. Proc. R. Soc. Lond. 458, 683-704.
203. Nelisse, H., Onsay, T. and Atalla, N. (2003) Structure borne insertion loss of sound package components. Society of Automotive Engineers, SAE paper 03NVC-185, Traverse City, Michigan.
204. Pope, L.D., Wilby, E.G., Willis, C.M. and Mayes, W.H. (1983) Aircraft Interior Noise Models: Sidewall trim, stiffened structures, and Cabin Acoustics with floor partition. J. Sound Vib. 89(3), 371-417.
205. Thomasson, S. I. (1980) On the absorption coefficient. Acustica 44, 265-273.
206. Villot, M., Guigou, C. and Gagliardini, L. (2001) Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures. J. Sound Vib., 245 (3), 433-455.
207. Anciant, M., Mebarek, L., Zhang, C. and Monet-Descombey, J. (2006) Full trimmed vehicle simulation by using Rayon-VTM. JSAE.
208. Atalla N., Panneton, R. and Debergue, P. (1998) A mixed displacement pressure formulation for poroelastic materials. J. Acoust. Soc. Amer. 104, 1444-1452.
209. Atalla N., Hamdi, M.A. and Panneton, R. (2001a) Enhanced weak integral formulation for the mixed (u,p) poroelastic equations. J. Acoust. Soc. Am. 109(6), 3065-3068.
210. Atalla N., Sgard, F., Olny, X. and Panneton, R. (2001b) Acoustic absorption of macro-perforated porous materials. J. Sound Vib. 243(4), 659-678.
211. Atalla, N., Amedin, C.K., Atalla, Y., Sgard, F. and Osman, H. (2003) Numerical modeling and experimental investigation of the absorption and transmission loss of heterogeneous porous materials. Proceedings of 10 th International congress on Sound and Vibration, ICSV12, pp 4673-4680.
212. Atalla, N., Sgard, F. and Amedin, C.K. (2006) On the modeling of sound radiation from poroelastic materials. J. Acoust. Soc. Amer. 120(4), 1990-1995.
213. Beranek, I.I. and Vér, I.L. (1992) Noise and Vibration Control Engineering. Principles and Application. John Wiley & Sons, New York.
214. Castel, F. (2005) Modélisation numérique de matériaux poreux hétérogènes. Application `a l'absorption' basse fréquence. Phd thesis, Université de Sherbrooke, Canada.
215. Chung, J.Y and Blaser, D.A. (1980) Transfer function method of measuring in-duct acoustic properties. J. Acoust. Soc. Amer. 68(3), 907-913.
216. Coyette, J. and Pelerin, Y. (1994) A generalized procedure for modeling multi-layer insulation Systems. Proceedings of 19th International Seminar on Modal Analysis, 1189-1199.
217. Coyette, J.P. and Wynendaele, H. (1995) A finite element model for predicting the acoustic transmission characteristics of layered structures. Proceedings of INTER-NOISE 95, 1279-1282.
218. Craggs, A. (1978) A finite element model for rigid porous absorbing materials. J. Sound Vib. 61, 101-111.
219. Dauchez, N., Sahraoui, S. and Atalla, N. (2001) Convergence of poroelastic finite elements based on Biot displacement formulation. J. Acoust. Soc. Amer. 109(1), 33-40.
220. Dauchez, N., Sahraoui, S. and Atalla, N. (2002) Dissipation mechanisms in a porous layer bonded onto a plate. J. Sound Vib. 265, 437-449.
221. Dazel, O., Sgard, F., Lamarque, C.-H. and Atalla, N. (2002) An extension of complex modes for the resolution of finite-element poroelastic problems. J. Sound and Vib. 253(2), 421-445.
222. Dazel O. (2005) Synthèse modale pour les matériaux poreux. PhD Thesis, INSA de Lyon.
223. Dazel, O., Sgard, F., Beckot, F-X. and Atalla, N. (2008) Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations, J. Acoust. Soc. Amer. 123(4), 2054-2063.
224. Debergue P, Panneton, R. and Atalla, N. (1999) Boundary conditions for the weak formulation of of the mixed (u,p) poroelasticity problem. J. Acoust. Soc. Amer. 106(5), 2383-2390.
225. Duval, A., Baratier, J., Morgenstern, C., Dejaeger, L., Kobayashi, N. and Yamaoka, H. (2008) Trim FEM simulation of a dash and floor insulator cut out modules with structureborne and airborne excitations. Acoustics 08, Joint ASA, SFA and Euronoise Meeting, Paris.
226. Göransson, P. (1998) A 3-D symmetric finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium. Int. J. Num. Meth. 41, 67-192.
227. Hamdi, M.A, Atalla, N., Mebarek, L. and Omrani, A. (2000) Novel mixed finite element formulation for the analysis of sound absorption by porous materials. Proceedings of 29th International Congress and Exhibition on Noise Control Engineering, InterNoise, Nice, France.
228. Hörlin, N.E, Nordström, M and Göransson, P. (2001) A 3-D hierarchical FE formulation of Biot's equations for elastoacoutsic modeling of porous media. J. Sound Vib. 254(4), 633-652.
229. Hörlin, N.E. (2004) Hierarchical finite element modeling of Biot's equations for vibro-acoustic modeling of layered poroelastic media. PhD Thesis, KTH Royal Institute of Technology, Stockholm, Sweden.
230. Horoshenkov, K.V. and Sakagami, K. (2000) A method to calculate the acoustic response of a thin, baffled, simply supported poroelastic plate. J Acoust. Soc. Amer. 110(2), 904-917.
231. Jaouen, L., Brouard, B., Atalla, N. and Langlois, C. (2005) A simplified numerical model for a plate backed by a thin foam layer in the low frequency range. J. Sound Vib. 280(3-5), 681-698.
232. Johansen, T.F., Allard, J.F. and Brouard, B. (1995) Finite element method for predicting the acoustical properties of porous samples. Acta Acustica 3, 487-491.
233. Kang, Y.J. and Bolton, J.S. (1995) Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements. J. Acoust. Soc. Amer. 98, 635-643.
234. Kang, Y., Gardner, B. and Bolton, J. (1999) An axisymmetric poroelastic finite element formulation. J. Acoust. Soc. Amer., 106(2), 565-574.
235. Langlois C., Panneton R. and Atalla N. Polynomial relations for quasi-static mechanical characterization of isotropic poroelastic materials. J. Acoust. Soc. Amer. 110(6), 3032-3040.
236. Langlois, C. (2003) Modélisation des problèmes vibroacoustiques de basses fréquences par elements finis, MSc Thesis, Université de Sherbrooke, Canada.
237. Leroy, P. (2008) Les mousses adaptatives pour l'amélioration de l'absorption acoustique: modélisation, mise en oeuvre, mécanismes de contr̂ole. PhD Thesis, Universite de Sherbrooke.
238. Omrani, A., Mebarek, L. and Hamdi, M.A. (2006) Transmission loss modeling of trimmed vehicle components, Proceedings of ISMA 2006, Leuven, Belgium.
239. Olny, X. and Boutin, C. (2003) Acoustic wave propagation in double porosity media, J. Acoust. Soc. Amer. 114, 73-89.
240. Panneton, R., Atalla, N. and Charron, F. (1995) A finite element formulation for the vibro-acoustic behaviour of double plate structures with cavity absorption. Can. Aero. Space J. 41, 5-12.
241. Panneton, R. (1996) Modélisation numérique par éléments finis des structures complexes absorbantes. PhD Thesis, Université de Sherbrooke, Québec, Canada.
242. Panneton, R. and Atalla, N. (1996) Numerical prediction of sound transmission through multilayer systems with isotropic poroelastic materials. J. Acoust. Soc.Amer. 100(1), 346-354.
243. Panneton, R. and Atalla, N. (1997) An efficient finite element scheme for solving the three-dimensional poroelasticity problem in acoustics. J. Acoust. Soc. Amer. 101(6), 3287-3298.
244. Pilon, D., (2003) Modélisation axisymétrique de la formulation {u, P} pour l'étude de l'influence des conditions aux limites d'échantillons poreux sur leur caractérisation: application au tube de Kundt et au rigidimètre. MSc Thesis, Université de Sherbrooke, Canada.
245. Rigobert, S. (2001) Modélisation par éléments finis des systèmes élasto-poro-acoustiques couplées: éléments hiérarchiques, maillages incompatibles, modèles simplifiés. PhD Thesis, Université de Sherbrooke, Canada.
246. Rigobert, S., Atalla, N. and Sgard, F. (2003) Investigation of the convergence of the mixed displacement pressure formulation for three-dimensional poroelastic materials using hierarchical elements. J. Acoust. Soc. Amer. 114(5), 2607-2617.
247. Sgard F., Atalla, N. and Panneton, R. (1997) A modal reduction technique for the finite-element formulation of Biot's poroelasticity equations in acoustics. 134th ASA Meeting, San Diego.
248. Sgard F., Atalla, N. and Nicolas, J. (2000) A numerical model for the low-frequency diffuse field sound transmission loss of double-wall sound barriers with elastic porous lining. J. Acoust. Soc. Amer. 108(6), 2865-2872.
249. Sgard, F. (2002) Modélisation par éléments finis des structures multi-couches complexes dans le domaine des basses Fréquences. HDR Thesis, Université Claude Bernard Lyon I-INSA de Lyon, France.
250. Sgard, F., Olny, X., Atalla, N. and Castel, F. (2005) On the use of perforations to improve the sound absorption of porous materials. Applied acoustics 66, 625-651.
251. Sgard, F., Atalla, N. and Amedin, C.K., (2007) Vibro-acoustic behavior of a cavity backed by a plate coated with a meso-heterogeneous porous material. Acta Acustica 93(1), 106-114.
252. Takahashi, D. & and M. Tanaka, M. (2002) Flexural vibration of perforated plates and porous elastic materials under acoustic loading. J. Acoust. Soc. Amer. 112, 1456-1464.