M. Abramowitz and I. A. , Stegun : Handbook of mathematical functions with formulas, graphs, and mathematical tables. Courier Corporation, 1964.

A. Bendali and M. Fares, Boundary Integral Equations Methods in Acoustic Scattering, Magoulès, éd. : Computational Methods for Acoustics Problems, pp.1-36, 2007.
DOI : 10.4203/csets.18.1

URL : https://hal.archives-ouvertes.fr/hal-00952225

A. Bendali, M. Fares, E. Piot, and S. Tordeux, Mathematical Justification of the Rayleigh Conductivity Model for Perforated Plates in Acoustics, SIAM Journal on Applied Mathematics, vol.73, issue.1, pp.438-459, 2013.
DOI : 10.1137/120867123

URL : https://hal.archives-ouvertes.fr/hal-00860712

H. Bodén, One-sided multi-port techniques for characterisation of in-duct samples with nonlinear acoustic properties, Journal of Sound and Vibration, vol.331, issue.13, pp.3050-3067, 2012.
DOI : 10.1016/j.jsv.2012.02.013

G. Boyer, Etude de stabilité et simulation numérique de l'écoulement interne des moteurs à propergol solide simplifiés, Thèse de doctorat, 2012.

M. Bruneau, Manuel d'acoustique fondamentale, Hermes, 1998.

P. F. Byrd and M. D. Friedman, Handbook of elliptic integrals for engineers and scientists, 1971.
DOI : 10.1007/978-3-642-65138-0

E. Copson, On the problem of the electrified disc, Proc. Edinburgh Math. Soc, pp.14-19, 1947.
DOI : 10.1017/S0013091500027644

I. B. Crandall, Theory of Vibration System and Sound, 1926.

A. Cummings and I. Chang, The transmission of intense transient and multiple frequency sound waves through orifice plates with mean fluid flow, Revue de Physique Appliqu??e, vol.21, issue.2, pp.151-161, 1986.
DOI : 10.1051/rphysap:01986002102015100

URL : https://hal.archives-ouvertes.fr/jpa-00245420

X. Dai, X. Jing, and X. Sun, Discrete vortex model of a Helmholtz resonator subjected to high-intensity sound and grazing flow, The Journal of the Acoustical Society of America, vol.132, issue.5, pp.2988-2996, 2012.
DOI : 10.1121/1.4757736

M. Dauge and S. Tordeux, Vial : Selfsimilar perturbation near a corner : matching versus multiscale expansions for a model problem, Around the Research of Vladimir Maz'ya II, pp.95-134, 2010.

J. D. Eldredge, D. J. Bodony, and M. Shoeybi, Numerical Investigation of the Acoustic Behavior of a Multi-Perforated Liner, 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), pp.2007-3683, 2007.
DOI : 10.2514/6.2007-3683

C. Heuwinkel, A. Fischer, I. Rohle, L. Enghardt, F. Bake et al., Characterization of a Perforated Liner by Acoustic and Optical Measurements, 16th AIAA/CEAS Aeroacoustics Conference, 2010.
DOI : 10.2514/6.2010-3765

M. S. Howe, On the Theory of Unsteady High Reynolds Number Flow Through a Circular Aperture, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.366, issue.1725, pp.205-223, 1725.
DOI : 10.1098/rspa.1979.0048

M. S. Howe, Acoustics of Fluid-Structure Interactions, 1998.

I. J. Hughes and A. P. Dowling, The absorption of sound by perforated linings, Journal of Fluid Mechanics, vol.22, issue.-1, pp.299-335, 1990.
DOI : 10.1017/S0022112088002216

U. Ingard, On the Theory and Design of Acoustic Resonators, The Journal of the Acoustical Society of America, vol.25, issue.6, pp.1037-1061, 1953.
DOI : 10.1121/1.1907235

C. Ji and D. Zhao, Lattice Boltzmann investigation of acoustic damping mechanism and performance of an in-duct circular orifice, The Journal of the Acoustical Society of America, vol.135, issue.6, pp.3243-3251, 2014.
DOI : 10.1121/1.4876376

X. Jing, Effect of Plate Thickness on Impedance of Perforated Plates with Bias Flow, AIAA Journal, vol.38, issue.9, pp.1573-1578, 2000.
DOI : 10.2514/2.1139

G. Jourdain and L. Eriksson, Numerical Validation of a Time Domain Perforated Plate Model with Nonlinear and Inertial Effects, Journal of Computational Acoustics, vol.22, issue.04, pp.22-2014
DOI : 10.1142/S0218396X1450009X

S. Kabanikhin, V. Popie, and M. Shishlenin, Tordeux : Determination of the impedance of a multiperforated plate : an inverse problem, the Fifth International Scientific Conference and Young Scientists School "Theory and Computational Methods for Inverse and Ill-posed Problems, 2013.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics de Course of theoretical physics, 1987.

S. Laurens, E. Piot, A. Bendali, M. Fares, and S. Tordeux, Effective conditions for the reflection of an acoustic wave by low-porosity perforated plates, Journal of Fluid Mechanics, vol.115, pp.448-480, 2014.
DOI : 10.1016/j.jcp.2009.03.026

URL : https://hal.archives-ouvertes.fr/hal-00769393

S. Laurens, S. Tordeux, A. Bendali, M. Fares, and P. R. Kotiuga, Lower and upper bounds for the Rayleigh conductivity of a perforated plate, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.6, pp.471691-1712, 2013.
DOI : 10.1051/m2an/2013082

URL : https://hal.archives-ouvertes.fr/hal-00686438

F. G. Leppington and H. Levine, Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures, Journal of Fluid Mechanics, vol.8, issue.01, pp.61109-127, 1973.
DOI : 10.1017/S0022112073000601

T. Luong, M. S. Howe, and R. S. Mcgowan, On the Rayleigh conductivity of a bias-flow aperture, Journal of Fluids and Structures, vol.21, issue.8, pp.769-778, 2005.
DOI : 10.1016/j.jfluidstructs.2005.09.010

V. Mattesi, Small heterogeneities in the context of time-domain wave propagation equation : asymptotic analysis and numerical calculation, Thèse de doctorat, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01111046

T. H. Melling, The acoustic impendance of perforates at medium and high sound pressure levels, Journal of Sound and Vibration, vol.29, issue.1, pp.1-65, 1973.
DOI : 10.1016/S0022-460X(73)80125-7

S. Mendez and J. D. Eldredge, Acoustic modeling of perforated plates with bias flow for Large-Eddy Simulations, Journal of Computational Physics, vol.228, issue.13, pp.4757-4772, 2009.
DOI : 10.1016/j.jcp.2009.03.026

A. Minotti, F. Simon, and F. Gantié, Characterization of an acoustic liner by means of Laser Doppler Velocimetry in a subsonic flow, Aerospace Science and Technology, vol.12, issue.5, pp.398-407, 2008.
DOI : 10.1016/j.ast.2007.09.007

A. Most, Etude numérique et expérimentale des écoulements pariétaux avec transfert de masse à travers une paroi multi-perforée, Thèse de doctorat, 2007.

J. Nédélec, Acoustic and electromagnetic equations : integral representations for harmonic problems, 2001.

A. Nielsen, Acoustic resonators of circular cross-section and with axial symmetry. Akad, 1949.

H. Parisot-dupuis, F. Simon, E. Piot, and F. Micheli, Non-intrusive planar velocity-based nearfield acoustic holography in moving fluid medium, The Journal of the Acoustical Society of America, vol.133, issue.6, pp.4087-4097, 2013.
DOI : 10.1121/1.4802643

E. Piot, F. Micheli, and J. Breil, Mesure de vitesse acoustique de part et d'autre d'une plaque multi-perforée, avec écoulement transversant. Essais pour l'ANR acoustique et paroi multi-perforée, 2011.

E. Piot, F. Micheli, and F. Simon, Méthodes de mesure optique appliquées à la caractérisation d'absorbants acoustiques en écoulement, 2010.

E. Piot, F. Micheli, F. Simon, and J. Breil, Mesure de vitesse acoustique de part et d'autre d'une plaque multi-perforée, sans écoulement. Essais pour l'ANR acoustique et paroi multi-perforée. Rap. tech, 2010.

V. Popie, E. Piot, F. Simon, and S. Tordeux, Impedance eduction of perforated plates at low strouhal numbers and high bias flow mach number, Proceedings of the 21st AIAA/CEAS Aeroacoustics Conference, p.3275, 2015.

V. Popie, E. Piot, S. Tordeux, and F. Vuillot, Theoretical and Numerical Investigations of Acoustic Response of a Multiperforated Plate for Combustor Liners, Volume 4A: Combustion, Fuels and Emissions, 2015.
DOI : 10.1115/GT2015-42922

J. Primus, Détermination de l'impédance acoustique de matériaux absorbants en écoulement par méthode inverse et mesures LDV, Thèse de doctorat, 2012.

J. Primus, E. Piot, and F. Simon, An adjoint-based method for liner impedance eduction: Validation and numerical investigation, Journal of Sound and Vibration, vol.332, issue.1, 2012.
DOI : 10.1016/j.jsv.2012.07.051

J. Primus, E. Piot, F. Simon, M. G. Jones, and W. R. Watson, ONERA-NASA cooperative effort on liner impedance eduction, 19th AIAA/CEAS Aeroacoustics Conference, 2013.
DOI : 10.2514/6.2013-2273

S. W. Rienstra, Hirschberg : An introduction to acoustics, 2004.

J. Roche, Simulation numérique de l'absorption acoustique de matériaux résonants en présence d'écoulement, Thèse de doctorat, 2011.

J. Roche, L. Leylekian, G. Delattre, and F. Vuillot, Aircraft Fan Noise Absorption: DNS of the Acoustic Dissipation of Resonant Liners, 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), pp.2009-3146, 2009.
DOI : 10.2514/6.2009-3146

J. Roche, F. Vuillot, L. Leylekian, G. Delattre, F. Simon et al., Numerical and Experimental Study of Resonant Liners Aeroacoustic Absorption Under Grazing Flow, 16th AIAA/CEAS Aeroacoustics Conference, pp.2010-3767, 2010.
DOI : 10.2514/6.2010-3767

J. Sanchez-hubert and E. Sanchez-palencia, Acoustic fluid flow through holes and permeability of perforated walls, Journal of Mathematical Analysis and Applications, vol.87, issue.2, pp.427-453, 1982.
DOI : 10.1016/0022-247X(82)90133-0

S. A. Sauter and C. Schwab, Boundary element methods, 2011.

A. Scarpato, S. Ducruix, and T. Schuller, Optimal and off-design operations of acoustic dampers using perforated plates backed by a cavity, Journal of Sound and Vibration, vol.332, issue.20, pp.4856-4875, 2013.
DOI : 10.1016/j.jsv.2013.03.030

K. Schmidt, A. Thöns-zueva, and P. Joly, High-order asymptotic expansion for the acoustics in viscous gases close to rigid walls, Mathematical Models and Methods in Applied Sciences, vol.24, issue.09, pp.1823-1855, 2014.
DOI : 10.1142/S0218202514500080

URL : https://hal.archives-ouvertes.fr/hal-01116024

C. K. Tam, H. Ju, M. G. Jones, W. R. Watson, and T. L. , A computational and experimental study of slit resonators, Journal of Sound and Vibration, vol.284, issue.3-5, pp.947-984, 2005.
DOI : 10.1016/j.jsv.2004.07.013

C. K. Tam, H. Ju, M. G. Jones, W. R. Watson, and T. L. , A computational and experimental study of resonators in three dimensions, Journal of Sound and Vibration, vol.329, issue.24, pp.5164-5193, 2010.
DOI : 10.1016/j.jsv.2010.06.005

C. K. Tam, H. Ju, and B. E. Walker, Numerical simulation of a slit resonator in a grazing flow under acoustic excitation, Journal of Sound and Vibration, vol.313, issue.3-5, pp.449-471, 2008.
DOI : 10.1016/j.jsv.2007.12.018

C. K. Tam, K. A. Kurbatskii, K. K. Ahuja, and R. J. , A NUMERICAL AND EXPERIMENTAL INVESTIGATION OF THE DISSIPATION MECHANISMS OF RESONANT ACOUSTIC LINERS, Journal of Sound and Vibration, vol.245, issue.3, pp.545-557, 2001.
DOI : 10.1006/jsvi.2001.3571

E. O. Tuck, Matching problems involving flow through small holes Advances in Applied Mechanics, pp.89-158, 1975.

M. Van-dyke, Perturbation Method in Fluid Mechanics, Journal of Applied Mechanics, vol.43, issue.1, 1975.
DOI : 10.1115/1.3423785

Q. Zhang and D. J. Bodony, Numerical Simulation of Two-Dimensional Acoustic Liners with High-Speed Grazing Flow, AIAA Journal, vol.49, issue.2, pp.365-382, 2011.
DOI : 10.2514/1.J050597

Q. Zhang and D. J. Bodony, Numerical investigation and modelling of acoustically excited flow through a circular orifice backed by a hexagonal cavity, Journal of Fluid Mechanics, vol.vol. II, pp.367-401, 2012.
DOI : 10.2514/3.5019

D. Zhao, L. Ang, and C. Ji, Numerical and experimental investigation of the acoustic damping effect of single-layer perforated liners with joint bias-grazing flow, Journal of Sound and Vibration, vol.342, pp.152-167, 2015.
DOI : 10.1016/j.jsv.2014.12.035