E. Nennig, M. B. Perrey-debain, and . Tahar, A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow, The Journal of the Acoustical Society of America, vol.128, issue.6, pp.3308-3320, 2010.
DOI : 10.1121/1.3506346

URL : https://hal.archives-ouvertes.fr/hal-00694671

B. Nennig, M. B. Tahar, and E. Perrey-debain, A displacement-pressure finite element formulation for analyzing the sound transmission in ducted shear flows with finite poroelastic lining, The Journal of the Acoustical Society of America, vol.130, issue.1, pp.42-51, 2011.
DOI : 10.1121/1.3598451

URL : https://hal.archives-ouvertes.fr/hal-00694763

R. Nennig, E. Binois, N. Perrey-debain, and . Dauchez, A homogenization method used to predict the performance of silencers containing parallel splitters, The Journal of the Acoustical Society of America, vol.137, issue.6, pp.3221-3231, 2015.
DOI : 10.1121/1.4921598

URL : https://hal.archives-ouvertes.fr/hal-01178969

D. Aurégan, . Kumar, and . Singh, Experimental observation of a hydrodynamic mode in a flow duct with a porous material, The Journal of the Acoustical Society of America, vol.136, issue.2, pp.567-572, 2014.
DOI : 10.1121/1.4884768

J. Astley, A comparative note on the effects of local versus bulk reaction models for air moving ducts lined on all sides, Journal of Sound and Vibration, vol.117, issue.1, pp.191-197, 1987.
DOI : 10.1016/0022-460X(87)90445-7

J. B. Tanneau, P. Casimir, and . Lamary, Optimization of multilayered panels with poroelastic components for an acoustical transmission objective, The Journal of the Acoustical Society of America, vol.120, issue.3, pp.1227-1238, 2006.
DOI : 10.1121/1.2228663

J. Groby, A. Duclos, O. Dazel, L. Boeckx, and W. Lauriks, Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions, The Journal of the Acoustical Society of America, vol.130, issue.6, pp.3071-3780, 2011.
DOI : 10.1121/1.3652865

Y. Nennig, J. Renou, Y. Groby, and . Aurégan, A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions, The Journal of the Acoustical Society of America, vol.131, issue.5, pp.3841-3852, 2012.
DOI : 10.1121/1.3693655

URL : https://hal.archives-ouvertes.fr/hal-01179031

J. Groby, B. Nennig, C. Lagarrigue, B. Brouard, O. Dazel et al., Enhancing the absorption properties of acoustic porous plates by periodically embedding Helmholtz resonators, The Journal of the Acoustical Society of America, vol.137, issue.1, pp.273-280, 2015.
DOI : 10.1121/1.4904534

URL : https://hal.archives-ouvertes.fr/hal-01179024

F. Boutin and . Becot, Theory and experiments on poro-acoustics with inner resonators, Wave Motion, vol.54, pp.76-99, 2015.
DOI : 10.1016/j.wavemoti.2014.11.013

J. S. Yang, Y. Y. Lee, and . Kim, Metaporous layer to overcome the thickness constraint for broadband sound absorption, Journal of Applied Physics, vol.117, issue.17, p.174903, 2015.
DOI : 10.1103/PhysRevLett.110.175501

B. Griffiths, S. Nennig, and . Job, Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption, The Journal of the Acoustical Society of America, vol.141, issue.1, pp.254-264, 2017.
DOI : 10.1121/1.4973691

URL : https://hal.archives-ouvertes.fr/hal-01456305

J. S. Yang, Y. Y. Lee, and . Kim, Multiple slow waves in metaporous layers for broadband sound absorption, Journal of Physics D: Applied Physics, vol.50, issue.1, p.15301, 2017.
DOI : 10.1088/1361-6463/50/1/015301

G. Romero-garcia, O. Theocharis, A. Richoux, V. Merkel, V. Tournat et al., Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators, Scientific Reports, vol.547, issue.1, p.19519, 2016.
DOI : 10.1038/srep04674

J. Tester, The optimization of modal sound attenuation in ducts, in the absence of mean flow, Journal of Sound and Vibration, vol.27, issue.4, pp.477-513, 1973.
DOI : 10.1016/S0022-460X(73)80358-X

. Cremer, Theory of sound attenuation in a rectangular duct with an absorbing wall and the resultant maximum attenuation coefficient, Acustica, vol.2, pp.249-263, 1953.

. Kato, Perturbation Theory for Linear Operators, 1980.

D. Heiss and A. L. Sannino, Avoided level crossing and exceptional points, Journal of Physics A: Mathematical and General, vol.23, issue.7, p.1167, 1990.
DOI : 10.1088/0305-4470/23/7/022

D. Heiss, Repulsion of resonance states and exceptional points, Physical Review E, vol.43, issue.1, pp.929-932, 2000.
DOI : 10.1103/PhysRevA.43.4159

. Berry, Physics of Nonhermitian Degeneracies, Czechoslovak Journal of Physics, vol.54, issue.10, pp.1039-1047, 2004.
DOI : 10.1023/B:CJOP.0000044002.05657.04

A. Hernández, A. Jáuregui, and . Mondragón, Energy eigenvalue surfaces close to a degeneracy of unbound states: Crossings and anticrossings of energies and widths, Physical Review E, vol.39, issue.2, p.26221, 2005.
DOI : 10.1115/1.3424591

W. Bi and . Pagneux, New insights into mode behaviours in waveguides with impedance boundary conditions, 2015.

V. Bi and . Pagneux, Resonance trapping " dans un guide traité par une impédance locale ( " trapping resonance " in a locally reacting lined waveguide), CFA 2016, 2016.

W. Xiong, Y. Bi, and . Aurégan, Fano resonance scatterings in waveguides with impedance boundary conditions, The Journal of the Acoustical Society of America, vol.139, issue.2, pp.764-772, 2016.
DOI : 10.1121/1.4941568

B. Nennig, Y. Renou, and Y. Aurégan, On the use of periodic inclusions embedded in porous lining to enhanced attenuation in waveguides, Acoustics 2012, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00810614

C. Engström, C. Hafner, and K. Schmidt, Computations of Lossy Bloch Waves in Two-Dimensional Photonic Crystals, Journal of Computational and Theoretical Nanoscience, vol.6, issue.3, pp.775-783, 2009.
DOI : 10.1166/jctn.2009.1108

M. Collet, M. Ouisse, M. Ruzzene, and . Ichchou, Floquet???Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems, International Journal of Solids and Structures, vol.48, issue.20, pp.2837-2848, 2011.
DOI : 10.1016/j.ijsolstr.2011.06.002

URL : https://hal.archives-ouvertes.fr/hal-01516397

K. Tisseur and . Meerbergen, The Quadratic Eigenvalue Problem, SIAM Review, vol.43, issue.2, pp.235-286, 2001.
DOI : 10.1137/S0036144500381988

A. Redon, J. Bonnet-ben-dhia, S. S. Mercier, and . Poernomo, Non-reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow, International Journal for Numerical Methods in Engineering, vol.71, issue.6, pp.1360-1378, 2011.
DOI : 10.1016/0022-460X(80)90424-1

URL : https://hal.archives-ouvertes.fr/hal-00717640

B. Lawrie and I. D. Abrahams, An orthogonality relation for a class of problems with high-order boundary conditions; applications in sound-structure interaction, The Quarterly Journal of Mechanics and Applied Mathematics, vol.52, issue.2, pp.161-181, 1999.
DOI : 10.1093/qjmam/52.2.161

J. Geuzaine and . Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering, vol.69, issue.4, pp.1309-1331, 2009.
DOI : 10.1007/978-3-642-59223-2

. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013

URL : https://hal.archives-ouvertes.fr/hal-01476313

J. E. Hernandez, V. Roman, and . Vidal, SLEPc, ACM Transactions on Mathematical Software, vol.31, issue.3, pp.351-362, 2005.
DOI : 10.1145/1089014.1089019

M. Aurégan and . Leroux, Experimental evidence of an instability over an impedance wall in a duct with flow, Journal of Sound and Vibration, vol.317, issue.3-5, pp.432-439, 2008.
DOI : 10.1016/j.jsv.2008.04.020