L. Arnaud, Vibrations d'usinage : la bête noire de l'usinage. Revue la forge, 2010.

H. William, P. Lee, C. Jennings, H. Kisslinger, and . Kanamori, International handbook of earthquake & engineering seismology, 2002.

M. Guesdon, M. Pluviose, and . Watremetz, Vibrations d??es ?? la turbulence du vent, La Houille Blanche, issue.3-4, pp.3-4217, 1988.
DOI : 10.1051/lhb/1988017

URL : http://www.shf-lhb.org/10.1051/lhb/1988017/pdf

H. Rene, . Miller, W. Charles, and . Ellis, Helicopter blade vibration and flutter, Journal of the American Helicopter Society, vol.1, issue.3, pp.19-38, 1956.

E. Christopher and . Brennen, Hydrodynamics of pumps, 2011.

L. Witek, Experimental crack propagation and failure analysis of the first stage compressor blade subjected to vibration, Engineering Failure Analysis, vol.16, issue.7, pp.2163-2170, 2009.
DOI : 10.1016/j.engfailanal.2009.02.014

H. Richard, . Kemp, H. Marvin, . Hirschberg, C. William et al., Theoretical and experimental analysis of the reduction of rotor blade vibration in turbomachinery through the use of modified stator vane spacing, 1958.

J. Malcolm and . Crocker, Handbook of noise and vibration control, 2007.

L. Cremer and M. Heckl, Structure-borne sound : Structural vibrations and sound radiation at audio frequencies, 1988.

J. Frank, P. Fahy, and . Gardonio, Sound and structural vibration : radiation, transmission and response. Academic press, 2007.

V. Denis, Amortissement vibratoire de poutres par effet Trou Noir Acoustique, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01075826

F. Charles and . Desmond, Viscous vibration damping, US Patent, vol.3448, p.830, 1969.

C. Silva, Vibration damping, control, and design, 2007.
DOI : 10.1201/9781420053227

W. Weaver-jr, P. Stephen, D. H. Timoshenko, and Y. , Vibration problems in engineering, 1990.

A. Granato and K. Lücke, Theory of Mechanical Damping Due to Dislocations, Journal of Applied Physics, vol.4, issue.6, pp.583-593, 1956.
DOI : 10.1080/14786440408520326

D. Robert, L. H. Corsaro, and . Sperling, Sound and vibration damping with polymers , dallas tx, april 9-14 symposium series, 1989.

B. Nakra, Vibration control with viscoelastic materials. iii. The Shock and Vibration Digest, pp.17-22, 1984.
DOI : 10.1177/058310247600800603

D. Ahid, . Nashif, I. David, . Jones, P. John et al., Vibration damping, 1985.

J. Daniel and . Inman, Vibration with control, 2017.

A. Majid, Dissipation de l'énergie en mécanique vibratoire : opérateur d'hystérésis , phénomène métrique, 2002.

A. Guran, . Feeny, Y. Klarbring, and . Ishida, Impact and Friction of Solids, Structures and Intelligent Machines, Memoriam of PD Panagiotopoulos, 1950.
DOI : 10.1142/4480

URL : http://www.worldscientific.com/doi/pdf/10.1142/9789812792518_fmatter

G. Iain and . Main, Vibrations and Waves in Physics, 1993.

L. Gaul and R. Nitsche, Friction control for vibration suppression Dynamical contact problems with friction, Mechanical Systems and Signal Processing, pp.139-150, 2000.

L. Pust, L. Pe?ek, and A. Radolfová, Various types of dry friction characteristics for vibration damping, Engineering Mechanics, vol.18, issue.3-4, pp.203-224, 2011.

D. Robert and . Blevins, Flow-induced vibration. Van Nostrand Reinhold, 1977.

F. Axisa, Modélisation des systèmes mécaniques, 2001.

C. Park and A. Baz, Vibration damping and control using active constrained layer damping : A survey. The Shock and vibration digest, pp.355-364, 1999.
DOI : 10.1177/058310249903100501

N. Rizet, Contrôle actif de vibrations utilisant des matériaux piézo-électriques, 1999.

G. Bernard, Contrôle actif des vibrations, R6200), pp.6200-6201, 2002.

V. Roberti, Contrôle de structures : théories et applications, 1994.

I. Wayan and S. , Contrôle vibratoire des structures, 2000.

I. David and . Jones, Handbook of viscoelastic vibration damping, 2001.

E. Eric, . Ungar, M. Edward, and . Kerwin-jr, Plate damping due to thickness deformations in attached viscoelastic layers, The Journal of the Acoustical Society of America, vol.36, issue.2, pp.386-392, 1964.

H. Oberst and K. Frankenfeld, Über die dämpfung der biegeschwingungen dünner bleche durch fest haftende beläge, Acta Acustica united with Acustica, vol.2, issue.6, pp.181-194, 1952.

E. E. Ungar, Loss Factors of Viscoelastically Damped Beam Structures, The Journal of the Acoustical Society of America, vol.34, issue.8, pp.1082-1089, 1952.
DOI : 10.1121/1.1918249

M. Edward and . Kerwin-jr, Damping of flexural waves by a constrained viscoelastic layer, The Journal of the Acoustical society of America, vol.31, issue.7 140, pp.952-962, 1959.

D. Ross, E. E. Ungar, and E. M. Kerwin, Damping of plate flexural vibrations by means of viscoelastic laminae, Structural Damping, pp.49-87, 1960.

E. Eric, . Ungar, M. Edward, and . Kerwin-jr, Loss factors of viscoelastic systems in terms of energy concepts, The Journal of the acoustical Society of America, vol.34, issue.7, pp.954-957, 1962.

A. George and . Lesieutre, Vibration damping and control using shunted piezoelectric materials. The Shock and Vibration Digest, pp.187-195, 1998.

G. Song, H. Sethi, and . Li, Vibration control of civil structures using piezoceramic smart materials: A review, Engineering Structures, vol.28, issue.11, pp.1513-1524, 2006.
DOI : 10.1016/j.engstruct.2006.02.002

R. Philip and . Dahl, Solid friction damping of mechanical vibrations, AIAA journal, vol.14, issue.12, pp.1675-1682, 1976.

A. Yoshiaki, Y. Yasunori, Y. Isao, and Y. Jinnouchi, Impact damper with granular materials : 3rd report, indicial response, Bulletin of JSME, vol.28, issue.240, pp.1211-1217, 1985.

S. Simonian and A. Structures, Particle dam- ping applications, 45th Structural Dynamics & Materials Conference, p.1906, 2004.

C. Salueña, T. Pöschel, E. Sergei, and . Esipov, Dissipative properties of vibrated granular materials, Physical Review E, vol.79, issue.4, p.4422, 1999.
DOI : 10.1103/PhysRevLett.79.833

S. Kuebler, Vibration dampner for sports racket, US Patent, vol.5792, p.11, 1998.

H. Ashley, On passive damping mechanisms in large space structures, Journal of Spacecraft and Rockets, vol.21, issue.5, pp.448-455, 1984.
DOI : 10.2514/3.25679

R. Ehrgott, H. Panossian, G. Davis, and A. Structures, Modeling Techniques for Evaluating the Effectiveness of Particle Damping in Turbomachinery, 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p.2690, 2009.
DOI : 10.2514/6.2009-2690

J. Pieter and D. Hartog, Mechanical vibrations . Courier Corporation, 1985.

R. Rana and T. Soong, Parametric study and simplified design of tuned mass dampers. Engineering structures, pp.193-204, 1998.
DOI : 10.1016/s0141-0296(97)00078-3

Y. Chen and Y. Huang, Timoshenko beam with tuned mass dampers and its design curves, Journal of Sound and Vibration, vol.278, issue.4-5, pp.873-888, 2004.
DOI : 10.1016/j.jsv.2003.10.013

T. Pinkaew, P. Lukkunaprasit, and . Chatupote, Seismic effectiveness of tuned mass dampers for damage reduction of structures, Engineering Structures, vol.25, issue.1, pp.39-46, 2003.
DOI : 10.1016/S0141-0296(02)00115-3

J. Wang, B. Lin, and . Chen, Vibration suppression for high-speed railway bridges using tuned mass dampers, International Journal of Solids and Structures, vol.40, issue.2, pp.465-491, 2003.
DOI : 10.1016/S0020-7683(02)00589-9

R. Adkins, A. Jones, and . Nashif, Effect of tuned dampers on vibrations of simple structures., AIAA Journal, vol.35, issue.2, pp.310-315, 1967.
DOI : 10.1121/1.1918152

I. David and . Jones, Response and damping of a simple beam with tuned dampers, The journal of the acoustical society of America, vol.42, issue.1, pp.50-53, 1967.

J. Snowdon, Vibration of Cantilever Beams to which Dynamic Absorbers are Attached, The Journal of the Acoustical Society of America, vol.39, issue.5A, pp.878-886, 1966.
DOI : 10.1121/1.1909966

C. Vemula, A. Norris, and G. Cody, ATTENUATION OF WAVES IN PLATES AND BARS USING A GRADED IMPEDANCE INTERFACE AT EDGES, Journal of Sound and Vibration, vol.196, issue.1, pp.107-127, 1996.
DOI : 10.1006/jsvi.1996.0471

M. Mironov, Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval, Journal of Soviet Physics Acoustics-USSR, vol.34, issue.3, pp.318-319, 1988.

E. Bowyer, V. Krylov, and D. O. Boy, Damping of flexural vibrations in rectangular plates by slots of power-law profile, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00810719

A. Azbaid-el-ouahabi, V. Victor, . Krylov, J. Daniel, and . Boy, Investigation of the acoustic black hole termination for sound waves propagating in cylindrical waveguides, INTER-NOISE and NOISE- CON Congress and Conference Proceedings, pp.636-645, 2015.

L. Zhao, C. Stephen, F. Conlon, and . Semperlotti, An experimental study of vibration based energy harvesting in dynamically tailored structures with embedded acoustic black holes, Smart Materials and Structures, vol.24, issue.6, p.65039, 2015.
DOI : 10.1088/0964-1726/24/6/065039

C. Stephen, . Conlon, B. John, . Fahnline, R. Micah et al., Vibration control using grids of acoustic black holes : How many is enough, INTER-NOISE and NOISE-CON Congress and Conference Proceedings, pp.3139-3152, 2015.

F. Semperlotti and H. Zhu, Acoustic meta-structures based on periodic acoustic black holes, The Journal of the Acoustical Society of America, vol.137, issue.4, pp.2265-2265, 2015.
DOI : 10.1121/1.4920263

X. Jia, Y. Du, and K. Zhao, Vibration Control of Variable Thickness Plates With Embedded Acoustic Black Holes and Dynamic Vibration Absorbers, ASME 2015 Noise Control and Acoustics Division Conference, 2015.
DOI : 10.1115/NCAD2015-5914

M. Mironov, Analytical solution of black hole equation and some consequences, INTER-NOISE and NOISE-CON Congress and Conference Proceedings, pp.1577-1581, 2016.

T. Liling, C. Li, J. Hongli, and Q. Jinhao, Enhanced acoustic black hole effect using a modified thickness profile, 2016.

V. Denis, C. Touzé, and F. Gautier, Effects of geometrical nonlinearities on the acoustic black hole effect, INTER-NOISE and NOISE-CON Congress and Conference Proceedings, pp.4431-4441, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01354775

P. Feurtado, Assessing acoustic black hole performance via wavenumber transforms, INTER-NOISE and NOISE-CON Congress and Conference Proceedings, pp.458-463, 2016.

V. Victor and . Krylov, New type of vibration dampers utilising the effect of acoustic'black holes'. Acta Acustica united with Acustica, pp.830-837, 2004.

E. Bowyer, V. Victor, and . Krylov, Slots of Power-Law Profile as Acoustic Black Holes for Flexural Waves in Metallic and Composite Plates, Structures, pp.48-58
DOI : 10.1016/j.istruc.2016.02.002

. Vb-georgiev, . Cuenca, . Gautier, V. Simon, and . Krylov, Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect, Journal of Sound and Vibration, vol.330, issue.11, pp.2497-2508, 2011.
DOI : 10.1016/j.jsv.2010.12.001

V. Denis, A. Pelat, and F. Gautier, Scattering effects induced by imperfections on an acoustic black hole placed at a structural waveguide termination, Journal of Sound and Vibration, vol.362, pp.56-71, 2016.
DOI : 10.1016/j.jsv.2015.10.016

URL : https://hal.archives-ouvertes.fr/hal-01288280

S. Foucaud, G. Michon, Y. Gourinat, A. Pelat, and F. Gautier, Artificial cochlea and acoustic black hole travelling waves observation: Model and experimental results, Journal of Sound and Vibration, vol.333, issue.15, pp.3428-3439, 2014.
DOI : 10.1016/j.jsv.2014.03.016

URL : https://hal.archives-ouvertes.fr/hal-01111368

L. Tang, L. Cheng, H. Ji, and J. Qiu, Characterization of acoustic black hole effect using a one-dimensional fully-coupled and wavelet-decomposed semi-analytical model, Journal of Sound and Vibration, vol.374, pp.172-184, 2016.
DOI : 10.1016/j.jsv.2016.03.031

P. Feurtado and S. Conlon, Investigation of boundary-taper reflection for acoustic black hole design, Noise Control Engineering Journal, vol.63, issue.5, pp.460-466, 2015.
DOI : 10.3397/1/376341

V. Denis, F. Gautier, A. Pelat, and J. Poittevin, Measurement and modelling of the reflection coefficient of an Acoustic Black Hole termination, Journal of Sound and Vibration, vol.349, pp.67-79, 2015.
DOI : 10.1016/j.jsv.2015.03.043

URL : https://hal.archives-ouvertes.fr/hal-01288278

V. Denis, . Pelat, B. Gautier, and . Elie, Modal Overlap Factor of a beam with an acoustic black hole termination, Journal of Sound and Vibration, vol.333, issue.12, pp.2475-2488, 2014.
DOI : 10.1016/j.jsv.2014.02.005

URL : https://hal.archives-ouvertes.fr/hal-01288274

E. Bowyer, D. O. Boy, V. Victor, J. L. Krylov, and . Horner, Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile, Applied Acoustics, vol.73, issue.5, pp.514-523, 2012.
DOI : 10.1016/j.apacoust.2011.12.010

W. Huang, H. Ji, J. Qiu, and L. Cheng, Wave Energy Focalization in a Plate With Imperfect Two-Dimensional Acoustic Black Hole Indentation, Journal of Vibration and Acoustics, vol.138, issue.6, p.61004, 2016.
DOI : 10.1115/1.4034080

URL : http://hdl.handle.net/10397/62034

J. Yeon, L. , and W. Jeon, Vibration damping using a spiral acoustic black hole a, The Journal of the Acoustical Society of America, vol.141, issue.3, pp.1437-1445, 2017.

V. Denis, A. Pelat, C. Touzé, and F. Gautier, Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity, International Journal of Non-Linear Mechanics, vol.94, 2016.
DOI : 10.1016/j.ijnonlinmec.2016.11.012

URL : https://hal.archives-ouvertes.fr/hal-01442428

V. Victor, R. Krylov, and . Winward, Experimental investigation of the acoustic black hole effect for flexural waves in tapered plates, Journal of Sound and Vibration, vol.300, issue.1, pp.43-49, 2007.

D. O-'boy, V. Victor, V. Krylov, and . Kralovic, Damping of flexural vibrations in rectangular plates using the acoustic black hole effect, Journal of Sound and Vibration, vol.329, issue.22, pp.4672-4688, 2010.

J. Cuenca, Wave models for the flexural vibrations of thin plates, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00442260

E. Bowyer, V. Victor, and . Krylov, Experimental investigation of damping flexural vibrations in glass fibre composite plates containing one- and two-dimensional acoustic black holes, Composite Structures, vol.107, pp.406-415, 2014.
DOI : 10.1016/j.compstruct.2013.08.011

URL : https://doi.org/10.1016/j.compstruct.2013.08.011

A. Philip, . Feurtado, C. Stephen, and . Conlon, Wavenumber transform analysis for acoustic black hole design, The Journal of the Acoustical Society of America, vol.140, issue.1, pp.718-727, 2016.

E. Bowyer, D. O. Boy, V. Victor, F. Krylov, A. Gautier-philip et al., Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile An experimental investigation of acoustic black hole dynamics at low, mid, and high frequencies, Applied Acoustics Journal of Vibration and Acoustics, vol.74115, issue.1386, pp.553-560061002, 2013.

C. Stephen, . Conlon, B. John, F. Fahnline, and . Semperlotti, Numerical analysis of the vibroacoustic properties of plates with embedded grids of acoustic black holes, The Journal of the Acoustical Society of America, vol.137, issue.1, pp.447-457, 2015.

H. Zhu and F. Semperlotti, Phononic thin plates with embedded acoustic black holes, Physical Review B, vol.34, issue.10, p.104304, 2015.
DOI : 10.1103/PhysRevE.70.055602

URL : http://arxiv.org/pdf/1410.1833

L. Tang and L. Cheng, Broadband locally resonant band gaps in periodic beam structures with embedded acoustic black holes, Journal of Applied Physics, vol.133, issue.19, 2017.
DOI : 10.1121/1.4890205

L. Zhao, C. Stephen, F. Conlon, and . Semperlotti, Broadband energy harvesting using acoustic black hole structural tailoring, Smart Materials and Structures, vol.23, issue.6, p.65021, 2014.
DOI : 10.1088/0964-1726/23/6/065021

J. J. Bayod, Application of Elastic Wedge for Vibration Damping of Turbine Blade, Journal of System Design and Dynamics, vol.5, issue.5, pp.1167-1175, 2011.
DOI : 10.1299/jsdd.5.1167

E. Bowyer, V. Victor, and . Krylov, Damping of flexural vibrations in turbofan blades using the acoustic black hole effect, Applied Acoustics, vol.76, pp.359-365, 2014.
DOI : 10.1016/j.apacoust.2013.09.009

A. Climente, D. Torrent, and J. Sánchez-dehesa, Omnidirectional broadband insulating device for flexural waves in thin plates, Journal of Applied Physics, vol.114, issue.21, p.214903, 2013.
DOI : 10.1006/jsvi.1995.0129

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, American Journal of Physics, vol.22, issue.6, 1953.
DOI : 10.1119/1.1933765

C. C. Mow and Y. H. Pao, The diffraction of elastic waves and dynamic stress concentrations . Taylor and Francis Group, 1973.

A. Norris and C. Vemula, Scattering of flexural waves on thin plates, Journal of Sound and Vibration, vol.181, issue.1, pp.115-125, 1995.
DOI : 10.1006/jsvi.1995.0129

C. Vemula and A. Norris, Flexural wave propagation and scattering on thin plates using Mindlin theory, Wave Motion, vol.26, issue.1, pp.1-12, 1997.
DOI : 10.1016/S0165-2125(97)00016-4

A. Vernon, . Squire, W. Tony, and . Dixon, Scattering of flexural waves from a coated cylindrical anomaly in a thin plate, Journal of Sound and Vibration, vol.236, issue.2, pp.367-373, 2000.

M. Laug, Traitement optique du signal et des images : bases théoriques et applications [Optical processing of the signal and images : theoretical bases and applications]. Cepadues Editions, 1980.

F. Craig, . Bohren, R. Donald, and . Huffman, Absorption and scattering of light by small particles, 2008.

A. Fresnel, Premier mémoire sur la diffraction de la lumière, Verdet et al. op. cit, issue.12, pp.12-1815

V. Vasundara and . Varadan, Acoustic, electromagnetic , and elastic wave scattering?focus on the T-matrix approach : international symposium held at the Ohio State University, 1979.

A. Edward and H. Love, The small free vibrations and deformation of a thin elastic shell, Philosophical Transactions of the Royal Society of London. A, vol.179, pp.491-546, 1888.

. Siméon-denis-poisson, Mémoire sur l'équilibre et le mouvement des corps élastiques et des fluides, Ann Chimie et Physique, vol.42, pp.145-171, 1829.

P. Stephen and . Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, issue.245, pp.41744-746, 1921.

P. Stephan and . Timoshenko, On the transverse vibrations of bars of uniform cross-section

P. Mccord and M. , Acoustical Society of America, and American Institute of Phy- sics. Vibration and sound

S. Mcgraw-hill-stephen-timoshenko, S. Woinowsky-krieger, and . Woinowsky, Theory of plates and shells, 1948.

F. Karl and . Graff, Wave motion in elastic solids, 1991.

J. Guyader, Vibrations des milieux continus, Hermes Science, 2002.

E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, 1945.

N. Hu, G. Chu, and . Hermann, Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, Journal of applied mechanics, vol.23, pp.532-540, 1956.

W. Wittrick, Analytical, three-dimensional elasticity solutions to some plate problems, and some observations on Mindlin's plate theory, International Journal of Solids and Structures, vol.23, issue.4, pp.441-464, 1987.
DOI : 10.1016/0020-7683(87)90010-2

K. Liew, Y. Xiang, C. Kitipornchai, and . Wang, Vibration of Mindlin plates : programming the p-version Ritz method, 1998.

Y. Yu, Vibrations of elastic plates : linear and nonlinear dynamical modeling of sandwiches, laminated composites, and piezoelectric layers, 2012.
DOI : 10.1007/978-1-4612-2338-2

S. Ya and . Uflyand, The propagation of waves in the transverse vibrations of bars and plates

R. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates, 1951.
DOI : 10.1007/978-1-4613-8865-4_29

A. W. Leissa, Vibration of Plates, N70-18461. NASA, 1969.

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions : with formulas, graphs, and mathematical tables, 1965.

T. Edmund, . Whittaker, N. George, and . Watson, A course of modern analysis : an introduction to the general theory of infinite processes and of analytic functions, with an acount of the principal transcendental functions Bessel functions for engineers, AKLOUCHE BIBLIOGRAPHIE, vol.161150, issue.145, 1935.

F. Arnold, . Nikiforov, . Vasili?, and . Uvarov, Fonctions spéciales de la physique mathématique

M. Christopher, P. Linton, and . Mciver, Handbook of mathematical techniques for wave/structure interactions, 2001.

M. Caleap, Modélisation de la propagation d'ondes élastiques antiplanes dans des milieux multifissurés, 2009.

O. Xeridat, Etude expérimentale de la propagation, de la diffusion et de la localisation des ondes de Lamb [Experimental study of the propagation, the scattering and the localization of Lamb waves], 2011.

W. Parnell and P. Martin, Multiple scattering of flexural waves by random configurations of inclusions in thin plates, Wave Motion, vol.48, issue.2, pp.161-175, 2011.
DOI : 10.1016/j.wavemoti.2010.10.004

O. Aklouche, A. Pelat, S. Maugeais, and F. Gautier, Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate, Journal of Sound and Vibration, vol.375, pp.38-52, 2016.
DOI : 10.1016/j.jsv.2016.04.034

F. Fahy and P. Gardonio, Sound and Structural Vibration, 2007.

K. W. Liew, C. M. Wang, Y. Xiang, and S. Kitipornchai, Vibration of Midlin plates, 1998.

D. O-'boy and V. Krylov, Damping of flexural vibrations in circular plates with tapered central holes, Journal of Sound and Vibration, vol.330, issue.10, pp.2220-2236, 2011.

H. Conway, Some special solutions for the flexural vibration of discs of varying thickness, Ingenieur-Archiv, vol.26, issue.6, pp.408-410, 1958.
DOI : 10.1007/BF00533453

E. Durand, Solutions numériques des équations algébriques [Numerical solutions of algebraic equations], 1971.

. Vb-georgiev, . Cuenca, . Gautier, V. Simon, and . Krylov, Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect, Journal of Sound and Vibration, vol.330, issue.11, pp.2497-2508, 2011.
DOI : 10.1016/j.jsv.2010.12.001

M. Callan, D. Linton, and . Evans, Trapped modes in two-dimensional waveguides, Journal of Fluid Mechanics, vol.13, issue.-1, pp.51-64, 1991.
DOI : 10.1017/S0022112085000714

P. Cobelli and V. Pagneux, Experimental observation of trapped modes in a water wave channel, EPL (Europhysics Letters), vol.88, issue.2, p.20006, 2009.
DOI : 10.1209/0295-5075/88/20006

R. Porter, Trapped waves in thin elastic plates, Wave Motion, vol.45, issue.1-2, pp.3-15, 2007.
DOI : 10.1016/j.wavemoti.2007.04.001

URL : http://www.maths.bris.ac.uk/~marp/abstracts/porter_wm06.pdf

V. Krylov and F. Tilman, Acoustic ???black holes??? for flexural waves as effective vibration dampers, Journal of Sound and Vibration, vol.274, issue.3-5, pp.605-619, 2004.
DOI : 10.1016/j.jsv.2003.05.010

M. Géradin, J. Daniel, and . Rixen, Mechanical vibrations : theory and application to structural dynamics, 2014.

I. Newton, D. Bernoulli, C. Maclaurin, and L. Euler, Philosophiae naturalis principia mathematica, p.1833
DOI : 10.5479/sil.52126.39088015628399

I. Newton, Principia mathematica. Newton's principia, p.634, 1934.

L. Brillouin, Wave propagation in periodic structures : electric filters and crystal lattices, Courier Corporation, 2003.

D. John, . Joannopoulos, G. Steven, J. N. Johnson, . Winn et al., Photonic crystals : molding the flow of light, 2011.

H. Bouasse, Cristallographie géométrique : groupes de déplacements, 1929.

C. Kittel, Introduction to solid state physics, 2005.

G. Floquet, Sur les ??quations diff??rentielles lin??aires ?? coefficients p??riodiques, Annales scientifiques de l'École normale supérieure, pp.47-88, 1883.
DOI : 10.24033/asens.220

E. Mathieu, Traité de physique mathématique, p.1873

G. William and H. , The collected mathematical works of George William Hill. Carnegie institution of Washington, 1906.

R. Campbell and J. Pérès, Théorie générale de l'équation de mathieu et de quelques autres équations différentielles de la mécanique, 1955.

F. Bloch, Über die quantenmechanik der elektronen in kristallgittern. Zeitschrift für Physik A Hadrons and Nuclei, pp.555-600, 1929.
DOI : 10.1007/bf01339455

A. Duclos, Diffusion multiple en fluide visco-thermique, cas du cristal phononique à deux dimensions, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00305480

S. Benchabane, Guidage et filtrage des ondes dans les cristaux phononiques, 2006.
URL : https://hal.archives-ouvertes.fr/tel-00140347

Q. Rolland, Couplages acousto-optiques dans les cristaux photoniques et phononiques, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00916313

D. Mead, WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES: RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON, 1964???1995, Journal of Sound and Vibration, vol.190, issue.3, pp.495-524, 1964.
DOI : 10.1006/jsvi.1996.0076

R. Martinezsala, . Sancho, V. Juan, V. Sánchez, . Gómez et al., Sound attenuation by sculpture, Nature, vol.10, issue.6554, pp.241-241, 1995.
DOI : 10.1364/JOSAB.10.000314

M. Michael, . Sigalas, N. Eleftherios, and . Economou, Elastic and acoustic wave band structure, Journal of sound and vibration, vol.158, issue.2, pp.377-382, 1992.

Z. Hou, M. Badreddine, and . Assouar, Modeling of Lamb wave propagation in plate with two-dimensional phononic crystal layer coated on uniform substrate using plane-wave-expansion method, Physics Letters A, vol.372, issue.12, pp.2091-2097, 2008.
DOI : 10.1016/j.physleta.2007.10.080

S. Benchabane, A. Khelif, J. Rauch, L. Robert, and V. Laude, Evidence for complete surface wave band gap in a piezoelectric phononic crystal, Physical Review E, vol.1, issue.6, p.65601, 2006.
DOI : 10.1016/S0038-1098(96)00716-8

S. Mohammadi, A. Asghar-eftekhar, D. William, A. Hunt, and . Adibi, High-Q micromechanical resonators in a two-dimensional phononic crystal slab, Applied Physics Letters, vol.94, issue.5, p.51906, 2009.
DOI : 10.1103/PhysRevLett.94.223902

T. Wu, L. Wu, and Z. Huang, Frequency band-gap measurement of two-dimensional air/silicon phononic crystals using layered slanted finger interdigital transducers, Journal of Applied Physics, vol.27, issue.9, p.94916, 2005.
DOI : 10.1080/02533839.2004.9670952

W. Bragg, An introduction to crystal analysis, 1929.

Z. Liu, X. Zhang, Y. Mao, Y. Zhu, Z. Yang et al., Locally Resonant Sonic Materials, Science, vol.289, issue.5485, pp.1734-1736, 2000.
DOI : 10.1126/science.289.5485.1734

J. Hsu and T. Wu, Lamb waves in binary locally resonant phononic plates with two-dimensional lattices, Applied Physics Letters, vol.90, issue.20, p.90201904, 2007.
DOI : 10.1103/PhysRevB.74.144303

G. Wang, X. Wen, J. Wen, L. Shao, and Y. Liu, Two-dimensional locally resonant phononic crystals with binary structures. Physical review letters, p.93154302, 2004.
DOI : 10.1103/physrevlett.93.154302

W. Xiao, Y. Zeng, and . Cheng, Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs, Applied Acoustics, vol.69, issue.3, pp.255-261, 2008.
DOI : 10.1016/j.apacoust.2006.09.003

O. Bauchau and J. Craig, Euler-bernoulli beam theory Elastic wave band gaps in flexural vibrations of straight beams, Structural analysis, pp.173-221001, 2005.

J. Søndergaard and J. , Phononic band gaps and vibrations in one-and twodimensional mass?spring structures, Journal of Sound and Vibration, vol.266, issue.5, pp.1053-1078, 2003.

S. Manvir, . Kushwaha, . Halevi, . Martinez, B. Dobrzynski et al., Theory of acoustic band structure of periodic elastic composites, Physical Review B, vol.49, issue.4, p.2313, 1994.

Z. Yao, G. Yu, Y. Wang, and Z. Shi, Propagation of bending waves in phononic crystal thin plates with a point defect, International Journal of Solids and Structures, vol.46, issue.13, pp.2571-2576, 2009.
DOI : 10.1016/j.ijsolstr.2009.02.002

G. Zong-jian-yao, Y. Yu, Z. Wang, J. Shi, and . Li, Propagation of flexural waves in phononic crystal thin plates with linear defects The algebraic eigenvalue problem, Journal of Zhejiang University-SCIENCE A, vol.11204, issue.87, pp.827-834, 1965.

J. Dedieu and F. Tisseur, Perturbation theory for homogeneous polynomial eigenvalue problems. Linear algebra and its applications, pp.71-94, 2003.
DOI : 10.1016/s0024-3795(01)00423-2

URL : https://doi.org/10.1016/s0024-3795(01)00423-2

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

F. Tisseur, Backward error and condition of polynomial eigenvalue problems, Linear Algebra and its Applications, vol.309, issue.1-3, pp.339-361, 2000.
DOI : 10.1016/S0024-3795(99)00063-4

URL : https://doi.org/10.1016/s0024-3795(99)00063-4

D. Yu, J. Wen, Y. Liu, J. Qiu, and G. Wang, Flexural vibrations band gaps in periodic beams including rotary inertia and shear deformation effects, Chinese Journal of Mechanical Engineering (English Edition), vol.19, issue.01, pp.25-27, 2006.
DOI : 10.3901/CJME.2006.01.025

L. Junyi, D. Ruffini, and . Balint, Measuring the band structures of periodic beams using the wave superposition method, Journal of Sound and Vibration, vol.382, issue.148, pp.158-178, 2016.
DOI : 10.1016/j.jsv.2016.07.005

URL : http://spiral.imperial.ac.uk/bitstream/10044/1/39611/9/JSV-D-15-01571R4ReducedResolution.pdf