Z. Liu, Locally Resonant Sonic Materials, Science, vol.289, issue.5485, pp.1734-1736, 2000.
DOI : 10.1126/science.289.5485.1734

S. A. Cummer, J. Christensen, and A. Alù, Controlling sound with acoustic metamaterials, Nature Reviews Materials, vol.348, issue.3, p.16001, 2016.
DOI : 10.1126/science.aac4360

G. Ma and P. Sheng, Acoustic metamaterials: From local resonances to broad horizons, Science Advances, vol.2, issue.2, p.1501595, 2016.
DOI : 10.1126/sciadv.1501595

URL : http://advances.sciencemag.org/content/advances/2/2/e1501595.full.pdf

Y. Chen, H. Liu, M. Reilly, H. Bae, and M. Yu, Enhanced acoustic sensing through wave compression and pressure amplification in anisotropic metamaterials, Nature Communications, vol.3, p.5247, 2014.
DOI : 10.1103/PhysRevLett.103.033902

URL : http://www.nature.com/articles/ncomms6247.pdf

G. Wang, X. Wen, J. Wen, L. Shao, and Y. Liu, Two-Dimensional Locally Resonant Phononic Crystals with Binary Structures, Physical Review Letters, vol.52, issue.15, p.154302, 2004.
DOI : 10.1103/PhysRevB.28.1711

K. M. Ho, C. K. Cheng, Z. Yang, X. Zhang, and P. Sheng, Broadband locally resonant sonic shields, Applied Physics Letters, vol.83, issue.26, pp.5566-5568, 2003.
DOI : 10.1121/1.384778

Y. Xiao, J. Wen, and X. Wen, Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators, New Journal of Physics, vol.14, issue.3, p.33042, 2012.
DOI : 10.1088/1367-2630/14/3/033042

H. Zhang, Y. Xiao, J. Wen, D. Yu, and X. Wen, Ultra-thin smart acoustic metasurface for low-frequency sound insulation, Applied Physics Letters, vol.108, issue.14, p.141902, 2016.
DOI : 10.1088/0964-1726/20/1/015026

J. Mei, Dark acoustic metamaterials as super absorbers for low-frequency sound, Nature Communications, vol.66, p.756, 2012.
DOI : 10.1016/j.apacoust.2004.11.005

URL : http://www.nature.com/articles/ncomms1758.pdf

J. B. Pendry and J. Li, An acoustic metafluid: realizing a broadband acoustic cloak, New Journal of Physics, vol.10, issue.11, p.115032, 2008.
DOI : 10.1088/1367-2630/10/11/115032

URL : http://iopscience.iop.org/article/10.1088/1367-2630/10/11/115032/pdf

N. Stenger, M. Wilhelm, and M. Wegener, Experiments on Elastic Cloaking in Thin Plates, Physical Review Letters, vol.108, issue.1, p.14301, 2012.
DOI : 10.1121/1.1739482

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, An elastomechanical unfeelability cloak made of pentamode metamaterials, Nat. Commun, vol.5, p.4130, 2014.

X. Ni, Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow, New Journal of Physics, vol.17, issue.5, p.53016, 2015.
DOI : 10.1088/1367-2630/17/5/053016

M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, Experimental Demonstration of Ordered and Disordered Multiresonant Metamaterials for Lamb Waves, Physical Review Letters, vol.220, issue.23, p.234301, 2014.
DOI : 10.1063/1.4773369

R. P. Moiseyenko, Y. Pennec, R. Marchal, B. Bonello, and B. Djafari-rouhani, Broadband attenuation of Lamb waves through a periodic array of thin rectangular junctions, Physical Review B, vol.90, issue.13, p.134307, 2014.
DOI : 10.1103/PhysRev.48.928

URL : https://hal.archives-ouvertes.fr/hal-01233804

L. Cai, X. Han, and X. Wen, Band-structure results for elastic waves interpreted with multiple-scattering theory, Physical Review B, vol.60, issue.15, p.153101, 2006.
DOI : 10.1063/1.1722545

G. Ma, Y. Min, S. Xiao, Z. Yang, and P. Sheng, Acoustic metasurface with hybrid resonances, Nature Materials, vol.3, issue.9, pp.873-878, 2014.
DOI : 10.1016/j.apacoust.2004.11.005

J. Zhao, B. Bonello, and O. Boyko, Focusing of the lowest-order antisymmetric Lamb mode behind a gradient-index acoustic metalens with local resonators, Physical Review B, vol.93, issue.17, p.174306, 2016.
DOI : 10.1103/PhysRevB.77.094304

URL : https://hal.archives-ouvertes.fr/hal-01414724

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-rouhani, Acoustic band structure of periodic elastic composites, Physical Review Letters, vol.86, issue.13, pp.2022-2025, 1993.
DOI : 10.1016/0038-1098(93)90888-T

M. I. Hussein, M. J. Leamy, and M. Ruzzene, Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook, Applied Mechanics Reviews, vol.66, issue.4, p.40802, 2014.
DOI : 10.1115/1.4026911

Y. Xiao, J. Wen, G. Wang, and X. Wen, Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators, Journal of Vibration and Acoustics, vol.135, issue.4, p.41006, 2013.
DOI : 10.1115/1.4024214

Y. Xiao, J. Wen, and X. Wen, Flexural wave band gaps in locally resonant thin plates with periodically attached spring???mass resonators, Journal of Physics D: Applied Physics, vol.45, issue.19, p.195401, 2012.
DOI : 10.1088/0022-3727/45/19/195401

M. Lapine, M. Gorkunov, and K. Ringhofer, Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements, Physical Review E, vol.22, issue.6, p.65601, 2003.
DOI : 10.1109/55.919228

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear Properties of Left-Handed Metamaterials, Physical Review Letters, vol.28, issue.3, p.37401, 2003.
DOI : 10.1063/1.1359141

URL : http://arxiv.org/pdf/cond-mat/0303443

N. Zheludev, The Road Ahead for Metamaterials, Science, vol.87, issue.5873, pp.582-583, 2010.
DOI : 10.1126/science.1152793

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, : Nonlinear metamaterials, Reviews of Modern Physics, vol.17, issue.3, pp.1093-1123, 2014.
DOI : 10.1016/j.photonics.2011.04.002

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, Linear and nonlinear wave propagation in negative refraction metamaterials, Physical Review B, vol.91, issue.16, p.165112, 2004.
DOI : 10.1103/PhysRevLett.91.037401

N. I. Zheludev and Y. S. Kivshar, From metamaterials to metadevices, Nature Materials, vol.85, issue.11, pp.917-924, 2012.
DOI : 10.1103/PhysRevB.85.205123

A. Rose, D. Huang, and D. R. Smith, Controlling the Second Harmonic in a Phase-Matched Negative-Index Metamaterial, Physical Review Letters, vol.107, issue.6, p.63902, 2011.
DOI : 10.1103/PhysRevB.67.113103

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. Zheludev, Electromagnetic wave analogue of an electronic diode, New Journal of Physics, vol.13, issue.3, p.33025, 2011.
DOI : 10.1088/1367-2630/13/3/033025

URL : https://doi.org/10.1088/1367-2630/13/3/033025

Z. Wang, Harmonic Image Reconstruction Assisted by a Nonlinear Metmaterial Surface, Physical Review Letters, vol.106, issue.4, p.47402, 2011.
DOI : 10.1109/22.788605

G. Gallavotti, The Fermi-Pasta-Ulam Problem: A Status Report, 2008.
DOI : 10.1007/978-3-540-72995-2

N. Li, : Phononics: Manipulating heat flow with electronic analogs and beyond, Reviews of Modern Physics, vol.21, issue.3, p.1045, 2012.
DOI : 10.1063/1.3679694

URL : http://arxiv.org/pdf/1108.6120

V. F. Nesterenko, C. Daraio, E. B. Herbold, and S. Jin, Anomalous Wave Reflection at the Interface of Two Strongly Nonlinear Granular Media, Physical Review Letters, vol.36, issue.15, p.158702, 2005.
DOI : 10.1016/j.physleta.2004.04.042

C. Daraio, V. F. Nesterenko, E. Herbold, and S. Jin, Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals, Physical Review E, vol.80, issue.2, p.26610, 2006.
DOI : 10.1111/j.1151-2916.1997.tb03074.x

R. K. Narisetti, M. Ruzzene, and M. J. Leamy, A Perturbation Approach for Analyzing Dispersion and Group Velocities in Two-Dimensional Nonlinear Periodic Lattices, Journal of Vibration and Acoustics, vol.133, issue.6, p.61020, 2011.
DOI : 10.1115/1.4004661

N. Boechler, Discrete Breathers in One-Dimensional Diatomic Granular Crystals, Physical Review Letters, vol.6934, issue.24, p.244302, 2010.
DOI : 10.1103/PhysRevE.67.066608

URL : https://hal.archives-ouvertes.fr/hal-00624744

E. Kim, Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures, Physical Review Letters, vol.114, issue.11, p.118002, 2015.
DOI : 10.1103/PhysRevE.54.3621

S. Y. Wang and V. F. Nesterenko, Attenuation of short strongly nonlinear stress pulses in dissipative granular chains, Physical Review E, vol.34, issue.6, p.62211, 2015.
DOI : 10.1103/PhysRevE.72.016603

J. Lydon, G. Theocharis, and C. Daraio, Nonlinear resonances and energy transfer in finite granular chains, Physical Review E, vol.91, issue.2, p.23208, 2015.
DOI : 10.1016/j.physleta.2003.10.012

B. Liang, B. Yuan, and J. C. Cheng, Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems, Physical Review Letters, vol.37, issue.10, p.104301, 2009.
DOI : 10.1063/1.2974811

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, An acoustic rectifier, Nature Materials, vol.34, issue.12, pp.989-992, 2010.
DOI : 10.1121/1.401444

N. Boechler, G. Theocharis, and C. Daraio, Bifurcation-based acoustic switching and rectification, Nature Materials, vol.94, issue.9, pp.665-668, 2011.
DOI : 10.1103/PhysRevLett.94.108001

C. M. Donahue, P. W. Anzel, L. Bonanomi, T. A. Keller, and C. Daraio, Experimental realization of a nonlinear acoustic lens with a tunable focus, Applied Physics Letters, vol.10, issue.1, p.14103, 2014.
DOI : 10.1016/j.ijsolstr.2012.02.013

X. Fang, J. Wen, J. Yin, D. Yu, and Y. Xiao, Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: Theoretical study, Physical Review E, vol.94, issue.5, p.52206, 2016.
DOI : 10.1209/0295-5075/101/44003

X. Fang, J. Wen, J. Yin, and D. Yu, Wave propagation in nonlinear metamaterial multi-atomic chains based on homotopy method, AIP Advances, vol.6, issue.12, p.121706, 2016.
DOI : 10.1115/1.4024214

URL : http://aip.scitation.org/doi/pdf/10.1063/1.4971761

X. Fang, J. Wen, B. Bonello, J. Yin, and D. Yu, Wave propagation in one-dimensional nonlinear acoustic metamaterials, New Journal of Physics, vol.19, issue.5, p.53007, 2017.
DOI : 10.1088/1367-2630/aa6d49

URL : https://hal.archives-ouvertes.fr/hal-01488622

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2014.

V. I. Babitsky, Theory of Vibro-Impact Systems and Applications, 1998.
DOI : 10.1007/978-3-540-69635-3

Y. V. Mikhlin, A. F. Vakakis, and G. Salenger, DIRECT AND INVERSE PROBLEMS ENCOUNTERED IN VIBRO-IMPACT OSCILLATIONS OF A DISCRETE SYSTEM, Journal of Sound and Vibration, vol.216, issue.2, pp.227-250, 1998.
DOI : 10.1006/jsvi.1998.1613

URL : https://hal.archives-ouvertes.fr/hal-01352131

X. Fang, J. Wen, J. Yin, and D. Yu, Highly efficient continuous bistable nonlinear energy sink composed of a cantilever beam with partial constrained layer damping, Nonlinear Dynamics, vol.83, issue.1, pp.2677-2695, 2017.
DOI : 10.1016/S0022-460X(82)80099-0

B. P. Bernard, M. J. Mazzoleni, N. Garraud, D. P. Arnold, and B. P. Mann, Experimental investigation of bifurcation induced bandgap reconfiguration, Journal of Applied Physics, vol.6, issue.8, p.84904, 2014.
DOI : 10.1088/1748-3182/3/3/034001

H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, 2004.
DOI : 10.1017/CBO9780511755798

M. T. Rosenstein, J. J. Collins, and C. J. De-luca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena, vol.65, issue.1-2, pp.117-134, 1993.
DOI : 10.1016/0167-2789(93)90009-P

URL : http://www.cs.umass.edu/~mtr/papers/RosensteinM93.ps.gz

H. Kantz, A robust method to estimate the maximal Lyapunov exponent of a time series, Physics Letters A, vol.185, issue.1, pp.77-87, 1994.
DOI : 10.1016/0375-9601(94)90991-1

M. Petyt, Introduction to Finite Element Vibration Analysis, 2010.

X. Fang, J. Wen, B. Bonello, and J. Yin, Wave propagation in onedimensional nonlinear acoustic metamaterials. Pre-print at https://arxiv.org/ abs, p.6761, 1703.
DOI : 10.1088/1367-2630/aa6d49

URL : https://hal.archives-ouvertes.fr/hal-01488622