H. Frahm, Device for damping vibrations of bodies. United states patent office, pp.1-9, 1911.

R. E. Roberson, Synthesis of a nonlinear dynamic vibration absorber. Portions of a dissertation submitted to the Department of Applied Mechanics, Washington University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, pp.205-220, 1952.

D. R. Smith and N. Kroll, Negative Refractive Index in Left-Handed Materials, Physical Review Letters, vol.85, issue.14, pp.2933-2936, 2000.
DOI : 10.1103/PhysRevLett.85.2933

H. Chen and C. T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Applied Physics Letters, vol.91, issue.18, pp.183518-183519, 2007.
DOI : 10.1063/1.2803315

Y. Ding, Z. Liu, C. Qiu, and J. Shi, Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density, Physical Review Letters, vol.99, issue.9, pp.93904-93905, 2007.
DOI : 10.1103/PhysRevLett.99.093904

P. Sheng, J. Mei, Z. Liu, and W. Wen, Dynamic mass density and acoustic metamaterials, Physica B: Condensed Matter, vol.394, issue.2, pp.256-261, 2007.
DOI : 10.1016/j.physb.2006.12.046

Z. Yang, J. Mei, M. Yang, N. H. Chan, and P. Sheng, Membrane-Type Acoustic Metamaterial with Negative Dynamic Mass, Physical Review Letters, vol.101, issue.20, pp.204301-204302, 2008.
DOI : 10.1103/PhysRevLett.101.204301

S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, Acoustic metamaterial with negative density, Physics Letters A, vol.373, issue.48, pp.4464-4469, 2009.
DOI : 10.1016/j.physleta.2009.10.013

X. Zhou and G. Hu, Analytic model of elastic metamaterials with local resonances, Physical Review B, vol.79, issue.19, pp.195109-195110, 2009.
DOI : 10.1103/PhysRevB.79.195109

X. N. Liu, G. K. Hu, G. Huang, and C. T. Sun, An elastic metamaterial with simultaneously negative mass density and bulk modulus, Applied Physics Letters, vol.98, issue.25, p.251907, 2011.
DOI : 10.1063/1.3597651

S. Li and X. L. Gao, Handbook of Micromechanics and Nanomechanics, 2013.
DOI : 10.1201/b14795

M. I. Hussein and M. J. Frazize, Metadamping: An emergent phenomenon in dissipative metamaterials, Journal of Sound and Vibration, vol.332, issue.20, pp.4767-4774, 2013.
DOI : 10.1016/j.jsv.2013.04.041

D. , D. Vescovo, and I. Giorgio, Dynamic problems for metamaterials: Review of existing models and ideas for further research, International Journal of Engineering Science, vol.80, pp.153-172, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00947477

X. Wang, Dynamic behaviour of a metamaterial system with negative mass and modulus, International Journal of Solids and Structures, vol.51, issue.7-8, pp.1534-1541, 2014.
DOI : 10.1016/j.ijsolstr.2014.01.004

R. Zhu, X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, A chiral elastic metamaterial beam for broadband vibration suppression, Journal of Sound and Vibration, vol.333, issue.10, pp.2759-2773, 2014.
DOI : 10.1016/j.jsv.2014.01.009

X. Wang, H. Zhao, Z. Luo, and . Huang, Membrane-constrained acoustic metamaterials for low frequency sound insulation, Applied Physics Letters, vol.108, issue.4, p.41905, 2016.
DOI : 10.1063/1.4940717

C. Soize, Vibration damping in low-frequency range due to structural complexity. A model based on the theory of fuzzy structures and model parameters estimation, Computers & Structures, vol.58, issue.5, pp.901-915, 1995.
DOI : 10.1016/0045-7949(95)00207-W

URL : https://hal.archives-ouvertes.fr/hal-00770275

O. Gendelman, L. I. Manevitch, A. F. Vakakis, and R. Mcloskey, Energy Pumping in Nonlinear Mechanical Oscillators: Part I???Dynamics of the Underlying Hamiltonian Systems, Journal of Applied Mechanics, vol.68, issue.1, pp.34-41, 2001.
DOI : 10.1115/1.1345524

A. F. Vakakis and O. Gendelman, Energy Pumping in Nonlinear Mechanical Oscillators: Part II???Resonance Capture, Journal of Applied Mechanics, vol.68, issue.1, pp.42-48, 2001.
DOI : 10.1115/1.1345525

A. F. Vakakis, Shock Isolation Through the Use of Nonlinear Energy Sinks, Journal of Vibration and Control, vol.9, issue.1-2, pp.79-93, 2003.
DOI : 10.1177/107754603030742

G. W. Milton, M. Briane, and J. R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics, vol.8, issue.10, pp.1-20, 2006.
DOI : 10.1088/1367-2630/8/10/248

URL : https://hal.archives-ouvertes.fr/hal-00452194

A. Carrella, M. J. Brennan, and T. P. Waters, Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic, Journal of Sound and Vibration, vol.301, issue.3-5, pp.678-689, 2007.
DOI : 10.1016/j.jsv.2006.10.011

N. A. Alexander and F. Schilder, Exploring the performance of a nonlinear tuned mass damper, Journal of Sound and Vibration, vol.319, issue.1-2, pp.445-462, 2009.
DOI : 10.1016/j.jsv.2008.05.018

Z. Yang, H. M. Dai, N. H. Chan, G. C. Ma, and P. Sheng, Acoustic metamaterial panels for sound attenuation in the 50???1000 Hz regime, Applied Physics Letters, vol.96, issue.4, pp.41906-41907, 2010.
DOI : 10.1063/1.3299007

J. Auriault and C. Boutin, Long wavelength inner-resonance cut-off frequencies in elastic composite materials, International Journal of Solids and Structures, vol.49, issue.23-24, pp.3269-3281, 2012.
DOI : 10.1016/j.ijsolstr.2012.07.002

Y. Xiao, J. Wen, and X. Wen, Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators, Journal of Sound and Vibration, vol.331, issue.25, pp.5408-5423, 2012.
DOI : 10.1016/j.jsv.2012.07.016

S. Varanasi, J. S. Bolton, T. H. Siegmund, and R. J. Cipra, The low frequency performance of metamaterial barriers based on cellular structures, Applied Acoustics, vol.74, issue.4, pp.485-495, 2013.
DOI : 10.1016/j.apacoust.2012.09.008

L. D. Viet and N. B. Nghi, On a nonlinear single-mass two-frequency pendulum tuned mass damper to reduce horizontal vibration, Engineering Structures, vol.81, pp.175-180, 2014.
DOI : 10.1016/j.engstruct.2014.09.038

R. Y. Rubinstein and D. P. Kroese, Simulation and the Monte Carlo Method, 2008.

C. Soize, Fundamentals of Random Signal Analysis, Application to Modal Identification in Structural Dynamics, Course given at PUC-Rio University, 1996.

L. Guikhman and A. V. Skorokhod, The Theory of Stochastic Processes, 1979.
DOI : 10.1007/978-3-642-61921-2

M. B. Priestley, The Spectral Analysis of Time Series., Journal of the Royal Statistical Society. Series A (Statistics in Society), vol.151, issue.3, 1981.
DOI : 10.2307/2983035

M. Shinozuka, Simulation of Multivariate and Multidimensional Random Processes, The Journal of the Acoustical Society of America, vol.49, issue.1B, pp.357-367, 1971.
DOI : 10.1121/1.1912338

F. Poirion and C. Soize, Numerical methods and mathematical aspects for simulation of homogeneous and non homogeneous gaussian vector fields, Probabilistic Methods in Applied Physics, pp.17-53, 1995.
DOI : 10.1007/3-540-60214-3_50

URL : https://hal.archives-ouvertes.fr/hal-00770416

L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review, vol.159, issue.1, pp.98-103, 1967.
DOI : 10.1103/PhysRev.159.98

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration illustrated by the StrmerVerlet method, Acta Numerica, vol.12, pp.399-450, 2003.
DOI : 10.1017/S0962492902000144

C. Soize and I. E. Poloskov, Time-domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation, Computers & Mathematics with Applications, vol.64, issue.11, pp.3594-3612, 2012.
DOI : 10.1016/j.camwa.2012.09.010

URL : https://hal.archives-ouvertes.fr/hal-00746280