D. Ross, E. E. Ungar, and E. M. Kerwin, Damping of plate flexural vibrations by means of viscoelastic laminae, Structural damping, pp.49-97, 1959.

, J.P. Den Hartog. Mechanical Vibrations. McGraw-Hill, 1934.

H. C. Tsai and G. C. Lin, Optimum tuned mass dampers for minimizing steady-state response of support excited and damped system, Earthquake Engineering and Structural Dynamics, vol.11, pp.846-862, 1993.

S. Krenk and J. Hogsberg, Tuned mass absorber on a flexible structure, Journal of Sound and Vibration, vol.333, pp.1577-1595, 2014.

M. A. Mironov, Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval, 1988.

V. V. Krylov and F. J. 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.

V. B. Georgiev, J. Cuenca, F. Gautier, L. Simon, and V. V. 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.

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.

V. Denis, A. Pelat, F. Gautier, and B. 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.
URL : https://hal.archives-ouvertes.fr/hal-01288274

D. J. O'boy, V. V. Krylov, and V. 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.

M. R. Shepherd, C. A. Mccormick, S. C. Conlon, and P. A. Feurtado, Modeling and optimization of acoustic black hole vibration absorbers, The Journal of the Acoustical Society of America, vol.141, issue.5, pp.4034-4034, 2017.

L. Tang and L. Cheng, Enhanced acoustic black hole effect in beams with a modified thickness profile and extended platform, Journal of Sound and Vibration, vol.391, pp.116-126, 2017.

J. Deng, L. Zheng, P. Zeng, Y. Zuo, and O. Guasch, Passive constrained viscoelastic layers to improve the efficiency of truncated acoustic black holes in beams, Mechanical Systems and Signal Processing, vol.118, pp.461-476, 2019.

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

S. C. Conlon, J. B. Fahnline, and F. 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.

L. Zhao, S. C. Conlon, and F. Semperlotti, Broadband energy harvesting using acoustic black hole structural tailoring, Smart Materials and Structures, vol.23, issue.6, p.65021, 2014.

V. V. Krylov and R. E. Winward, Experimental investigation of the acoustic black hole effect for flexural waves in tapered plates, Journal of Sound and Vibration, vol.300, issue.1-2, pp.43-49, 2007.

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

E. P. Bowyer, D. J. O'boy, V. V. Krylov, and F. Gautier, Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile, Applied Acoustics, vol.74, issue.4, pp.553-560, 2013.

E. P. Bowyer, D. J. O'boy, V. V. Krylov, and J. L. 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.

P. A. Feurtado and S. C. Conlon, An experimental investigation of acoustic black hole dynamics at low, mid, and high frequencies, Journal of Vibration and Acoustics, vol.138, issue.6, p.61002, 2016.

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.

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, pp.134-145, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01442428

O. Gendelman, L. I. Manevitch, A. F. Vakakis, and R. M. Closkey, Energy pumping in nonlinear mechanical oscillators, I: dynamics of the underlying Hamiltonian systems, Journal of Applied Mechanics, vol.68, issue.1, pp.34-41, 2001.

A. F. Vakakis, L. I. Manevitch, O. Gendelman, and L. Bergman, Dynamics of linear discrete systems connected to local, essentially non-linear attachments, Journal of Sound and Vibration, vol.264, pp.559-577, 2003.
DOI : 10.1016/s0022-460x(02)01207-5

A. F. Vakakis, O. V. Gendelman, L. A. Bergman, D. M. Mcfarland, G. Kerschen et al., Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Springer, series: Solid Mechanics and its Applications, 2009.
DOI : 10.1098/rsta.2017.0132

Y. S. Lee, F. Nucera, A. F. Vakakis, D. M. Mcfarland, and L. A. Bergman, Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments, Physica D: Nonlinear Phenomena, vol.238, issue.18, pp.1868-1896, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01510829

C. H. Lamarque, O. V. Gendelman, A. T. Savadkoohi, and E. Etcheverria, Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink, Acta Mechanica, vol.221, issue.1 -2, pp.175-200, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00803449

E. Gourc, G. Michon, S. Séguy, and A. Berlioz, Targeted energy transfer under harmonic forcing with a vibro-impact nonlinear energy sink: Analytical and experimental developments, Journal of Vibration and Acoustics, vol.137, issue.3, p.31008, 2015.
DOI : 10.1115/1.4029285

URL : https://hal.archives-ouvertes.fr/hal-01820057

M. A. Al-shudeifat, A. F. Vakakis, and L. A. Bergman, Shock mitigation by means of low-to high-frequency nonlinear targeted energy transfers in a large-scale structure, Journal of Computational and Nonlinear Dynamics, vol.11, issue.2, p.21006, 2015.

G. Pennisi, C. Stephan, E. Gourc, and G. Michon, Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced, Nonlinear Dynamics, vol.88, issue.3, pp.1769-1784, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01829677

R. P. Goel, Transverse vibrations of tapered beams, Journal of Sound and Vibration, vol.47, issue.1, pp.1-7, 1976.
DOI : 10.1016/0022-460x(76)90403-x

J. R. Banerjee and F. W. Williams, Exact Bernoulli-Euler dynamic stiffness matrix for a range of tapered beams, International Journal for Numerical Methods in Engineering, vol.21, issue.12, pp.2289-2302, 1985.

R. A. Ibrahim, Vibro-impact dynamics: modeling, mapping and applications, vol.43, 2009.

S. Bilbao, A. Torin, and V. Chatziioannou, Numerical modeling of collisions in musical instruments, Acta Acustica united with Acustica, vol.101, issue.1, pp.155-173, 2015.

C. Issanchou, S. Bilbao, J. Carrou, C. Touzé, and O. Doaré, A modal-based approach to the nonlinear vibration of strings against a unilateral obstacle: Simulations and experiments in the pointwise case, Journal of Sound and Vibration, vol.393, pp.229-251, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01461730

W. Goldsmith, Impact. Courier Corporation, 2001.

V. Chatziioannou and M. Van-walstijn, Energy conserving schemes for the simulation of musical instrument contact dynamics, Journal of Sound and Vibration, vol.339, pp.262-279, 2015.

M. Farid and O. V. Gendelman, Response regimes in equivalent mechanical model of strongly nonlinear liquid sloshing, International Journal of Non-Linear Mechanics, vol.94, pp.146-159, 2017.

K. H. Hunt and F. R. Crossley, Coefficient of restitution interpreted as damping in vibroimpact, Journal of applied mechanics, vol.42, issue.2, pp.440-445, 1975.
URL : https://hal.archives-ouvertes.fr/hal-01333795

S. Bilbao, Numerical sound synthesis: finite difference schemes and simulation in musical acoustics, 2009.
DOI : 10.1007/978-3-662-55004-5_19

M. Van-walstijn and J. Bridges, Simulation of distributed contact in string instruments: a modal expansion approach, Signal Processing Conference (EUSIPCO), 2016 24th European, pp.1023-1027, 2016.

V. Yastrebov, Numerical Methods in Contact Mechanics. Wiley-ISTE, 2013.

B. Brogliato and V. Acary, Numerical methods for nonsmooth dynamical systems, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530