M. Giordano and . Jiang, Physical modeling of the piano, Eurasip Journal on Appl. Signal Proc, vol.7, pp.926-933, 2004.

A. Derveaux, P. Chaigne, E. Joly, and . Bécache, Time-domain simulation of a guitar: Model and method, The Journal of the Acoustical Society of America, vol.114, issue.6, pp.3368-3383, 2003.
DOI : 10.1121/1.1629302
URL : https://hal.archives-ouvertes.fr/hal-00989042

A. Rhaouti, P. Chaigne, and . Joly, Time-domain modeling and numerical simulation of a kettledrum, The Journal of the Acoustical Society of America, vol.105, issue.6, pp.3545-3562, 1999.
DOI : 10.1121/1.424679

. Bilbao, Conservative numerical methods for nonlinear strings, The Journal of the Acoustical Society of America, vol.118, issue.5, pp.3316-3327, 2005.
DOI : 10.1121/1.2046787

. Askenfelt, Observations on the transient components of the piano tone, pp.15-22, 1993.

H. A. Conklin and J. , Generation of partials due to nonlinear mixing in a stringed instrument, The Journal of the Acoustical Society of America, vol.105, issue.1, pp.536-545, 1999.
DOI : 10.1121/1.424589

A. J. Giordano and . Korty, Motion of a piano string: Longitudinal vibrations and the role of the bridge, The Journal of the Acoustical Society of America, vol.100, issue.6, pp.3899-3908, 1996.
DOI : 10.1121/1.417219

H. A. Conklin and J. , Design and tone in the mechanoacoustic piano. Part II. Piano structure, The Journal of the Acoustical Society of America, vol.100, issue.2, pp.695-708, 1996.
DOI : 10.1121/1.416233

. Balmes, Modeling damping at the material and structure level, Proceedings of the 24th IMAC Conference and exposition on structural dynamics, pp.1314-1353, 2006.

H. Jarvelainen, V. Valimaki, and M. Karjalainen, Audibility of the timbral effects of inharmonicity in stringed instrument tones, Acoustics Research Letters Online, vol.2, issue.3, pp.79-84, 2001.
DOI : 10.1121/1.1374756

B. Bank and H. Lehtonen, Perception of longitudinal components in piano string vibrations, The Journal of the Acoustical Society of America, vol.128, issue.3, pp.117-123, 2010.
DOI : 10.1121/1.3453420

A. Chaigne and . Askenfelt, Numerical simulations of piano strings. I. A physical model for a struck string using finite difference methods, The Journal of the Acoustical Society of America, vol.95, issue.2, pp.1112-1118, 1994.
DOI : 10.1121/1.408459

H. A. Conklin and J. , Design and tone in the mechanoacoustic piano. Part III. Piano strings and scale design, The Journal of the Acoustical Society of America, vol.100, issue.3, pp.1286-1298, 1996.
DOI : 10.1121/1.416017

. Brezinski, Schur complements and applications in numerical analysis of Numerical methods and algorithms, pp.227-258, 2005.

S. Bécache, P. Fauqueux, and . Joly, Stability of perfectly matched layers, group velocities and anisotropic waves, Journal of Computational Physics, vol.188, issue.2, pp.399-403, 2003.
DOI : 10.1016/S0021-9991(03)00184-0

J. Chabassier and S. Imperiale, Stability and dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string, Wave Motion, vol.50, issue.3, pp.456-480, 2013.
DOI : 10.1016/j.wavemoti.2012.11.002
URL : https://hal.archives-ouvertes.fr/hal-00738233

. Fletcher, Normal Vibration Frequencies of a Stiff Piano String, The Journal of the Acoustical Society of America, vol.36, issue.1, pp.203-209, 1964.
DOI : 10.1121/1.1918933

S. Bensa, R. Bilbao, and . Kronland-martinet, The simulation of piano string vibration: From physical models to finite difference schemes and digital waveguides, The Journal of the Acoustical Society of America, vol.114, issue.2
DOI : 10.1121/1.1587146

J. Chabassier, A. Chaigne, and P. Joly, Time domain simulation of a piano. Part 1: model description, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.5, 2012.
DOI : 10.1051/m2an/2013136
URL : https://hal.archives-ouvertes.fr/hal-01085477

G. Weinreich, Coupled piano strings, The Journal of the Acoustical Society of America, vol.63, issue.S1, pp.1474-1484, 1977.
DOI : 10.1121/1.2016722

. Stulov, Dynamic behavior and mechanical features of wool felt, Acta Mechanica, vol.169, issue.1-4, pp.13-21, 2004.
DOI : 10.1007/s00707-004-0104-3

J. P. Giordano and I. Winans, Piano hammers and their force compression characteristics: Does a power law make sense?, The Journal of the Acoustical Society of America, vol.107, issue.4, pp.2248-2255, 2000.
DOI : 10.1121/1.428505

H. Bilhuber and C. A. Johnson, The Influence of the Soundboard on Piano Tone Quality, The Journal of the Acoustical Society of America, vol.11, issue.3, pp.311-320, 1940.
DOI : 10.1121/1.1916039

J. Mamou-mani, C. Frelat, and . Besnainou, Numerical simulation of a piano soundboard under downbearing, The Journal of the Acoustical Society of America, vol.123, issue.4, pp.2401-2406, 2008.
DOI : 10.1121/1.2836787

K. Hasselman, Modal coupling in lightly damped structures, AIAA Journal, vol.14, issue.11, pp.1627-1628, 1976.
DOI : 10.2514/3.7259

X. Ege, M. Boutillon, and . Rébillat, Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid-frequency ranges, Journal of Sound and Vibration, vol.332, issue.5
DOI : 10.1016/j.jsv.2012.10.012
URL : https://hal.archives-ouvertes.fr/hal-00743291

M. Podlesak and A. R. Lee, Dispersion of waves in piano strings, The Journal of the Acoustical Society of America, vol.83, issue.1, pp.305-317, 1988.
DOI : 10.1121/1.396432

J. Cuenca and R. Caussé, Three-dimensional interaction between strings, bridge and soundboard in modern piano's treble range, Proc. of the 19th International Congress on Acoustics, pp.1705-1710, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01161420

A. Chabassier, P. Chaigne, and . Joly, Transitoires de piano et non-linéarités des cordes : Mesures et simulations (Piano transients and strings nonlinearity: Measurements and simulations), Proceedings of the 10th French Acoustical Society Meeting, p.225, 2010.

B. Bank and L. Sujbert, Generation of longitudinal vibrations in piano strings: From physics to sound synthesis, The Journal of the Acoustical Society of America, vol.117, issue.4, pp.2268-2278, 2005.
DOI : 10.1121/1.1868212

J. Chabassier and P. Joly, Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: Application to the vibrating piano string, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.45-48, pp.2779-2795, 2010.
DOI : 10.1016/j.cma.2010.04.013
URL : https://hal.archives-ouvertes.fr/inria-00534473

. Lambourg, Modèle temporel pour la simulation numérique de plaques vibrantes

. Applicationàapplicationà-la-synthèse-sonore, Time-domain modeling for the numerical simulation of vibrating plates. Application to sound synthesis, 1997.

E. Askenfelt and . Jansson, From touch to string vibrations. II: The motion of the key and hammer, The Journal of the Acoustical Society of America, vol.90, issue.5, pp.2383-2393, 1991.
DOI : 10.1121/1.402043

A. Touzé and . Chaigne, Lyapunov exponents from experimental time series: Application to cymbal vibrations, Acustica united with Acta Acustica, vol.86, pp.557-567, 2000.

W. D. Anderssen and . Stuart, The challenge of piano maker, The Math. Scientist, vol.32, pp.71-82, 2007.

J. Chabassier and M. Duruflé, Physical parameters for piano modeling, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00688679