, 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
, Analyse et synthèse de sons de piano par modèles physiques et de signaux, 2003.
, 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
, Conserved quantities of some Hamiltonian wave equations after full discretization, Numerische Mathematik, vol.103, issue.2, pp.197-223, 2006.
DOI : 10.1007/s00211-006-0680-3
, Numerical simulation of piano strings. i. a physical model for a struck string usin finite-difference methods, pp.1112-1118, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00688964
, Explicit energy-conserving schemes for the three-body problem, Journal of Computational Physics, vol.83, issue.2, pp.485-493, 1989.
DOI : 10.1016/0021-9991(89)90132-0
, 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
, 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
, Accuracy and conservation properties in numerical integration: the case of the korteweg-de-vries equation, Numerische Mathematik, vol.75, issue.4, pp.421-445, 1997.
, Standard nearest-neighbour discretizations of Klein???Gordon models cannot preserve both energy and linear momentum, Journal of Physics A: Mathematical and General, vol.39, issue.23, pp.7217-7226, 2006.
DOI : 10.1088/0305-4470/39/23/003
, Finite-difference schemes for nonlinear wave equation that inherit energy conservation property, Journal of Computational and Applied Mathematics, vol.134, issue.1-2, pp.37-57, 2001.
DOI : 10.1016/S0377-0427(00)00527-6
, 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
, Hyperbolic systems of conservation laws, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00113734
, Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13-14, pp.1763-1783, 2000.
DOI : 10.1016/S0045-7825(00)00189-4
URL : https://hal.archives-ouvertes.fr/hal-01363585
, On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry, Computer Methods in Applied Mechanics and Engineering, vol.134, issue.3-4, pp.197-222, 1996.
DOI : 10.1016/0045-7825(96)01009-2
, Conservative numerical methods for, Journal of Computational Physics, vol.56, issue.1, pp.28-41, 1984.
DOI : 10.1016/0021-9991(84)90081-0
, Backward analysis of numerical integrators and symplectic methods, Ann. Numer. Math, vol.1, issue.1-4, pp.107-132, 1994.
, The life-span of backward error analysis for numerical integrators, Numerische Mathematik, vol.76, issue.4, pp.441-462, 1997.
DOI : 10.1007/s002110050271
, Differential equations, dynamical systems, and an introduction to chaos, p.417, 2004.
, Formation of singularities in one-dimensional nonlinear wave propagation, Communications on Pure and Applied Mathematics, vol.5, issue.3, pp.377-405, 1974.
DOI : 10.1002/cpa.3160270307
, Effective computational methods for wave propagation, 2008.
, Symplectic-energy-momentum preserving variational integrators, Journal of Mathematical Physics, vol.40, issue.7, p.3353, 1999.
DOI : 10.1063/1.532892
URL : http://authors.library.caltech.edu/3727/1/KANjmp99.pdf
, On a class of discretizations of Hamiltonian nonlinear partial differential equations, Physica D: Nonlinear Phenomena, vol.183, issue.1-2, pp.68-86, 2003.
DOI : 10.1016/S0167-2789(03)00153-2
, Formation of singularities for wave equations including the nonlinear vibrating string, Communications on Pure and Applied Mathematics, vol.23, issue.3, pp.241-263, 1980.
DOI : 10.1002/cpa.3160330304
, Transverse and longitudinal mode coupling in a free vibrating soft string, Physics Letters A, vol.310, issue.2-3, pp.148-160, 2003.
DOI : 10.1016/S0375-9601(03)00264-0
, Global classical solutions for a class of quasilinear hyperbolic systems, Applicable Analysis, vol.28, issue.3-4, 1994.
DOI : 10.1080/00036810108840968
, A NON-STANDARD FINITE-DIFFERENCE SCHEME FOR CONSERVATIVE OSCILLATORS, Journal of Sound and Vibration, vol.240, issue.3, pp.587-591, 2001.
DOI : 10.1006/jsvi.2000.3167
, A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton's principle, Journal of Sound and Vibration, vol.285, issue.1-2, pp.477-482, 2005.
DOI : 10.1016/j.jsv.2004.09.027
, Theoretical Acoustics, 1968.
DOI : 10.1063/1.3035602
, Characteristics of piano sound spectra, 1993.
, Backward Error Analysis for Numerical Integrators, SIAM Journal on Numerical Analysis, vol.36, issue.5, pp.1549-1570, 1999.
DOI : 10.1137/S0036142997329797
, Numerical solutions of forced vibration and whirling of a nonlinear string using the theory of a cosserat point, Journal of Sound and Vibration, vol.197, issue.1, pp.85-101, 1996.
, Symplectic integrators for Hamiltonian problems: an overview, Acta Numerica, vol.432, 1991.
DOI : 10.1016/0021-8928(84)90078-9
, Numerical solution of a nonlinear Klein-Gordon equation, Journal of Computational Physics, vol.28, issue.2, pp.271-278, 1978.
DOI : 10.1016/0021-9991(78)90038-4
, Mécanique de la corde vibrante, 1993.
, Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation, Computer Methods in Applied Mechanics and Engineering, vol.107, issue.3, pp.341-391, 1993.
DOI : 10.1016/0045-7825(93)90073-7
, Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators, Physics Letters A, vol.133, issue.3, pp.134-139, 1988.
DOI : 10.1016/0375-9601(88)90773-6