Free Access
Volume 50, Number 1, January-February 2016
Page(s) 93 - 133
Published online 16 November 2015
  1. J. Bensa, S. Bilbao, R. Kronland-Martinet and J. O. Smith III, The simulation of piano string vibration: from physical models to finite difference schemes and digital waveguides. J. Acoust. Soc. Am. 114 (2003) 1095–1107. [Google Scholar]
  2. D.P. Bertsekas, Nonlinear Programming, 2nd edn.. Athena Scientific (1999) 1–780. [Google Scholar]
  3. J. Berthaut, M.N. Ichchou and L. Jezequel, Piano soundboard: structural behavior, numerical and experimental study in the modal range. Appl. Acoust. 64 (2003) 1113–1136. [CrossRef] [Google Scholar]
  4. S. Bilbao, Conservative numerical methods for nonlinear strings. J. Acoust. Soc. Am. 118 (2005) 3316–3327. [CrossRef] [Google Scholar]
  5. X. Boutillon, Model for piano hammers: Experimental determination and digital simulation. J. Acoust. Soc. Am. 83 (1988) 746–754. [CrossRef] [Google Scholar]
  6. B. Bank and L. Sujbert, A piano model including longitudinal string vibrations. Proc. of the Digital Audio Effects Conference (2004) 89–94. [Google Scholar]
  7. J. Chabassier, Modélisation et simulation numérique d’un piano par modèles physiques. Ph.D. thesis, École Polytechnique (2012). [Google Scholar]
  8. J. Chabassier and M. Duruflé, Physical parameters for piano modeling. Technical Report RT-0425, INRIA (2012). [Google Scholar]
  9. J. Chabassier and M. Duruflé, Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound. J. Sound Vibr. 333 (2014) 7198–7215. [CrossRef] [Google Scholar]
  10. 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 50 (2012) 456–480. [CrossRef] [Google Scholar]
  11. J. Chabassier and S. Imperiale, Introduction and study of fourth order theta schemes for linear wave equations. J. Comput. Appl. Math. 245 (2013) 194–212. [CrossRef] [Google Scholar]
  12. J. Chabassier and P. Joly, Energy preserving schemes for nonlinear hamiltonian systems of wave equations. application to the vibrating piano string. Comput. Meth. Appl. Mech. Eng. 199 (2010) 2779–2795. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Chabassier, A. Chaigne and P. Joly, Time domain simulation of a piano. Part I: Model description. ESAIM: M2AN 48 (2014) 1241–1278. [CrossRef] [EDP Sciences] [Google Scholar]
  14. A. Chaigne and A. Askenfelt, Numerical simulation of piano strings I. A physical model for a struck string using finite-difference methods. J. Acoust. Soc. Am. 95 (1994) 1112–1118. [CrossRef] [Google Scholar]
  15. A. Chaigne and A. Askenfelt, Numerical simulations of piano strings II. Comparisons with measurements and systematic exploration of some hammer string parameters. J. Acoust. Soc. Am. 95 (1994) 1631–1640,. [CrossRef] [Google Scholar]
  16. G. Cohen and P. Grob, Mixed higher order spectral finite elements for reissner–mindlin equations. SIAM J. Sci. Comput. 29 (2007) 986–105. [CrossRef] [Google Scholar]
  17. F. Collino and C. Tsogka, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66 (2001) 294–307. [Google Scholar]
  18. H.A. Conklin, Piano strings and “phantom” partials. J. Acoust. Soc. Am. 102 (1997) 659. [CrossRef] [Google Scholar]
  19. R. Dautray, J.L. Lions, C. Bardos, M. Cessenat, P. Lascaux, A. Kavenoky, B. Mercier, O. Pironneau, B. Scheurer and R. Sentis, Mathematical analysis and numerical methods for science and technology. In vol. 6. Springer (2000). [Google Scholar]
  20. G. Derveaux, A. Chaigne, P. Joly and E. Bécache, Time-domain simulation of a guitar: Model and method. J. Acoust. Soc. Am. 114 (2003) 3368–3383. [CrossRef] [PubMed] [Google Scholar]
  21. J. Diaz and M. Grote. Energy conserving explicit local time-stepping for second-order wave equations. Siam J. Sci. Comput. 31 (2009) 1985–2014. [CrossRef] [MathSciNet] [Google Scholar]
  22. K. Ege, X. Boutillon and M. Rébillat, Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid-frequency ranges. J. Sound Vibr. 332 (2013) 1288–1305. [CrossRef] [Google Scholar]
  23. S. Fauqueux and G. Cohen, Mixed finite elements with mass-lumping for the transient wave equation. J. Comput. Acoustics 8 (2000) 171–188. [CrossRef] [Google Scholar]
  24. T. Fouquet F. Collino and P. Joly, Conservative space-time mesh refinement methods for the fdtd solution of maxwell’s equations. J. Comput. Phys. 211 (2006) 9–35. [CrossRef] [MathSciNet] [Google Scholar]
  25. N. Giordano, Simple model of a piano soundboard. J. Acoust. Soc. Am. 102 (1997) 1159–1168. [CrossRef] [Google Scholar]
  26. N. Giordano and M. Jiang, Physical modeling of the piano. EURASIP J. Appl. Signal Process. 2004 (2004) 926–933. [CrossRef] [Google Scholar]
  27. J.R. Hutchinson, Shear coefficients for timoshenko beam theory. J. Appl. Mech. 68 (2000) 87–92. [CrossRef] [Google Scholar]
  28. A. Izadbakhsh, J. McPhee and S. Birkett, Dynamic modeling and experimental testing of a piano action mechanism with a flexible hammer shank. J. Comput. Nonlin. Dyn. 3 (2008) 1–10. [CrossRef] [Google Scholar]
  29. P. Joly, Variational methods for time-dependent wave propagation problems. In vol. 31: Topics in Computational Wave Propagation. Springer, Berlin (2003) 201–264. [Google Scholar]
  30. J. Kindel and I. Wang, Vibrations of a piano soundboard: Modal analysis and finite element analysis. J. Acoust. Soc. Am. Suppl. 1 81 (1987) S61. [CrossRef] [Google Scholar]
  31. A. Mamou-Mani, J. Frelat and C. Besnainou, Numerical simulation of a piano soundboard under downbearing. J. Acoust. Soc. Am. 123 (2008) 2401–2406. [CrossRef] [PubMed] [Google Scholar]
  32. L. Ortiz-Berenguer and F. Casajus-Quiros, Modeling of piano sounds using fem simulation of soundboard vibration. Proc. of Acoustics 08 Paris (2008) 6252–6256. [Google Scholar]
  33. G.R.W. Quispel and G.S Turner, Discrete gradient methods for solving odes numerically while preserving a first integral. J. Phys. A 29 (1996) 341–349. [CrossRef] [MathSciNet] [Google Scholar]
  34. L. Rhaouti, A. Chaigne and P. Joly, Time-domain modeling and numerical simulation of a kettledrum. J. Acoust. Soc. Am. 105 (1999) 3545–3562. [CrossRef] [Google Scholar]
  35. W. Strauss and L. Vazquez, Numerical solution of a nonlinear klein-gordon equation. J. Comput. Phys. 28 (1978) 271–278. [Google Scholar]
  36. G. Weinreich, Coupled piano strings. J. Acoust. Soc. Am. 62 (1977) 1474–1484. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you