Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

Conference object English OPEN
Karkar , Sami ; Vergez , Christophe ; Cochelin , Bruno (2012)
  • Publisher: HAL CCSD
  • Subject: [ PHYS.MECA.ACOU ] Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph] | physical models | numerical continuation | [ SPI.ACOU ] Engineering Sciences [physics]/Acoustics [physics.class-ph] | periodic solutions | nonlinear dynamical systems

International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a se... View more
  • References (11)
    11 references, page 1 of 2

    [1] Sami Karkar, Christophe Vergez, and Bruno Cochelin. Toward the systematic investigation of periodic solutions in single reed woodwind instruments. In Proceedings of the 20th International Symposium on Music Acoustics (Associated Meeting of the International Congress on Acoustics). International Commission for Acoustics, August 2010.

    [2] Fabrice Silva. Emergence des auto-oscillations dans un instrument de musique a` anche simple (Sound production in single reed woodwind instruments). PhD thesis, Aix-Marseille University, LMA - CNRS, 2009.

    [3] Bruno Cochelin and Christophe Vergez. A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions. Journal of Sound and Vibration, 324:243-262, 2009.

    [4] A. Hirschberg. Mechanics of Musical Instruments, chapter 7, pages 291-369. Number 355 in CISM Courses and Lectures. Springer, Wien - New York, 1995.

    [5] Fabrice Silva. Moreesc, modal resonator-reed interaction simulation code, 2009. (last viewed 3/16/2011).

    [6] Sami Karkar, Re´my Arquier, Bruno Cochelin, Christophe Vergez, Arnaud Lazarus, and Olivier Thomas. MANLAB 2.0, an interactive continuation software, 2010. (last visited 28/06/2011).

    [7] E. J. Doedel and B. E. Oldeman. AUTO-07P : Continuation and Bifurcation Software for Ordinary Differential Equations. Concordia University, Montreal, Canada, January 2009. (last visited 28 feb. 2012).

    [8] Philippe Guillemain, Jean Kergomard, and Thierry Voinier. Real-time synthesis of clarinet-like instruments using digital impedance models. Journal of the Acoustical Society of America, 118(1):483-494, 2005.

    [9] A. Lazarus and O. Thomas. A harmonic-based method for computing the stability of periodic solutions of dynamical systems. Comptes Rendus de Me´canique, 338:510-517, 2010.

    [10] Sami Karkar, Christophe Vergez, and Bruno Cochelin. Oscillation threshold of a clarinet model: a numerical continuation approach. Journal of the Acoustical Society of America, 131:698-707, jan 2012.

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