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Article Dans Une Revue Journal of Sound and Vibration Année : 2013

Flute-like musical instruments: a toy model investigated through numerical continuation

Soizic Terrien
Christophe Vergez
Benoît Fabre

Résumé

Self-sustained musical instruments (bowed string, woodwind and brass instruments) can be modeled by nonlinear lumped dynamical systems. Among these instruments, flutes and flue organ pipes present the particularity to be modeled as a delay dynamical system. In this paper, such a system, a toy model of flute-like instruments, is studied using numerical continuation. Equilibrium and periodic solutions are explored with respect to the blowing pressure, with focus on amplitude and frequency evolutions along the different solution branches, as well as "jumps" between periodic solution branches. The influence of a second model parameter (namely the inharmonicity) on the behaviour of the system is addressed. It is shown that harmonicity plays a key role in the presence of hysteresis or quasi-periodic regime. Throughout the paper, experimental results on a real instrument are presented to illustrate various phenomena, and allow some qualitative comparisons with numerical results.
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Dates et versions

hal-00721873 , version 1 (30-07-2012)
hal-00721873 , version 2 (06-02-2013)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

Citer

Soizic Terrien, Christophe Vergez, Benoît Fabre. Flute-like musical instruments: a toy model investigated through numerical continuation. Journal of Sound and Vibration, 2013, 332 (15), pp.3833-3848. ⟨10.1016/j.jsv.2013.01.041⟩. ⟨hal-00721873v2⟩
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