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Deux études d'un instrument de musique de type clarinette : analyse des fréquences propres du résonateur et calcul des auto-oscillations par décomposition modale

Abstract : Woodwind instruments are self-sustained oscillators resulting from the interaction between a linear resonator and a nonlinear excitator. This thesis is devoted to the study of the natural oscillations (the resonance frequencies and modes) of such systems, from two different points of view.

The first part deals with the analysis of the resonance frequencies. With the use of frequency dependent length corrections, we estimate systematically the effect on the resonance frequencies of different bore perturbations inserted in cylindrical instruments. Applications to a clarinet resonator and comparisons with impedance measurements are then presented. A relatively good overall compensation between tone holes, bore taper and bell is highlighted and the origin of the tuning default between the first two registers of the clarinet is discussed. Then, we focus on the effect of the register hole only using an elementary model. Performing optimization on the register hole location results in an "optimal" location, close to the one chosen by clarinet makers ; then attempts are made numerically to improve the situation by introducing small perturbations in the higher part of the resonator.

The second part is devoted to the study of the self-sustained oscillations with the help of modal analysis. The foundations of the modelling procedure are briefly reviewed (unidimensional dissipative system) resulting in two equivalent formulations. The decomposition of the Green function on the modes of the resonator leads to an original description of the dynamics similar to a Van der Pol equation when only one mode is considered. The reduction to one mode is investigated analytically giving information about stability. Then, a numerical study is performed with emphasis to a multimodes resonator. Even if the dynamic is ensured by a few number of components, all of them participate in the oscillation by nonlinear coupling. A variation in the playing frequency is also highlighted during initial transients. Finally, the decomposition is validated with the harmonic balance technique.
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Contributor : Vincent Debut <>
Submitted on : Monday, March 7, 2005 - 3:06:46 PM
Last modification on : Thursday, January 23, 2020 - 6:22:03 PM
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  • HAL Id : tel-00008711, version 1

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Vincent Debut. Deux études d'un instrument de musique de type clarinette : analyse des fréquences propres du résonateur et calcul des auto-oscillations par décomposition modale. Acoustique [physics.class-ph]. Université de la Méditerranée - Aix-Marseille II, 2004. Français. ⟨tel-00008711⟩

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