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How well can linear stability analysis predict the behavior of an outward valve brass instrument model ?

Lionel Velut 1 Christophe Vergez 1 Joël Gilbert 2 Mithra Djahanbani 1
1 Sons
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille] : UPR7051
Abstract : A physical model of brass instrument is considered in this paper : a one degree-of-freedom outward striking valve for the lips, non-linearly coupled to a modal representation of the air column. It is studied through linear stability analysis of the equilibrium solution. This approach provides the threshold value of the blowing pressure at which an instability occurs, and the value of the frequency of this instability. The validity of the results of this method is theoretically limited to the neighborhood of the equilibrium solution. This paper checks the efficiency of linear stability analysis to understand the behavior of the model computed through time-domain simulations. As expected, a good agreement is observed between linear stability analysis and numerical simulations of the complete nonlinear model around the oscillation threshold. For blowing pressures far above the oscillation threshold, the picture is more contrasted. In most cases tested, a periodic regime coherent with the linear stability analysis results is observed, but over-blowing, quasi-periodicity and period-doubling also occur. Interestingly, linear stability analysis predicts the production of the pedal note by a trombone, for which only nonlinear hypotheses had been previously proposed. LSA also predicts the production of a saxhorn note that had never been documented, but known by musicians.
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https://hal.archives-ouvertes.fr/hal-01245846
Contributeur : Lionel Velut <>
Soumis le : jeudi 17 décembre 2015 - 17:03:55
Dernière modification le : lundi 23 novembre 2020 - 21:12:03
Archivage à long terme le : : vendredi 18 mars 2016 - 14:50:27

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  • HAL Id : hal-01245846, version 1

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Lionel Velut, Christophe Vergez, Joël Gilbert, Mithra Djahanbani. How well can linear stability analysis predict the behavior of an outward valve brass instrument model ?. 2015. ⟨hal-01245846v1⟩

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