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Analysis of the self-sustained oscillation of clarinet-like musical instruments using the nonlinear modes approach

Abstract : Musical wind instruments are interesting examples of nonlinear vibrating systems. The way in which a self- sustained oscillation is formed is surprisingly complex, even for a simplified model. In short, a wind instrument consists of a resonator and a generator. The resonator is the air column inside the instrument, and is usually characterized by the linear wave equation. The generator consists of some kind of pressure controlled valve, where the relationship between air flow and pressure is starkly non-linear. A simplistic model of sound generation can be based on the assumption that the pressure controlled valve functions as a negative resistance at one of the resonance frequencies of the resonator. Such a model, however, neglects the modal coupling due to the non-linearities that are ultimately the primary reason why different wind instument sound so different. The aim of this paper is to study how limit cycles of a clarinet-like instrument can be treated in the framework of nonlinear normal modes (NNM). The reason for persunig this subject is to ultimately be able to derive models of reduced complexity, which are of interest for sound synthesis. Another goal is to identify important control parameters (functions of such entities as blowing pressure, pincing force and position of the player’s lips on the reed etc) which can be regulated by a musician in an intuitive way, without a long period of training.
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https://hal.archives-ouvertes.fr/hal-00093638
Contributor : Sergio Bellizzi <>
Submitted on : Wednesday, September 13, 2006 - 3:49:24 PM
Last modification on : Thursday, January 23, 2020 - 6:22:04 PM

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  • HAL Id : hal-00093638, version 1

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Daniel Noreland, Sergio Bellizzi, Robert Bouc, Bruno Cochelin, Jean Kergomard, et al.. Analysis of the self-sustained oscillation of clarinet-like musical instruments using the nonlinear modes approach. 2nd International Conference on Nonlinear Normal Modes and Localization in Vibrating Systems, Jun 2006, Samos, Greece. ⟨hal-00093638⟩

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