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