Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 521–534 | Cite as

Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure

Original Paper

Abstract

Reed instruments are modeled as self-sustained oscillators driven by the pressure inside the mouth of the musician. A set of nonlinear equations connects the control parameters (mouth pressure, lip force) to the system output, hereby considered as the mouthpiece pressure. Clarinets can then be studied as dynamical systems; their steady behavior being dictated uniquely by the values of the control parameters. Considering the resonator as a lossless straight cylinder is a dramatic yet common simplification that allows for simulations using nonlinear iterative maps.

This paper investigates analytically the effect of a linearly increasing blowing pressure on the behavior of this simplified clarinet model. When the control parameter varies, results from the so-called dynamic bifurcation theory are required to properly analyze the system. This study highlights the phenomenon of bifurcation delay and defines a new quantity, the dynamic oscillation threshold. A theoretical estimation of the dynamic oscillation threshold is proposed and compared with numerical simulations.

Keywords

Musical acoustics Clarinet-like instruments Iterated maps Dynamic bifurcation Bifurcation delay Transient processes 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • B. Bergeot
    • 1
  • A. Almeida
    • 1
  • C. Vergez
    • 2
  • B. Gazengel
    • 1
  1. 1.Laboratoire d’Acoustique de l’Université du Maine (LAUM-CNRS UMR 6613)Le Mans Cedex 9France
  2. 2.Laboratoire de Mécanique et Acoustique (LMA-CNRS UPR7051)Marseille Cedex 20France

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