Nonlinear modes of clarinet-like musical instruments

Abstract : The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Type de document :
Article dans une revue
Journal of Sound and Vibration, Elsevier, 2009, 324 (3-5), pp.983-1002. 〈10.1016/j.jsv.2009.02.043〉
Liste complète des métadonnées

Littérature citée [32 références]  Voir  Masquer  Télécharger
Contributeur : Christophe Vergez <>
Soumis le : jeudi 19 mars 2009 - 16:31:27
Dernière modification le : lundi 29 janvier 2018 - 16:06:02
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:23:41


Fichiers produits par l'(les) auteur(s)



Daniel Noreland, Sergio Bellizzi, Christophe Vergez, Robert Bouc. Nonlinear modes of clarinet-like musical instruments. Journal of Sound and Vibration, Elsevier, 2009, 324 (3-5), pp.983-1002. 〈10.1016/j.jsv.2009.02.043〉. 〈hal-00180211v2〉



Consultations de la notice


Téléchargements de fichiers