1. Nonlinear modes of clarinet-like musical instruments
- Author
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Robert Bouc, Sergio Bellizzi, Daniel Noreland, Christophe Vergez, Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM), The study presented in this paper was lead with the support of the French National Research Agency ANR winthin the CONSONNES project. The first author was financed by the French Ministry of Research through a post-doctoral grant., ANR-05-BLAN-0097,CONSONNES,CONtrôle de SONs instrumentaux Naturels Et Synthétiques(2005), and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Acoustics and Ultrasonics ,Modal analysis ,FOS: Physical sciences ,Musical instrument ,02 engineering and technology ,Physics - Classical Physics ,01 natural sciences ,PACS: 43.75.Pq 43.25.Ts ,0203 mechanical engineering ,Normal mode ,Control theory ,Limit cycle ,0103 physical sciences ,invariant manifold ,Transient response ,amplitude-phase formulation ,010301 acoustics ,Mathematics ,[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph] ,Mechanical Engineering ,Mathematical analysis ,reed woodwind instruments ,Classical Physics (physics.class-ph) ,Condensed Matter Physics ,[PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph] ,Nonlinear system ,020303 mechanical engineering & transports ,Mechanics of Materials ,Phase space ,Ordinary differential equation ,nonlinear modes ,reduced model - Abstract
International audience; 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.
- Published
- 2009