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Modeling the Mechanical Response of Clarinet Reed
Ye Lu2011-03-14
Reed Instruments
Stefan Bilbao, 2009, Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics
A Single-reed Woodwind Mouthpiece
F. Avanzini and M. van Walstijn, “Modeling the mechanical response of the reed-mouthpiece-lip system of a clarinet. 1. A one-dimensional distributed model”, Acta Acust, 90, 537-547 (2004).
Single degree of freedom with constant parameters can only be assumed for oscillations at small amplitudes
Reed beating is usually incorporated in a non-physical way by imposing a maximum allowed displacement for the reed tip
The dependence of the reed-mouthpiece system on the lip embouchure is not considered in lumped model
Disadvantage of Lumped Model
A bar with non-uniform cross-sectional area
Clamped to the mouthpiece at one end
Additional constraints provided by the mouthpiece profile and interaction with the lip
Distributed Representation of the Reed
The Model
One-dimensional: assume no torsional modes in the reed
No attempt to model the air flow in the reed channel or to simulate the acoustical resonator
Limitation of the Model
Boundary Conditions
Interaction with the mouthpiece and the lip
Interaction with the mouthpiece and the lip
Measurements
Finite Difference Method
Numerical Simulation
Some Schemes
Some Schemes
Discretization
Unconditional stable when Θ > 1/4
Implicit θ-Scheme
Implicit θ-Scheme
http://www.tandfonline.com/doi/abs/10.1080/10236190802385298#preview
The reed tip can not exceed a certain value
The tip is not stopped suddenly but rather gradually
Simulation Result
Convergence of the Scheme
Thank You!