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Modeling the Mechanical Response of Clarinet Reed

Modeling the Mechanical Response of Clarinet Reed

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Modeling the Mechanical Response of Clarinet Reed

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  1. Modeling the Mechanical Response of Clarinet Reed Ye Lu 2011-03-14

  2. Reed Instruments

  3. A Single-reed Woodwind Mouthpiece • Stefan Bilbao, 2009, Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics

  4. 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”, ActaAcust, 90, 537-547 (2004).

  5. Disadvantage of Lumped Model • 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

  6. Distributed Representation of the Reed • 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

  7. The Model

  8. Limitation of 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

  9. Boundary Conditions

  10. Interaction with the mouthpiece and the lip

  11. Interaction with the mouthpiece and the lip

  12. Measurements

  13. Numerical Simulation • Finite Difference Method

  14. Some Schemes

  15. Some Schemes

  16. Discretization

  17. Implicit θ-Scheme • Unconditional stable when Θ > 1/4

  18. Implicit θ-Scheme http://www.tandfonline.com/doi/abs/10.1080/10236190802385298#preview

  19. Simulation Result • The reed tip can not exceed a certain value • The tip is not stopped suddenly but rather gradually

  20. Convergence of the Scheme

  21. Thank You!