NINTH INTERNATIONAL CONGRESS ONSOUND AND VIBRATIONS, ICSV9SIMULATION OF WIND INSTRUMENTS BASED ONA BOUNDARY INTEGRAL FORMULATION FORTHE INPUT IMPEDANCE EVALUATION

摘要

The numerical simulation of a reed-driven musical instrument represents a challengingrnproblem, due to the strong nonlinear coupling between the dynamics of excitingrndevice (the reed) and the acoustics of the instrument bore. One of the most diu000ecultrnissues is the accurate prediction of the harmonic response of the air column. This isrntypically given in terms of input impedance spectrum Zin(!), which represents the ratiornbetween pressure and mass row at the input section of the instrument. Classicalrnmathematical models are usually valid for simple geometries (cylindrical, conical, exponentialrn...), and based on a-priori assumptions about the radiation impedance at thernopen end of the tube. In addition, accurate measurements of such quantities are notrneasy to obtain, due to large dynamic range of Zin, and the inruence of the experimentalrnuncertainities (geometry, temperature, etc. ) on the results. In this work, a BoundaryrnIntegral Equation approach for the prediction of the acoustic response of the instrumentrnis presented. This is valid for arbitrary geometries, including tuning holes. The methodrnis applied to evaluate the input impedance of instruments of the clarinettes and saxophonernfamilies. Using the same mathematical model, the transfer function relating therninrow Uin to the pressure at arbitrary locations in the feld, is calculated as well.