Finite Element Modeling of Woodwind Instruments（有限元建模的木管乐器）.pdf

Proceedings of 20th International Symposium on Music Acoustics (Associated Meeting of the International Congress on Acoustics) 25-31 August 2010, Sydney and Katoomba, Australia Finite Element Modeling of Woodwind Instruments Antoine Lefebvre and Gary P. Scavone Computational Acoustic Modeling Laboratory (CAML) Centre for Interdisciplinary Research in Music Media and Technology (CIRMMT) Schulich School of Music of McGill University 555 Sherbrooke Street West, Montreal, QC H3A 1E3, Canada PACS: 43.75.Ef,43.20.Mv ABSTRACT The input impedance of simple woodwind-like instruments is evaluated using the Finite Element Method (FEM) and compared to theoretical calculations based on the transmission-matrix method (TMM). Thermoviscous losses are accounted for with an impedance boundary condition based on acoustic boundary layer theory. The systems are surrounded by a spherical radiation domain with a second-order non-reflecting spherical-wave boundary condition on its outer surface. For simple geometries, the FEM results are shown to match theory with great accuracy. When considering toneholes, boundary layer losses must be added to the TMM model to achieve good agreement with the FEM calculations. For geometries with multiple closed or open toneholes, discrepancies between the FEM and the TMM results become more significant and appear related to internal or external interactions. For closed side holes, this effect is more important at low frequencies, thus affecting the first few resonances. For open side hol