Stage M2 – Categorisation of trumpets by numerical continuation using a two dof lip model

Yamaha Corporation, leader in musical instruments, has a steady research activity in musical acoustics through its Research & Development centre in Japan. Since 2018, a collaboration has been established between the Laboratory of Mechanics and Acoustics (LMA) in Marseille and the R&D division of Yamaha. The objective of this joint research is to develop advanced physical models of wind musical instruments allowing to compute various quantitative indicators related to the performance of musical instruments (intonation, ease of play, timbre). The developed technologies aim at providing Yamaha designers with innovative tools for numerically aided design of wind musical instruments, such as the trumpet or the saxophone.

In this context, a method of numerical continuation based on the Asymptotic Numerical Method implemented in LMA software MANLAB, has been applied to physical models of brass instruments in order to calculate bifurcation diagrams associated to the production of different notes in the trumpet. This approach has enabled quantitative comparison of different models of trumpets on the basis of descriptors extracted from these bifurcation diagrams. Nevertheless, some limitations remain to
be overcome: the lip model considered so far is based on a simple 1 degree-of-freedom oscillator that, despite its efficiency, could be refined to better represent the lips of the player. The accuracy of this trumpet categorization depends on uncertainties at important stages of the modelling procedure (impedance measurement of the instrument, extraction of modal parameters from the impedance) that are not considered in current analysis.
These problematics are at the core of the two objectives of the internship which involves both experimental and numerical work, and will include regular online reporting to Yamaha R&D team in Japan.

Application (CV + cover letter): vincent.freour(a)music.yamaha.com