Internship location : Laboratory of Mechanics and Acoustics – Marseille
Net compensation : 591,51 €/month
Application (CV + cover letter) : vincent.freour[at]music.yamaha.com

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 [1]. 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 :
 1- Implement a physical model of brass instruments that includes the 2 dof lip model proposed in [2]. Using the numerical continuation program MANLAB, compute the bifurcation diagrams of different notes on different Bb trumpets, which impedance will have been measured experimentally.
 2- Considering the uncertainties on some geometrical parameters of the lip model, as well as on the impedance parameters, quantify the effects of these uncertainties on the descriptors extracted from the bifurcation diagrams, and propose a new categorisation of the different trumpets.

This internship involves both experimental and numerical work, and will include regular online reporting to Yamaha R&D team in Japan.

References :
[1] V. Fréour et al. Numerical continuation of a physical model of brass instruments : Application to trumpet comparison, Journal of the Acoustical Society of America, 148 (2), 2020, pp 748-758
[2] S. Adachi & M. Sato, Trumpet sound simulation using a two-dimensional lip vibration model, Journal of the Acoustical Society of America, 99 (2), 1996, pp 1200-1209