Modélisation physique d'instruments de musique en systèmes dynamiques et inversion
Résumé
The self-sustained musical instruments are nonlinear dynamical systems with many regimes of oscillation, even including chaotic ones. Modelling them leads to natural sounds and behaviours. But controlling them is difficult, leading to the question of the inversion: which control for this target sound? The results of the thesis compiled here concern the brass instruments. Three problems are presented: an inversion process for a sub-determined problem, representing lossy curved acoustic waveguides (involving fractional derivatives) with quadripoles including delays, as well as the acoustic radiation. The originality of this work consists of converting mechanical and acoustic problems into automatic ones, which are well-adapted to the simulation (sound synthesis) and the inversion (capture of musical interpretations).