Denis Matignon has always been keen to combine music and mathematics. To design the sound synthesis of wind musical instruments during his thesis, the key was to look at an unsolved equation with fractional partial derivatives which can take account of the viscous and thermal effects that have characteristic lengths in air. He used a "fractional derivative". Applied twice, the fractional derivative to order one-half returns the classical derivative, the same one that enables the speed to be obtained from the distance or even the acceleration from the speed.
By solving this equation, Denis Matignon created a model capable of accounting for the propagation of sound from wind musical instruments, including visco-thermal losses at the walls, in order to recreate them in the most realistic way in sound synthesis. For this work, carried out at IRCAM (Institute for Research and Acoustics/Music Coordination), he received the prize for the best automatics thesis in France awarded by AFCET in 1994. A lecturer in the Signal and Image Processing Department at Télécom Paris Tech, he received this award in the Salle des Illustres in the Capitole, a sign foreshadowing his arrival in Toulouse in 2007 as Professor and Head of the Applied Mathematics team at ISAE-SUPAERO.
FROM MUSIC TO SILENCING JET ENGINES
Fifteen years later, Estelle Piot, a researcher at ONERA, is using the fractional derivative, not to create synthetic sounds, but to lessen noise nuisances. Together, they decided to carry out a thesis on designing a modeling system capable of representing the micro-perforated liners used to reduce the noise of aircraft engines. This project proved to be a real success since their modeling system is now being taken onboard by aircraft manufacturer Airbus.
Following this first research project, ISAE-SUPAERO and ONERA are continuing their collaboration through a PhD thesis aimed at modeling the noise reduction of aircraft nacelles by the use of porous materials. Since a noise consists of several sound frequencies, it is important to locate the frequency band in which the noise is located for acoustic liners to be effective. "Where applied mathematics become applicable mathematics"...
SOUNDPROOFING LINERS FOR QUIETER AIRCRAFT ENGINES
In order to support the aeronautical sector in its phonic transition, ISAE-SUPAERO, in partnership with ONERA, is conducting research on how to reduce aircraft jet noise. Using this complex mathematical data set, researchers model the propagation of the sound within aircraft engines through absorbent materials lining the nacelle, using micro-perforated liners or porous materials.
Porous materials are currently the only effective insulators for suppressing sound on all frequencies of a given noise and are particularly suitable for the aeronautical sector. This thesis aims to support manufacturers and airlines in their move towards sound ecology. Proof that here applied mathematics become applicable mathematics.
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