Highlights
Fractal® Sound Barrier
Submitted by the Institute for Pure and Applied Mathematics (IPAM)
The study of the vibrations in domains with boundaries or interfaces of irregular
geometry is a complex mathematical problem, for which many questions are still
unsolved. Nevertheless, it has been known for a long time that objects of irregular
shape or geometry are “bad resonators”. From the seminal work of Bernard Sapoval,
a physicist at the Ecole Polytechnique (France), this idea was applied to acoustic
vibrations, and experimentally tested in the lab in the 1980’s. It led to the
invention of a revolutionary type of acoustic barrier. Together with Marcel Filoche,
also a physicist at the Ecole Polytechnique, and in collaboration with Colas®, a
private company specializing in road construction, a prototype made out of concrete
wood was constructed. The geometry of this barrier was inspired by fractal geometry,
since it includes holes at very different scales, ranging from 30cm to submillimeter
pores of the material. This acoustic barrier, now a commercial product patented under
the name Fractal wall®, is characterized by a complicated shape and absorbs on average
98% of the incident acoustic energy in the audio spectrum, for normalized traffic noise.
The absorption and acoustic properties of this structure are intimately linked to the
spectral properties of the Laplacian operator in complex domains. By allowing a deep
and fruitful interaction between mathematicians and physicists, the IPAM programs
“Random Shapes” (coorganized by B. Sapoval), and “Laplacian eigenvalues and eigenfunctions:
Theory, computation and applications” have had a considerable impact on the understanding
of such systems. In particular, they helped to put the concept of wave localization, which
plays an essential role in their acoustic properties, into a theoretical framework. Doing
so, they have contributed to development of new collaborations and to opening of new
research directions in this domain.
