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Optimal absorption of acoustical waves by a boundary

Abstract : In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the energy of a sound wave, we consider a frequency model (the Helmholtz equation) with a damping on the boundary. The damping on the boundary is firstly related with the damping in the volume, knowing the macroscopic parameters of a fixed porous medium. Once the well-posedness results are proved for the time-dependent and the frequency models in the class of bounded $n$-sets (for instance, locally uniform domains with a $d$-set boundary, containing self-similar fractals or Lipschitz domains as examples), the shape optimization problem of minimizing the acoustical energy for a fixed frequency is considered. To obtain an efficient wall shape for a large range of frequencies, we define the notion of $\epsilon$-optimal shapes and prove their existence in a class of multiscale Lipschitz boundaries when we consider energy dissipation on a finite range of frequencies, and in a class of fractals for an infinite frequency range. The theory is illustrated by numerical results.
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Contributor : Anna Rozanova-Pierrat <>
Submitted on : Thursday, February 22, 2018 - 12:37:23 PM
Last modification on : Thursday, July 2, 2020 - 9:12:02 AM


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  • HAL Id : hal-01558043, version 3


Frédéric Magoulès, Thi Phuong Kieu Nguyen, Pascal Omnes, Anna Rozanova-Pierrat. Optimal absorption of acoustical waves by a boundary . 2017. ⟨hal-01558043v3⟩



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