Design of an acoustic energy distributor using thin resonant slits

Lucas Chesnel (1, 2) , Sergei A Nazarov (3)

1 DeFI - Shape reconstruction and identification
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 SPbU - St Petersburg State University

We consider the propagation of time harmonic acoustic waves in a device with three channels. The wave number is chosen such that only the piston mode can propagate. The main goal of this work is to present a geometry which can serve as an energy distributor. More precisely, the geometry is first designed so that for an incident wave coming from one channel, the energy is almost completely transmitted in the two other channels. Additionally, tuning a bit two geometrical parameters, we can control the ratio of energy transmitted in the two channels. The approach is based on asymptotic analysis for thin slits around resonance lengths. We also provide numerical results to illustrate the theory.

Mots clés: Acoustic waveguide; energy distributor; asymptotic analysis; thin slit; scattering coefficients; complex resonance

Domaines: Equations aux dérivées partielles [math.AP]

Lucas Chesnel, Sergei A Nazarov. Design of an acoustic energy distributor using thin resonant slits. 2020. ⟨hal-03003171v1⟩