Sound attenuation optimization using metaporous materials tuned on exceptional points

Abstract

A metamaterial composed of a set of periodic rigid resonant inclusions embedded in a porous lining is investigated to enhance the sound attenuation in an acoustic duct at low frequencies. A transmission loss peak is observed on the measurements and corresponds to the crossing of the lower two Bloch modes of an infinite periodic material. Numerical parametric studies show that the optimum modal attenuation can be achieved at the exceptional point in the parameter plane of inclusion position and frequency, where the two lower modes merge.

A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides

“…4 where the air domain Ω a of height h a is lined with a porous material Ω p of thickness h p with an embedded rigid cylindrical inclusion of circular shape filled with air. This configuration has already been studied in [12]. We call Γ c the two interfaces between the air and the porous material whereas Γ inc and Γ w stands respectively for the surface of the inclusion and the rigid walls of the waveguide.…”

“…Thus the guiding structure consists of a regular d-periodic grid with d = [d, d, 0] t . The skeleton of the porous material is supposed to be infinitely rigid, thus the use of the Johnson-Champoux-Allard (JCA) equivalent fluid model [50] is appropriate and we call K p (ω) the equivalent bulk modulus and ρ p (ω) the density (see Appendix A in [12] for details). The sound speed in the porous material is given by c p (ω) = K p (ω)/ρ p (ω).…”

“…Geometry of the problem adapted from[12] colored by physical domain air (white), porous (blue) and the meshes used in the computation. Here, ha = 135 mm, hp = 25 mm, d = 24 mm.…”

Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points

“…Investigation of EPs in quantum mechanics, optics, electronics, mechanics or acoustics is the subject of intense ongoing research [42], e.g. [43] for damping of friction-induced instabilities, [44] for unidirectional invisibility in an acoustic waveguide, [45] for exciton-polaritons in semiconductor microcavities, [46] for coupled lasers, [47,48] for the design of acoustic metamaterials, [49] for the transient dynamics in the vicinity of EPs, or [50] for the intriguing acoustical properties of coupled cavities. Their importance in the understanding of thermoacoustic instabilities has been highlighted in [51].…”

Beyond the limitations of perturbation methods for real random eigenvalue problems using Exceptional Points and analytic continuation

“…It aims to identify the validity domain of such approaches and to extend it through analytic continuation. Eigenvalue perturbation is a widely spread mathematical problem [20,26] arising in many fields of application, ranging from noise attenuation in waveguides [27] to fluid-structure interaction like flutter [28,29]. These problems are inherently parametric and the behavior of eigenvalue loci, when parameters varies, has been widely studied for these applications in a deterministic framework.…”