Machine-Learning-Assisted Acoustic Consecutive Fano Resonances: Application to a Tunable Broadband Low-Frequency Metasilencer

The Fano resonance is a widespread wave-scattering phenomenon associated with an ultrasharp line shape, which just serves a narrow working frequency range around the interference frequency, rendering the realization of Fano-based applications extremely challenging. Here, we present and experimentally verify a mechanism of acoustic consecutive Fano resonances (ACFRs) with a symmetric profile for broadband sound attenuation, and extend to a practical implementation of a tunable low-frequency double-helix metasilencer. Based on the ACFRs’ dependence on material parameters in the bilayer metamaterial model, we employ an inverse design using Bayesian machine learning to search the optimal broadband insulating performance with a rapid convergence speed (15 iterations). For practical requirement, we extend the ACFRs’ prototype to a continuously tunable double-helix metastructure for broadband low-frequency sound attenuation. This broadband effect can be interpreted by the dual-band single-negativity property. A good agreement between numerical simulation and experiment evidences the effectiveness of the proposed metasilencer with tunable sound attenuation (>90%) in 425–865 Hz and high ventilation (>80%) at various double-helix combinations. Our proposed ACFRs’ mechanism and its associated metastructure would open routes to promising acoustic metamaterial-based applications, such as filtering, switching, and sensing, and beyond.

Figure 1

(a) Schematic diagram of the bilayer metamaterial placed perpendicular to the direction of wave propagation. The two-colored parts of the metamaterial are characterized by two effective mediums with different acoustic properties. (b) Transmission spectra through region 1, region 2, and the bilayer metamaterial, respectively. Here, the radius ratio r₁/r₂= 0.5, the refractive index ratio n₁/n₂= 0.2, and mass density ratio ρ₁/ρ₂= 0.1.

Figure 2

(a) Transmission spectra through the bilayer metamaterial for various values n₁/n₂ (r₁/r₂=0.5 and ρ₁/ρ₂= 0.2). (b) Transmission spectra for different values r₁/r₂ (n₁/n₂= 0.25 and ρ₁/ρ₂= 0.2). (c) Transmission spectra for different values r₁/r₂ (n₁/n₂= 0.25 and r₁/r₂= 0.5). (d) Schematic diagram of the proposed design method. (e) Maximum bandwidth in the current dataset as a function of the number of evaluations, where N_F is the sampling step length in the target frequency range [0.2n₂t/λ, 1.2n₂t/λ]. The initial dataset is marked with brown. (f) The optimal transmission spectrum for the bilayer metamaterial where n₁/n₂= 0.32, ρ₁/ρ₂= 0.29, and r₁/r₂= 0.50.

Figure 3

(a) Schematic diagram of the double-helix metasilencer placed perpendicular to the direction of wave propagation. The internal helix can be continuously screwed into the external helix. (b), (c) Geometrical details of the internal and external helixes.

Figure 4

(a) Transmission spectra of the helical channel, central channel, and the whole metasilencer (h = 150 mm). (b) Sound-pressure distributions and velocity streamlines on a metasilencer cut plane. (c) Illustration for the formation of the negative effective material parameters. The negative EBM and EMD frequency ranges are shaded orange and blue, respectively, and the positive passband is white. (d) Sound-pressure distributions and local velocity at two surfaces of the helical channel at the monopole and dipole modes.

Figure 5

Transmission spectra of the tunable double-helix metasilencer versus the helical depth h.

Figure 6

(a), (b), (c) Photos of the 3D-printed specimen of the designed double-helix metasilencer, external helix, and internal helix, respectively. (d) Schematics of the experimental setup. Measurements of the ventilation rate employ the same experimental setup. (e), (f), (g) Measured transmission loss, measured transmission, and simulated transmission for the metasilencer at various helical depths. (h) Measured ventilation rate for the metasilencer at various helical depths.