Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems

TLDR

The panels are built from a periodic array of waveguides loaded with Helmholtz resonators of progressively higher resonance frequencies, where the deepest resonator fixes the low‑cutoff, the preceding one matches impedance to the surrounding medium, and the structure achieves critical coupling with vanishing reflection. The design delivers perfect absorption at 300 Hz with a panel 40 times thinner than the wavelength, and quasi‑perfect absorption over 300–1000 Hz using a 9‑resonator panel only 10 times thinner than the wavelength at 300 Hz.

Abstract

Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying crosssection waveguides, each of them being loaded by Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300 Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.