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.

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

The reflection of sound of frequency below 1 kHz, by a rigid-backed structure that contains sub-wavelength resonators is studied in this work. In particular, only single mode reflected waves are considered, an approximation which is accurate in this low frequency regime. A method of analysis of absorption that uses the structure of the reflection coefficient in the complex frequency plane is proposed. In the absence of losses, the reflection coefficient supports pairs of poles and zeros that are complex conjugate and which have imaginary parts linked to the energy leakage by radiation. When losses are introduced and balanced to the leakage, the critical coupling condition is satisfied and total absorption is obtained. Examples of a slot resonator and of multiple Helmholtz resonators are analyzed to obtain both narrow and broadband total absorption.

Use of complex frequency plane to design broadband and sub-wavelength absorbers.

Radiation impedance of tubes with different flanges: numerical and experimental investigations

We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.

https://iopscience.iop.org/article/10.1088/1367-2630/16/9/093017/pdf

Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

A three-dimensional (3D) analytical approach is developed to account for the nonplanar wave propagation in the cavity and neck of “piston-driven” circular asymmetric Helmholtz resonators. The present 3D analytical results are compared with (1) the numerical predictions from the boundary element method (BEM) to evaluate the analytical approach; and (2) the one-dimensional (1D) solution to examine the effect of nonplanar waves at area discontinuity between the neck and the cavity. In order to improve the 1D solution, the end correction is also determined by using the 3D analytical approach. The effect of neck offset on the resonance frequency of circular asymmetric Helmholtz resonators is investigated. Predictions of resonance frequency and transmission loss from the present 3D and corrected 1D analytical approaches are, respectively, identical and close to the BEM results, while the corrected 1D approach provides a better accuracy compared to the 1D solutions with Ingard’s correction. Finally, the boundary...

A. Garcia

Papers

Simple discontinuities in acoustic waveguides at low frequencies: Critical analysis and formulae