Perfect Absorption of Sound by Rigidly-Backed High-Porous Materials

Abstract

[EN] We present the conditions to observe perfect sound absorption by rigidly-backed layers of rigid-frame highporous materials. We theoretically analyze different configurations of increasing complexity: a single layer of high-porous material, a layer of high-porous material with an air gap (air plenum), and an optimized multilayer structure. First, we show that to obtain normal incidence perfect sound absorption at the first so-called quarterwavelength resonance of a single rigidly-backed high-porous layer, the thickness of the material is strongly related to its flow resistivity. In particular, perfect sound absorption is observed when the quarter-wavelength resonance is around the characteristic Biot frequency of the high-porous media. We found that the optimal thickness of the layer is 4.64 smaller than the perfectly absorbed wavelength when using one-parameter empirical models for the effective parameters of the high-porous material. Then, we analyze the behavior of the structure for oblique angles of incidence, showing that perfect sound absorption is also produced for other incident angles and frequencies. Second, an air gap is introduced between the high-porous layer and the rigid backing. The gap allows to produce perfect sound absorption for structures thicker than the optimal one and for media with large intrinsic losses, i.e., for materials with high flow resistivity. Finally, optimized multilayer structures are proposed, which present broadband and perfect sound absorption. The existence of perfect absorption is related to the impedance matching, which is produced when the intrinsic losses of the system exactly compensate the leakage of the structure due to its resonance. Thus, to observe perfect sound absorption, in addition to and material properties, the total thickness of any multilayered porous structure is constrained to its quarter-wavelength resonance because of the lack of deep-subwavelength resonance in the system.