Subwavelength Broadband Perfect Absorption for Unidimensional Open-Duct Problems

Passive metamaterials provide efficient solutions for sound absorption in the low-frequency regime with deep subwavelength dimensions. They have been extensively applied in unidimensional reciprocal problems considering that an incident wave is either reflected or transmitted at the outlet boundary. However, the generalized problem with impedance boundary condition is not well understood yet. This work presents a general design methodology of metamaterial absorbers for open-duct problems, which is a special case of impedance outlet boundary encountered in broad practical applications, for example, noise-attenuation problems in heat ventilation and air conditioning systems. By properly using monopolar point scatterers made of arrays of Helmholtz resonators, the design process is significantly simplified; the transfer matrix modeling is sufficiently accurate to describe the acoustic response of the system. A single monopolar point scatterer is insufficient to attenuate both the reflected and radiated waves; a frequency-dependent maximum absorption exists and is derived analytically. To go beyond this absorption bound and achieve perfect absorption, at least two point scatterers are necessary. Specific designs are provided and validated experimentally for maximum or perfect absorption, either at single frequencies or over specific frequency bands.