Multiple resonances in lossy acoustic black holes - theory and experiment

Acoustic properties of the metamaterial graded absorber, also known as ``acoustic black hole'', are studied in the linear regime. The absorber consists of thin metallic circular plates, each with a central perforation, separated by annular air cavities. Radius of the perforation in each plate is gradually decreasing with the distance from the plate to the front surface, forming a central channel with a staircase radius profile. A semi-analytical equivalent fluid model accounting for the variations of both the effective density and compressibility of air inside this channel is developed, which incorporates the staircase variations of the perforation radius with distance and assumes motionless plates. The viscous and thermal losses inside the side cavities and the central channel are accounted for using a well-established Johnson-Champoux-Allard-Lafarge model. It is demonstrated that high absorption coefficient values are achieved in a wide range of frequencies starting from a few hundred Hz or less. At low frequencies, the resonances along the length of the structure, i.e. global resonances, are responsible for sound attenuation. At higher frequencies, the resonances of the lateral cavities, i.e. local resonances, play a major role. The upper boundary of the frequency range of high sound absorption is determined by the resonance frequency of the front annular plate. The model is validated against impedance tube measurements on five samples of different geometry and FEM models. FEM model predicts that the elasticity of the plates affects the absorption coefficient behaviour in the frequency range of plate resonances and at frequencies well below the plate resonances