A mass-spring analogy for modeling the acoustic behaviour of a metamaterial

Absorbing sound almost completely at specific frequencies with conventional acoustic materials whose thickness is at least 60 times smaller than the wavelength is a challenge, particularly at low frequencies. Fort this purpose, acoustic metamaterials are of a great interest. Here, the metamaterial is called multi-pancake cavities. It is composed of a main pore with a repetition of thin annular cavities (pancake cavities). Previous research has shown that this repetition increases the effective compressibility of the main pore. This increase makes it possible to decrease the effective sound speed in the material and, consequently, the main pore resonance frequencies. At these resonances, the metamaterial presents absorption peaks, the first one can have a wavelength to material thickness ratio of more than 60 (subwavelength material). To complete the analysis and prediction of absorption peaks (especially secondary peaks) of these metamaterials, it is proposed to adapt a conventional mass-spring model to this metamaterial. Due to the small cavity length-to-diameter ratios, radial propagation is considered inside the annular cavities. This model shows a good agreement with the results obtained by finite element method and by impedance tube measurements. Finally, comparisons with previous theoretical approaches are presented and discussed.