This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.
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.
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