Experimental Verification of Similarity Criteria for Sound Absorption of Simple Metamaterials

The paper concerns the dimensional analysis of simple acoustic metamaterials and its experimental verification in a computer model. Due to their decreased thickness possible because of the thermoviscous losses and sound dispersion that occur in acoustic metamaterials, such structures are gaining popularity, both as sound absorbers and diffusers. This implies the need to find their equivalents to be used at scale – both for modeling interiors with metamaterials and developing more complicated structures. The paper discusses the dimensional analysis performed for a generalized unit cell of a metamaterial with a resonator. The dimensional analysis shows the need for scaling both the geometrical dimensions of the structure and the parameters of the medium – air. The dimensional analysis was derived based on the transfer matrix method and was proven correct with the finite element method model. The paper also discusses the consequences of neglecting the air criteria, which are impossible to be fulfilled. This opens the question of finding new criterial numbers allowing the correct reflection of acoustic metamaterials at scale.