Numerical Investigation of Discrepancies Between Two-Dimensional and Three-Dimensional Acoustic Metamaterials

Abstract

In order to get insight information of the band structure of acoustic metamaterials (AMMs) in condensed matter, periodic lattice structures are analyzed using Bloch’s theorem. Typical approaches of the band structure computation methods, topology optimization, and tunable abilities cannot overcome the gap between the two-dimensional (2D) AMMs theoretical and three-dimensional (3D) specimens’ experimental data yet. In this work, the variation in the results of the band structure obtained from the 2D mathematical model computed with respect to the 3D experimental models, and related cause of the variation is explored. The band structures and mode shapes of the 2D AMMs, quasi-2D models, and 3D specimen models are followed to reveal the boundary conditions and source for the observed differences in band structures. The cause for the discrepancies is verified by using the finite element method (FEM) with corresponding boundary conditions. It is found that outcomes from computational data of the 2D AMMs model are diverted significantly by means of bandgap, band structure, and stress distribution in counterparts of the 3D specimen model. This approach can provide assistance for computing the band structure of 2D AMMs for practical applications.