Wave Propagation in One-Dimensional Diatomic Metamaterials with Indirect Interactions

In recent years, metamaterials have attracted numerous research attentions due to their applications in low-frequency vibration suppression and noise reduction. In this paper, the effect of indirect interactions on the wave propagation in one-dimensional diatomic metamaterials is investigated. The governing equations of a cell are obtained and using Bloch’s theorem, wave dispersion relations of these materials are obtained and then dispersion curves are plotted. The band gaps of the infinite lattice model are calculated. Furthermore, the influences of various parameters including various stiffness ratios are examined. The numerical results show that the indirect interactions affect the shape of the dispersion curves, while the range of the band-gap slightly changes. In addition, the results reveal the appearance of extra band gap in the proposed metamaterial. Parametric study shows that the extra band gap can be tuned by controlling the stiffness of elastic foundation. These results pave the path to a new generation of metamaterials.