Topological interface states in translational metamaterials for sub-wavelength in-plane waves

In this work, we numerically investigate topological interface states for subwavelength in-plane waves in elastic metamaterials composed mainly of translational resonators. The relationships among bandgap, effective mass and effective stiffness are analyzed for the mass-spring and continuum models. Besides, the locations of stop-bands and negative effective parameters are manipulated by tuning the parameters of translational resonances. It is observed that the topological phase transition occurs to the single mass-negative region from the single stiffness-negative region while the Zak phase varies following a shift in parameter changing. It also implies that the characteristic behavior of topological interface elastic waves can exist in the sub-wavelength region. Furthermore, the frequency response is analytically and computationally investigated in one heterostructure composed of two lattices with different negative effective properties, which show the existence of the sub-wavelength topological interface mode. Finally, we have further verified the dynamic behavior of the interface state by employing the transient response analysis computed by the finite element numerical approach.

Automated summary

In this study, topological interface states for subwavelength in-plane waves in elastic metamaterials were numerically investigated. The relationships among bandgap, effective mass, and effective stiffness were analyzed, and the manipulation of stop-bands and negative effective parameters by tuning the parameters of translational resonances was discussed. The study observed a topological phase transition from single mass-negative region to single stiffness-negative region, with a corresponding shift in parameter changing of Zak phase. The existence of characteristic behavior of topological interface elastic waves in the sub-wavelength region was confirmed.