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

Abstract

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.