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.

在这项工作中，我们在数值上研究了主要由平移谐振器组成的弹性超材料中亚波长面内波的拓扑界面状态。针对质量-弹簧模型和连续模型分析了带隙，有效质量和有效刚度之间的关系。此外，通过调节平移共振的参数来控制阻带和负有效参数的位置。观察到拓扑相变从单个刚度负区域向单个质量负区域发生，而Zak相随参数变化的移动而变化。这也暗示拓扑界面弹性波的特征行为可能存在于亚波长区域。此外，在一个由两个具有不同负有效特性的晶格组成的异质结构中，对频率响应进行了分析和计算研究，表明存在亚波长拓扑界面模式。最后，我们通过采用有限元数值方法计算的瞬态响应分析，进一步验证了界面状态的动态行为。