Robust elastic wave propagation against bending and weak perturbations can be realized at the edges by analyzing the topological states in mechanical systems. However, both longitudinal and transverse wave components of polarized elastic waves complicate their manipulation. Current studies on the topological properties of elastic waves mainly address a single polarization component, even though the diverse polarization characteristics show significant potential for advanced manipulation of elastic waves. In this study, a hexagonal lattice with additional masses is presented to discuss the topological properties, and the out-of-plane and in-plane polarized valley topological states are realized in the lattice system. First, the dynamical model of hexagonal lattice based on the Timoshenko beam theory is proposed to analyze the topological properties, and the out-of-plane polarized and in-plane polarized topological phases are realized by tuning the additional masses. Then the Symplectic solution method is introduced to simplify the calculation of band structures, and the polarized topological properties are obtained by calculating the Berry curvatures and Wannier centers. Subsequently, an interface with a sharp corner is constructed to demonstrate the existence of polarized topological edge states and corner states. Finally, we analyze the out-of-plane polarized and in-plane polarized topological states in the frequency domain and further realize the prediction of the topological corner states according to the polarization of the elastic waves. The proposed structures provide an effective way to tailor the multi-directional elastic wave propagation and realize the selective transmission of the single-polarized elastic waves.

中文翻译：

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六边形晶格中的极化弹性拓扑状态


通过分析机械系统中的拓扑状态，可以在边缘实现针对弯曲和弱扰动的稳健弹性波传播。然而，极化弹性波的纵波和横波分量都使它们的操作变得复杂。目前关于弹性波拓扑特性的研究主要涉及单个极化分量，尽管不同的极化特性显示出弹性波高级操纵的巨大潜力。在本研究中，提出了一个具有附加质量的六边形晶格来讨论拓扑性质，并在晶格系统中实现了面外和面内极化谷拓扑状态。首先，提出了基于 Timoshenko 光束理论的六边形晶格动力学模型来分析拓扑性质，并通过调整附加质量实现面外极化和面内极化拓扑相位。然后引入 Symplectic 解方法简化能带结构的计算，通过计算 Berry 曲率和 Wannier 中心得到极化拓扑性质。随后，构建了一个带有尖角的界面，以证明极化拓扑边缘状态和角状态的存在。最后，分析了频域中的面外极化和面内极化拓扑状态，进一步实现了根据弹性波极化对拓扑角态的预测。所提出的结构为定制多向弹性波传播和实现单极化弹性波的选择性传输提供了一种有效的方法。