Video 1 from Wave polarization and dynamic degeneracy in a chiral elastic lattice

This paper addresses fundamental questions arising in the theory of Bloch–Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of ‘topologically protected’ waveforms. Although practical applications of chiral elastic lattices are widely appreciated, especially in problems of controlling low-frequency vibrations, wave polarization and filtering, the fundamental questions of the relationship of these lattices to classical waveforms associated with longitudinal and shear waves retain a substantial scope for further development. The notion of chirality is introduced into the systematic analysis of dispersive elastic waves in a doubly-periodic lattice. Important quantitative characteristics of the dynamic response of the lattice, such as lattice flux and lattice circulation, are used in the analysis along with the novel concept of ‘vortex waveforms’ that characterize the dynamic response of the chiral system. We note that the continuum concepts of pressure and shear waves do not apply for waves in a lattice, especially in the case when the wavelength is comparable with the size of the elementary cell of the periodic structure. Special critical regimes are highlighted when vortex waveforms become dominant. Analytical findings are accompanied by illustrative numerical simulations.

本论文针对手性弹性晶格系统中布洛赫-弗洛凯波（Bloch–Floquet waves）理论所衍生的基础问题展开研究。该领域围绕“拓扑保护波形”的相关研究已获得广泛关注。尽管手性弹性晶格的实际应用价值已得到广泛认可，尤其在低频振动控制、波偏振调控与滤波等工程场景中，但其与纵波、横波等经典波形的关联机制仍存在大量有待进一步拓展的研究空间。本研究将手性概念引入双周期晶格（doubly-periodic lattice）的色散弹性波系统性分析框架之中。分析过程中，除采用用于表征手性系统动态响应的新型“涡旋波形（vortex waveforms）”概念外，还引入了晶格通量（lattice flux）、晶格环流（lattice circulation）等晶格动态响应的重要量化特征参数。需特别指出，连续介质框架下的压力波与剪切波概念并不适用于晶格波动场景，尤其当波长与周期结构原胞（elementary cell）的尺寸可比时，该局限性尤为显著。本研究重点凸显了涡旋波形占据主导地位的特殊临界工况。本文的解析结论均配有示范性数值仿真结果作为佐证。