DataSheet1_Multiband Pure Topological States in Elastic Structures.PDF

Inspired by notions of topological physics, recent years have witnessed the rapid development of mechanical metamaterials with novel properties of topological states. However, most of the current investigations have either focused on discrete mass-spring lattices, with topological states limited to a single operating band, or on various elaborate continuous elastic systems, enduring the drawbacks of modal couplings. It remains largely unexplored how to design topological elastic systems that naturally possess multiple operating bands and are free from modal couplings. In this study, we design an elastic system based on fundamental mechanical elements (beams, rods and nuts), which is capable of supporting multiband pure topological states. Through an equivalent beam-spring model with lumped masses together with finite element analysis, we demonstrate that our proposed structure exhibits multiple Dirac points (DPs) at different frequencies. We show that simply adjusting the heights of nuts fastened on beams can lift the degeneracies, giving rise to two kinds of valley Hall phases characterized by opposite valley Chern numbers. The dispersion diagram of the supercell formed by unit cells with different topological indices shows that there simultaneously exist perfectly pure interface modes (i.e., no other modes coexist) within two frequency ranges. Furthermore, numerical simulations demonstrate that the domain wall formed by structures with distinct topological properties supports topologically protected interface waves over dual frequency ranges. Our results have potential for the design of mechanical systems that need to work under changeable working frequencies and may have significant impact on many diverse fields such as vibration control, energy harvesting and seismic isolation.

受拓扑物理学(topological physics)理念的启发，近年来具备新奇拓扑态特性的机械超材料(mechanical metamaterials)得到了快速发展。然而，当前绝大多数研究要么聚焦于离散质量-弹簧晶格(mass-spring lattices)，其拓扑态仅局限于单一工作频段；要么针对各类复杂的连续弹性系统(continuous elastic systems)，却存在模态耦合(modal couplings)的固有缺陷。目前，如何设计能够天然拥有多个工作频段且无模态耦合问题的拓扑弹性系统，仍有待深入探索。本研究基于梁、杆与螺母等基础力学元件(fundamental mechanical elements)设计了一款弹性系统，该系统可支持多频带纯拓扑态(multiband pure topological states)。通过结合带有集中质量(lumped masses)的等效梁-弹簧模型(equivalent beam-spring model)与有限元分析(finite element analysis)，我们证明所提出的结构在不同频率处存在多个狄拉克点(Dirac points, DPs)。研究表明，仅通过调整紧固于梁上的螺母高度即可解除简并(degeneracies)，进而产生两类以相反谷陈数(valley Chern numbers)为特征的谷霍尔相(valley Hall phases)。由具有不同拓扑指数(topological indices)的原胞(unit cells)构成的超胞(supercell)的色散图谱(dispersion diagram)显示，在两个频率区间内同时存在完全纯的界面模式(interface modes)，即无其他模式共存。此外，数值模拟(numerical simulations)表明，由具有不同拓扑特性的结构构成的畴壁(domain wall)，可在双频段内支持受拓扑保护的界面波(topologically protected interface waves)。本研究成果可为需在可变工作频率下运行的机械系统设计提供参考思路，并有望在振动控制(vibration control)、能量收集(energy harvesting)以及隔震(seismic isolation)等诸多领域产生重要影响。