双层网络的全模态拓扑极化：麦克斯韦极限分析和3D打印原型实验
Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
摘要：
处于机械不稳定性边缘的周期性网络，称为麦克斯韦晶格，已知会在其边界上呈现零频率模式。特别地，拓扑极化的麦克斯韦晶格将这些零模式以通过晶格的能带结构的倒易空间拓扑而防止无序的方式聚焦到它们的边界之一。在这里，我们介绍了一类机械双层作为模型系统设计拓扑保护的边缘模式，耦合面内扩张和剪切模式的平面外弯曲模式，一个范例，我们称之为omnimodal极化。虽然这些结构表现出一个高维的设计空间，使其难以预测的拓扑极化的通用几何形状，我们能够确定一个家庭的镜像对称双层继承其本构单层的拓扑极化可以确定解析的面内模态本地化。重要的是，层之间的耦合导致出现全模式偏振，从而平面内和平面外边缘模式定位在同一边缘上。我们通过增材制造由弹性梁网络组成的镜像对称的拓扑偏振的可果美双层来证明这些理论结果，并通过有限元分析和激光振动测量实验来证实这种有限频率偏振。
英文摘要：
Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as omnimodal polarization. While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
