论文标题
kagome晶格超材料的客座 - hutchinson模式和周期机制的一些结果
Some results on the Guest-Hutchinson modes and periodic mechanisms of the Kagome lattice metamaterial
论文作者
论文摘要
晶格材料是有趣的机械超材料，其机械性能通常与机制的存在有关。周期性机制的存在可以通过宾客hutchinson（GH）模式的存在来指示，因为GH模式有时是周期性机制的无限版本。但是，并非每种GH模式都来自定期机制。本文的重点是：（1）阐明GH模式与周期机制之间的关系； （2）回答问题：哪些GH模式来自定期机制？我们主要关注特殊的晶格系统，即kagome晶格。我们的结果包括针对Kagome晶格的所有两周期机制的明确公式，以及GH模式的必要条件，通常来自定期机制。我们将必要的条件应用于两周期的GH模式，也将使用Bloch型边界条件在Kagome晶格的晶胞上使用Bloch型边界条件，并在Fleck和Hutchinson发现的一些特殊的GH模式上应用。
Lattice materials are interesting mechanical metamaterials, and their mechanical properties are often related to the presence of mechanisms. The existence of periodic mechanisms can be indicated by the presence of Guest-Hutchinson (GH) modes, since GH modes are sometimes infinitesimal versions of periodic mechanisms. However, not every GH mode comes from a periodic mechanism. This paper focuses on: (1) clarifying the relationship between GH modes and periodic mechanisms; and (2) answering the question: which GH modes come from periodic mechanisms? We focus primarily on a special lattice system, the Kagome lattice. Our results include explicit formulas for all two-periodic mechanisms of the Kagome lattice, and a necessary condition for a GH mode to come from a periodic mechanism in general. We apply our necessary condition to the two-periodic GH modes, and also to some special GH modes found by Fleck and Hutchinson using Bloch-type boundary conditions on the unit cell of the Kagome lattice.
