Abstract Approaches to systematic analysis of essentially nonlinear structures with multistable responses, controlled buckling and snapping behavior have received much attention recently in the context of mechanical metamaterials design. A snapping bistable element is generally a highly efficient damper, performing well even at very low forcing frequencies. In this paper, we transfer basic tools of the metamaterials analysis to macroscopic systems relevant to civil and mechanical engineering applications. Such systems are comprised of only several bistable elements. Followed by analysis of a single snapping bistable axial (two-force) element, we consider a combination of two elements with antisymmetric properties and demonstrate a robust tristable performance of the resultant structure in low-frequency or quasistatic tension-compression loading cycles. The tristability provides an overall response that is symmetric for tension and compression, which makes it interesting for applications in machinery and large-scale seismic structures.

中文翻译：

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关于轴向加载双稳态和三稳态超结构的综合稳定性分析

摘要 在机械超材料设计的背景下，对具有多稳态响应、受控屈曲和折断行为的基本非线性结构进行系统分析的方法最近受到了很多关注。咬合双稳态元件通常是一种高效阻尼器，即使在极低的强迫频率下也能表现良好。在本文中，我们将超材料分析的基本工具转移到与土木和机械工程应用相关的宏观系统。这种系统仅由几个双稳态元件组成。其次是对单个咬合双稳态轴向（双力）元件的分析，我们考虑了两个具有反对称特性的元素的组合，并在低频或准静态拉伸 - 压缩加载循环中展示了所得结构的稳健三稳态性能。三稳态提供了对拉伸和压缩对称的整体响应，这使得它在机械和大型抗震结构中的应用很有趣。