Abstract Metastructures consisting of planar arrangements of bi-stable snap-through beams are able to exhibit multiple stable configurations. Apart from the expected translational state transition, when all beam elements snap through, rotational states may exist as well. In this paper we explore the rotational properties of multi-stable metastructures on the basis of both experimental and theoretical investigations, and define the conditions for achieving rotational stable states. Results show that the metastructure is able to realize both translational and rotational states, while the rotational transitions require less energy as compared to their translational counterparts. The influence of geometric parameters on rotational stability is investigated via parametric studies. Furthermore, to determine the design criteria for rotational stability, a theoretical investigation based on mode superposition principle is performed to predict the nonlinear-deformation of a unit cell. The theoretical analysis predicts well the rotational snap-through transitions that are observed in finite element simulations. It is found that the rotational stability is determined by setting proper values for h/L and t/L (h, t, L represent apex height, thickness and span of the bi-stable beam structure, respectively). Finally, we experimentally demonstrate that the proposed metastructure with multiple layers is able to achieve large rotations and translations.

中文翻译：

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多稳定梁型超结构的旋转击穿行为

摘要 由双稳态突入梁的平面排列组成的超结构能够表现出多种稳定的配置。除了预期的平移状态转换之外，当所有梁单元快速通过时，旋转状态也可能存在。在本文中，我们在实验和理论研究的基础上探索了多稳态超结构的旋转特性，并定义了实现旋转稳定状态的条件。结果表明，元结构能够实现平移和旋转状态，而与平移对应物相比，旋转过渡需要更少的能量。通过参数研究研究了几何参数对旋转稳定性的影响。此外，为了确定旋转稳定性的设计标准，进行了基于模式叠加原理的理论研究，以预测晶胞的非线性变形。理论分析很好地预测了在有限元模拟中观察到的旋转快速过渡。发现旋转稳定性是通过设置适当的 h/L 和 t/L 值来确定的（h、t、L 分别代表双稳态梁结构的顶点高度、厚度和跨度）。最后，我们通过实验证明了所提出的具有多层的元结构能够实现大的旋转和平移。发现旋转稳定性是通过设置适当的 h/L 和 t/L 值来确定的（h、t、L 分别代表双稳态梁结构的顶点高度、厚度和跨度）。最后，我们通过实验证明了所提出的具有多层的元结构能够实现大的旋转和平移。发现旋转稳定性是通过设置适当的 h/L 和 t/L 值来确定的（h、t、L 分别代表双稳态梁结构的顶点高度、厚度和跨度）。最后，我们通过实验证明了所提出的具有多层的元结构能够实现大的旋转和平移。