弹性跳跃式失稳由几何对称性支配
Elastic snap-through instabilities are governed by geometric symmetries
AI总结：
本文通过数值与解析方法证明两个弹性条带系统等价，揭示跳跃式失稳由几何对称性决定，并基于降阶方法建立分岔预测规则，为弹性形状转变提供普适设计准则。
摘要：
许多弹性结构在两个可能的平衡状态之间表现出快速的形状转变：雨伞在强风中会翻转，hopper popper 玩具在翻面时会弹跳。这种跳跃式失稳是弹性储能与快速释放的普遍机制，并被从捕蝇草到力学超材料等许多生物和工程系统所利用。已知形状转变与系统经历的分岔类型有关，然而，迄今为止，对于选择这些分岔的机制尚无普遍理解。本文对近期文献中提出的两个系统进行了数值和解析分析，在这些系统中，初始处于屈曲状态的弹性条带通过旋转或平移其边界而被驱动经历形状转变。我们证明这两个系统在数学上是等价的，并识别出三个案例，它们涵盖了先前作者描述的全部转变范围。重要的是，利用降阶方法，我们确定了潜在分岔的性质，并解释了如何从几何对称性和对称破缺机制预测这些分岔，从而为弹性形状转变提供了普适的设计规则。
英文摘要：
Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside-out. This snap-through is a general motif for the storage and rapid release of elastic energy, and it is exploited by many biological and engineered systems from the Venus flytrap to mechanical metamaterials. Shape transitions are known to be related to the type of bifurcation the system undergoes, however, to date, there is no general understanding of the mechanisms that select these bifurcations. Here we analyze numerically and analytically two systems proposed in recent literature in which an elastic strip, initially in a buckled state, is driven through shape transitions by either rotating or translating its boundaries. We show that the two systems are mathematically equivalent, and identify three cases that illustrate the entire range of transitions described by previous authors. Importantly, using reduction order methods, we establish the nature of the underlying bifurcations and explain how these bifurcations can be predicted from geometric symmetries and symmetry-breaking mechanisms, thus providing universal design rules for elastic shape transitions.
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。
