纯弹性“突跳”不稳定性中的临界慢化
Critical slowing down in purely elastic `snap-through' instabilities
摘要：
许多弹性结构都有两种可能的平衡态：从在突然的阵风中翻转的雨伞，到纳米机电开关、折纸图案和在翻转后跳跃的料斗弹出器。这些系统通常通过快速的“跳跃”从一种状态转换到另一种状态。快速通过允许植物逐渐存储弹性能量，然后突然释放它以产生快速运动，如捕蝇草。类似地，蜂鸟的喙在飞行中捕捉昆虫，而技术应用正在越来越多地利用捕捉不稳定性。在所有这些场景中，正是重复生成快速运动的能力赋予了快照其实用性。然而，对突变速度的估计表明，它应该比通常观察到的更快。在这里，我们详细研究了快速通过的动力学，表明即使没有耗散，动力学在接近快速通过过渡时也会减慢。这让人想起在临界现象中观察到的减速，并提供了这种现象的手持演示，以及在弹性双稳态应用中调整动态响应的新工具。
英文摘要：
Many elastic structures have two possible equilibrium states: from umbrellas that become inverted in a sudden gust of wind, to nano-electromechanical switches, origami patterns and the hopper popper, which jumps after being turned inside-out. These systems typically transition from one state to the other via a rapid `snap-through'. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions, as in the Venus flytrap. Similarly, the beak of the hummingbird snaps through to catch insects mid-flight, while technological applications are increasingly exploiting snap-through instabilities. In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. Here, we study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena, and provides a handheld demonstration of such phenomena, as well as a new tool for tuning dynamic responses in applications of elastic bistability.
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