动态触发的突跳

中文摘要 AI 辅助

突跳是一种突然且大幅度的机械变形，通常通过将控制参数驱动超过分岔阈值来触发。在这里，我们研究了一个屈曲条带，当其一个夹具旋转时会发生鞍结分岔。我们通过实验、理论和数值方法证明，通过加速旋转可以显著降低有效的突跳阈值。对于执行时间短但仍长于基本弯曲周期的驱动，观察到条带在大部分加载过程中保持接近瞬时的准静态平衡。这使我们能够推导出一个能量准则，能够准确估计远低于鞍结分岔点的动态失稳阈值。另一方面，在非常接近分岔点时，准静态平衡的演化经历了几何加速，这带动了梁的整体运动。因此，比能量论证预测的更慢的夹具驱动就足以产生突跳。在该极限下，基于上述加速和梁最不稳定振动模式的临界减慢，推导出一个不同的标度律。更广泛地说，我们的结果表明，有限速率强迫可以在达到准静态失稳阈值之前触发突跳。

英文摘要

Snap-through is a sudden and large mechanical deformation that is usually triggered by driving a control parameter beyond a bifurcation threshold. Here, we study a buckled strip that undergoes a saddle-node bifurcation as one of its clamps is rotated. We show experimentally, theoretically, and numerically that the effective snapping threshold can be markedly lowered by speeding up the rotation. For actuation times that are short but nevertheless longer than the fundamental flexural period, the strip is observed to remain close to the instantaneous quasi-static equilibrium for most of the loading process. This allows us to derive an energetic criterion that accurately estimates a dynamic instability threshold well below the saddle-node bifurcation point. On the other hand, very near the bifurcation point, the evolution of the quasi-static equilibrium undergoes a geometric boost, which entrains the general motion of the beam. As a result, a slower actuation of the clamp than predicted by the energy argument suffices to produce snap-through. A distinct scaling is derived in that limit, based on the aforementioned boost and critical slowing down of the least stable vibration mode of the beam. More broadly, our results show how finite-rate forcing can trigger snap-through before the quasi-static instability threshold is reached

发表机构

• Université libre de Bruxelles (U.L.B.)（布鲁塞尔自由大学）
• Aix Marseille University, CNRS, Institut Universitaire des Systèmes Thermiques et Industriels（艾克斯马赛大学，法国国家科学研究中心，热系统与工业大学研究所）
• Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert（索邦大学，法国国家科学研究中心，让·勒朗·达朗贝尔研究所）
• Laboratoire d’Acoustique de l’Université du Mans (LAUM), IA-GS, CNRS（勒芒大学声学实验室（LAUM），IA-GS，法国国家科学研究中心）

机构由 AI 辅助整理，请以论文原文为准。