研究末端加载弹性杆的稳定性，揭示失稳机制与参数关系。
Stability analysis through folds: An end-loaded elastica with a lever arm
- 通过辨识变分问题的特征分支图，分析固定自由端系统的平衡路径。
- 发现杠杆臂加载下存在多种弹跳失稳现象，其发生依赖于系统参数。
- 成果可用于软体机器人臂等柔性执行器的设计优化。
许多物理系统可建模为参数依赖的变分问题。在诸多情况下，多个平衡态共存，需评估其稳定性并监测相互间的转变。通常，平衡态的稳定性特性在参数空间的折叠点附近发生变化。稳定性的变化方向蕴含于解的特定投影中，称为特征分支图。本文识别出具有固定-自由端特征的变分问题的此类投影，并以通过刚性杠杆臂施加末端载荷的弹性杆（Elastica）为例进行研究。通过数值示例揭示了多种弹跳失稳现象及其对系统参数的依赖关系。该研究成果在软体机器人臂及其他驱动器设计中具有潜在应用价值。
原文摘要 · Abstract (English)
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the stability characteristics of the equilibria change near folds in the parameter space. The direction of stability changes is embedded in a specific projection of the solutions, known as distinguished bifurcation diagrams. In this article, we identify such projections for variational problems characterized by fixed-free ends - a class of problems frequently encountered in mechanics. Using these diagrams, we study an Elastica subject to an end load applied through a rigid lever arm. Several instances of snap-back instability are reported, along with their dependence on system parameters through numerical examples. These findings have potential applications in the design of soft robot arms and other actuator designs.
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