发表机构
Newcastle University; Beihang University; University of Birmingham（纽卡斯尔大学; 北京航空航天大学; 伯明翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以双质量 von Mises 桁架为模型，揭示耦合多稳态系统的过渡路径受耦合刚度和加载速率调控，建立了通过弹性耦合与加载速率控制调节过渡路径的通用力学框架。
AI 中文摘要
多稳态力学系统可通过 snap-through 失稳存储和释放弹性能，但当存在多条可达路径时，控制稳态之间的过渡路径仍具挑战性。本文引入双质量 von Mises 桁架作为研究由耦合鞍结分岔控制的路径选择的通用模型，该系统由两个带几何缺陷的耦合 snap-through 单元组成，产生四种稳定构型：完全倒置态、完全自然态以及两种中间混合态。研究表明，耦合刚度会重组准静态分岔结构，并在释放时从三条过渡路径中进行选择：通过一种混合态的连续 snap-through、直接协同 snap-through，或通过另一种混合态的连续 snap-through。采用伪弧长延拓方法追踪相关的鞍结分岔，确定与每条准静态路径相关的参数区间。随后证明，动态分岔延迟提供了另一种与速率相关的路径选择机制：即使准静态分岔结构倾向于唯一的连续路径，有限速率加载会将 snap-through 延迟到超出对应静态鞍结点的位置，并可重新排序两个单元的 snap-through 序列。在每个鞍结点附近，耦合动力学的局部约化得到具有耦合相关临界点和系数的范式，所得理论识别出惯性主导和过阻尼区域中不同的与速率相关的延迟规律，并预测 snap-through 顺序反转的临界速率。这些结果为通过弹性耦合和加载速率控制来调节多稳态系统中的过渡路径建立了通用力学框架。
英文摘要
Multistable mechanical systems can store and release elastic energy through snap-through instabilities, but controlling transition pathways between stable states remains challenging when multiple routes are accessible. Here, we introduce a two-mass von Mises truss as a general model for studying pathway selection governed by coupled saddle-node bifurcations. The system consists of two coupled snap-through units with geometric imperfections, giving rise to four stable configurations: a fully inverted state, a fully natural state, and two intermediate mixed states. We show that the coupling stiffness reorganizes the quasi-static bifurcation structure and selects among three transition pathways under release: sequential snapping through one mixed state, direct cooperative snapping, or sequential snapping through the other mixed state. Using pseudo-arclength continuation, we track the relevant saddle-node bifurcations and identify the parameter regimes associated with each quasi-static pathway. We then demonstrate that dynamic bifurcation delay provides an additional rate-dependent mechanism for pathway selection. Even when the quasi-static bifurcation structure favours a unique sequential pathway, finite-rate loading delays snap-through beyond the corresponding static saddle-node points and can reorder the snapping sequence of the two units. A local reduction of the coupled dynamics near each saddle-node yields normal forms with coupling-dependent critical points and coefficients. The resulting theory identifies distinct rate-dependent delay laws in the inertia-dominated and overdamped regimes and predicts the critical rate at which the snapping order reverses. These results establish a general mechanics framework for tuning transition pathways in multistable systems through elastic coupling and loading-rate control.
Comments22 pages, 8 figures
