[论文解读] Transition Waves in Mechanical Metamaterials with Neighbor-Programmable Energy Landscapes

Eléonore Duval, Giada Risso+3 more|arXiv (Cornell University)|Mar 10, 2026

Acoustic Wave Phenomena Research被引用 0

一句话总结

论文展示了在一个1D相邻可编程机械单元阵列中的多米诺式跃迁波，结合实验和弹簧-质量模型，展示相邻状态如何形塑能量地景和波速。

ABSTRACT

Transition waves in mechanical metamaterials manifest themselves as propagating interfaces between different stable states in lattices composed of arrays of coupled, intrinsically bistable elements. Here, we show experimentally and numerically that arrays of elastic unit cells that are individually monostable, yet whose energy landscapes can be programmed through interactions with neighboring units, provide a rich and largely unexplored platform for transition wave propagation. We implement this concept by designing a unit cell comprising a von Mises truss supported by two vertical elastic beams. In one-dimensional arrays of such units, we demonstrate that each cell's energy landscape can change from monostable to bistable depending on the state of its neighbors. This neighbor-programmable energy landscape enables the controlled initiation and propagation of transition waves, giving rise to highly discrete, directionally unbiased, domino-like wave propagation. Experiments and numerical simulations show that the existence and speed of the waves are governed by geometric design and mass distribution. Our results establish neighboring effects as a distinct mechanism for transition wave propagation, expanding the design space of mechanical metamaterials beyond architectures that rely on intrinsically multistable building blocks.

研究动机与目标

• 研究相邻依赖的能量地景如何在机械超材料中实现跃迁波的产生。
• 证明单稳态单元在邻居状态影响下可转变为双稳态。
• 演示多米诺式波传播并量化波速及传播条件。
• 建立一个最简模型，捕捉设计几何对稳定性与波动力学的影响。

提出的方法

• 基于一个与两根竖直梁相连的冯-米塞斯（von Mises）桁架的单元电池设计。
• 制造1D阵列并进行准静态和动态实验，以观测能量地景和波传播。
• 通过力-位移曲线表征能量地景并重构势能U(v_top)。
• 开发一个带有质量、轴向和扭转弹簧及阻尼的弹簧-质量模型，以再现观测到的动力学。
• 使用数值积分（在JAX的ODEINT中）对N个单元的链进行波传播仿真。
• 通过改变h、w_beam和质量来研究设计空间对能量障碍和波速的影响。

Fig. 1: Transition waves in mechanical metamaterials with neighbor-programmable energy landscapes. a) Schematic of the unit cell. b) The von Mises truss exhibits two distinct stable equilibrium states: the natural, stress-free up state and the inverted down state . c) Experimental snapshots of the m

实验结果

研究问题

• RQ1 邻居状态能否对单位的能量地景进行编程，从单稳态转变为双稳态？
• RQ2 单元格几何和质量分布如何控制跃迁波的存在与速度？
• RQ3 多米诺式波传播对双向激发和扰动是否鲁棒？
• RQ4 能否通过局部修改质量或几何在需求时调节波速？

主要发现

• 一个相邻程序化单元的1D超材料支持离散的、类似多米诺的跃迁波传播。
• 基础几何下的波速c_wave为54.1单位/秒，几何改变后变为40.1和37.2单位/秒。
• 当能量障碍过大时传播失败（例如结构d无传播）。
• 能量地景会根据邻居状态从单稳态切换到双稳态，从而实现波的启动与传播。
• 弹簧-质量模型能够在各几何下准确再现单位位移与波速，阐明k_theta和k_beam如何支配ΔU和c_wave。
• 对拉环的质量调整在实验和数值上将波速从92.9单位/秒调至40.8单位/秒，且空间质量变化可在链内产生速度对比。

Fig. 2: Effect of geometry on wave propagation. Spatiotemporal displacement diagrams for the four geometries investigated, overlaid with the corresponding numerical predictions (red lines). Supplementary Video 2 presents the associated experimental recordings.