双曲空间中的机械连杆网络谱特性
Hyperbolic Space Spectral Characteristics in a Network of Mechanical Linkages
AI总结：
本研究通过数值与实验验证了双曲镶嵌机械晶格具有边界主导的振动谱和边缘波传播特性，开创了用于先进波控制的机械超材料新类别。
摘要：
我们研究了由弯曲双曲空间的镶嵌所定义的弹性晶格的动力学性质。这些晶格通过将规则双曲镶嵌的节点投影到平坦圆盘上，然后用简单的连杆连接这些节点而获得。数值和实验研究展示了它们的振动谱特性如何以高密度的局域在域边界的模式为特征。这些特性控制了宽带输入所诱导的波的传播。这暗示了在保护体介质免受边界入射扰动方面的应用潜力。我们通过评估和分析一个示例性双曲晶格的积分态密度和振动谱，揭示了其边界主导的性质。该晶格的动力学还通过与具有欧几里得和双曲性质分布的连续圆盘的比较而得以情境化，这证实了该晶格保留了在双曲平面中观察到的边界主导谱。然后，我们数值研究了晶格对入射在边界上的瞬态脉冲的响应，并发现发生了边缘受限的波传播。该晶格的模态和瞬态脉冲传播行为在一个铣削铝样品中得到了实验验证。通过利用双曲几何，我们的机械晶格开创了一类新型的机械超材料，其具有边界主导的波现象，类似于拓扑保护系统，适用于先进波控制的应用。
英文摘要：
We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those sites with simple linkages. Numerical and experimental investigations illustrate how their vibrational spectral properties are characterized by a high density of modes that are localized at the domain boundaries. Such properties govern the propagation of waves induced by broadband inputs. This suggests the potential for applications seeking the protection of bulk media from boundary-incident perturbations. We uncover the boundary-dominated nature of an exemplary hyperbolic lattice through the evaluation and analysis of its integrated density of states and vibrational spectrum. The dynamics of the lattice are also contextualized by comparing them with those of continuous disks characterized by Euclidean and hyperbolic property distributions, which confirms that the lattice retains the boundary-dominated spectrum observed in the hyperbolic plane. We then numerically investigate the response of the lattice to transient pulses incident on the boundary and find that edge-confined wave propagation occurs. The modal and transient pulse propagation behavior of the lattice is experimentally validated in a milled aluminum sample. By leveraging hyperbolic geometry, our mechanical lattice ushers in a novel class of mechanical metamaterials with boundary-dominated wave phenomena reminiscent of topologically protected systems suitable for applications in advanced wave control.
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