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Dynamics of elastic hyperbolic lattices
Extreme Mechanics Letters ( IF 4.3 ) Pub Date : 2021-10-08 , DOI: 10.1016/j.eml.2021.101491
Massimo Ruzzene 1 , Emil Prodan 2 , Camelia Prodan 3
Affiliation  

The hyperbolic space affords an infinite number of regular tessellations, as opposed to the Euclidean space. Thus, the hyperbolic space significantly extends the design space lattices, potentially providing access to unexplored wave phenomena. Here we investigate the dynamic behavior of hyperbolic tessellations governed by interactions whose strengths depend upon the distances between neighboring nodes. We find eigen-modes that are primarily localized either at the center or towards the boundary of the Poincaré disk, where hyperbolic lattices are represented. Hyperbolic translations of the seeding polygon produce distorted lattices, leading to a redistribution of the eigen-modes akin to edge-to-edge transitions. The spectral flow associated with these deformed lattices reveals a rich behavior that is characterized by modes that are spatially asymmetric and localized. The strength of the localization can be predicted from the slopes of the corresponding spectral branches, suggesting a potential topological origin for the observed phenomena. The rich yet predictable spectral flow and the high modal density of these lattices, along with the propensity of their modes to be strongly localized, suggest potential applications of hyperbolic lattices as vibration sensors, which operate over a large range of frequencies and exploit the sensitivity of localized modes to perturbations. In addition, hyperbolic lattices can inform the design of architected structural components with strong vibration attenuation and isolation capabilities.



中文翻译:

弹性双曲晶格动力学

与欧几里得空间相反,双曲空间提供了无限数量的规则镶嵌。因此,双曲线空间显着扩展了设计空间晶格,潜在地提供了对未探索的波浪现象的访问。在这里,我们研究了由相互作用控制的双曲曲面细分的动态行为,其强度取决于相邻节点之间的距离。我们发现本征模式主要位于庞加莱圆盘的中心或边界,其中表示双曲晶格。种子多边形的双曲线平移会产生扭曲的晶格,导致类似于边到边过渡的特征模式重新分布。与这些变形晶格相关的光谱流揭示了丰富的行为,其特征在于空间不对称和局部模式。可以从相应光谱分支的斜率预测定位的强度,这表明观察到的现象存在潜在的拓扑起源。这些晶格丰富但可预测的谱流和高模态密度,以及它们的模式强烈局部化的倾向,表明双曲晶格作为振动传感器的潜在应用,它在很大的频率范围内工作并利用微扰的局部模式。此外,双曲晶格可以为具有强大振动衰减和隔离能力的建筑结构部件的设计提供信息。可以从相应光谱分支的斜率预测定位的强度,这表明观察到的现象可能存在拓扑起源。这些晶格丰富但可预测的谱流和高模态密度,以及它们的模式强烈局部化的倾向,表明双曲晶格作为振动传感器的潜在应用,它在很大的频率范围内工作并利用微扰的局部模式。此外,双曲晶格可以为具有强大振动衰减和隔离能力的建筑结构部件的设计提供信息。可以从相应光谱分支的斜率预测定位的强度,这表明观察到的现象可能存在拓扑起源。这些晶格丰富但可预测的谱流和高模态密度,以及它们的模式强烈局部化的倾向,表明双曲晶格作为振动传感器的潜在应用,它在很大的频率范围内工作并利用微扰的局部模式。此外,双曲晶格可以为具有强大振动衰减和隔离能力的建筑结构部件的设计提供信息。这些晶格丰富但可预测的谱流和高模态密度,以及它们的模式强烈局部化的倾向,表明双曲晶格作为振动传感器的潜在应用,它在很大的频率范围内工作并利用微扰的局部模式。此外,双曲晶格可以为具有强大振动衰减和隔离能力的建筑结构部件的设计提供信息。这些晶格丰富但可预测的谱流和高模态密度,以及它们的模式强烈局部化的倾向,表明双曲晶格作为振动传感器的潜在应用,它在很大的频率范围内工作并利用微扰的局部模式。此外,双曲晶格可以为具有强大振动衰减和隔离能力的建筑结构部件的设计提供信息。

更新日期:2021-10-22
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