Dynamics of elastic hyperbolic lattices

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