Dynamics of elastic hyperbolic lattices

Massimo Ruzzene, Emil Prodan, Camelia Prodan

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Article number101491
JournalExtreme Mechanics Letters
StatePublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Bioengineering
  • Chemical Engineering (miscellaneous)
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • Mechanical Engineering


  • Hyperbolic lattices
  • Mode localization
  • Spectral properties


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