Topological Edge States in Quasiperiodic Locally Resonant Metastructures

In extending the ideas of topological phases of matter to acoustic and mechanical systems, a quasiperiodic arrangement of resonators introduces frequency band gaps in addition to the locally resonant gap. Here numerical evaluation of the spectrum as a function of the quasiperiodic arrangement reveals a structure reminiscent of the famous Hofstadter butterfly. The onset of the locally resonant band gap and topologically nontrivial gaps with associated edge states is demonstrated numerically and experimentally. These structural designs can induce wave localization and attenuation over multiple frequency bands, for applications in $e.g.$ vibration isolation and energy harvesting.