Exploring Topology of 1D Quasiperiodic Metastructures through Modulated LEGO Resonators

TL;DR

This paper demonstrates the experimental mapping of topological edge states in a quasiperiodic elastic metastructure using LEGO resonators, revealing new topological phenomena in aperiodic media.

Contribution

It introduces a versatile LEGO-based platform to experimentally explore topological properties and Hofstadter-like spectra in elastic quasiperiodic metastructures.

Findings

First experimental observation of Hofstadter-like spectrum in elastic medium

Topological edge states localized at boundaries are verified

Edge state locations can be tuned via modulation phase

Abstract

We investigate the dynamics and topology of metastructures with quasiperiodically modulated local resonances. The concept is implemented on a LEGO beam featuring an array of tunable pillar-cone resonators. The versatility of the platform allows the experimental mapping of the beam's Hofstadter-like resonant spectrum, which is the first reported observation for an elastic medium. The non-trivial spectral gaps are classified by evaluating the integrated density of states of the bulk bands, which is experimentally verified through the observation of topological edge states localized at the boundaries. Results also show that the spatial location of the edge states can be varied through the selection of the phase of the resonator's modulation law. The presented results open new pathways for the design of metastructures with novel functionalities going beyond those encountered in periodic media by exploiting aperiodic patterning of local resonances and suggest a simple, viable platform for the observation of a variety of topological phenomena.