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 Hofstadter-like resonant spectrum of an elastic medium, in the form of a beam waveguide. 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 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.
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2021
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