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Phononic canonical quasicrystalline waveguides

Gei, M; Chen, Z; Bosi, F; Morini, L; (2020) Phononic canonical quasicrystalline waveguides. Applied Physics Letters , 116 (24) , Article 241903. 10.1063/5.0013528. Green open access

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Abstract

The dynamic behavior of the class of periodic waveguides whose unit cells are generated through a quasicrystalline sequence can be interpreted geometrically in terms of a trace map that embodies the recursive rule obeyed by traces of the transmission matrices. We introduce the concept of canonical quasicrystalline waveguides, for which the orbits predicted by the trace map at specific frequencies, called canonical frequencies, are periodic. In particular, there exist three families of canonical waveguides. The theory reveals that for those (i) the frequency spectra are periodic and the periodicity depends on the canonical frequencies, (ii) a set of multiple periodic orbits exists at frequencies that differ from the canonical ones, and (iii) perturbation of the periodic orbit and linearization of the trace map define a scaling parameter, linked to the golden ratio, which governs the self-similar structure of the spectra. The periodicity of the waveguide responses is experimentally verified on finite specimens composed of selected canonical unit cells.

Type: Article
Title: Phononic canonical quasicrystalline waveguides
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/5.0013528
Publisher version: https://doi.org/10.1063/5.0013528
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/10101583
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