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Phononic canonical quasicrystalline waveguides

Gei, Massimiliano, Chen, Zhijiang, Bosi, Federico and Morini, Lorenzo 2020. Phononic canonical quasicrystalline waveguides. Applied Physics Letters 116 (24) , 241903. 10.1063/5.0013528

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: AIP Publishing
ISSN: 0003-6951
Date of First Compliant Deposit: 16 June 2020
Date of Acceptance: 4 June 2020
Last Modified: 31 Jul 2020 16:09
URI: http://orca.cf.ac.uk/id/eprint/132483

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