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On the universality of the frequency spectrum and band-gap optimisation of quasicrystalline-generated structured rods

Morini, L., Tetik, Z. G., Shmuel, G. and Gei, M. 2020. On the universality of the frequency spectrum and band-gap optimisation of quasicrystalline-generated structured rods. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences 378 (2162) , 20190240. 10.1098/rsta.2019.0240

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Abstract

The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths. It is then shown how the proposed compact description of the spectrum can be exploited (i) to find the widest band gap for a given configuration and (ii) to optimize the layout of the elementary cell in order to maximize the low-frequency band gap. The scaling property of the frequency spectrum, that is a distinctive feature of quasicrystalline-generated phononic media, is also confirmed by inspecting band-gap/pass-band regions on the torus for the elementary cells of different Fibonacci orders.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: The Royal Society
ISSN: 1364-503X
Date of First Compliant Deposit: 2 September 2019
Date of Acceptance: 5 August 2019
Last Modified: 30 Nov 2019 06:43
URI: http://orca.cf.ac.uk/id/eprint/125221

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