Silver-mean canonical quasicrystalline-generated phononic waveguides

Farhat, Afifa; Gei, Massimiliano

doi:10.1016/j.jsv.2021.116679

Cited by 6 publications

(1 citation statement)

References 31 publications

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“…Moreover, when both l and q are supposed to be one in the recursive relation m n , the standard Fibonacci sequence is retrieved. This case has been studied in the works of [74][75][76][77][78][79][80][81] that concern quasi-crystalline waveguides and in Bacigalupo et al [71] dealing with tunable hierarchical waveguides, where the self-similar pattern of many standard Fibonacci generations has been detected. In figure 2d,e, the Floquet multiplier χ and its reciprocal 1/χ are evaluated on the unit circle (black) by referring to the angular frequency corresponding to the self-similarity delimitations in the band structure, namely ω = 6.3 (d) and ω = 12.6 (e).…”

Section: Representative Examplesmentioning

confidence: 99%

Dynamic continualization of mechanical metamaterials with quasi-periodic microstructure

Del Toro,

De Bellis,

Bacigalupo

2024

Phil. Trans. R. Soc. A.

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This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet–Bloch theory to validate the proposed scheme. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1).’

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