Wave propagation in quasi-crystalline generated phononic structure

Farhat, Abdelbaset 2023. Wave propagation in quasi-crystalline generated phononic structure. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

Wave propagation in a class of two-phase phononic structures in which cells are generated according to Fibonacci sequences is investigated. The Fibonacci sequence is a one-dimensional quasi-crystalline rule. I studied axial waves in quasi-periodic infinite rods and flexural waves in quasi-periodic infinite beams. In the axial wave case, two-phase phononic rods whose elementary cells are designed adopt the quasi-crystalline silver mean Fibonacci substitution rule. The stop/pass-band spectra are studied with the aid of a trace-map formalism, which provides a geometrical interpretation of the recursive rule governing traces of the relevant transmission matrices: the traces of two consecutive elementary cells can be represented as a point on a surface defined by an invariant function of the circular frequency, and the recursivity implies the description of an orbit on a surface called Kohmoto’s surface. I showed that, for a sub-class of silver mean-generated waveguides, the orbits predicted by the trace map at specific frequencies are periodic. The configurations for which this occurs, called canonical, are also associated with periodic stop/pass-band diagrams along the frequency domain. Several types of periodic orbits exist, and each corresponds to a self-similar portion of the dynamic spectra whose scaling law can be studied by linearizing the trace map in the neighborhood of the orbit. The obtained results provide both a new piece of theory to better understand the behavior of classical two-phase composite periodic waveguides and an important advancement towards the design and realization of phononic quasi-crystalline-based metamaterials. For flexural waves of quasiperiodic infinite beams designed by adopting the quasi-crystalline golden mean Fibonacci substitution rule, I investigated the effect of the axial pre-stress on the dispersion diagrams. I also investigated the frequency shift of the stop/pass band positions. The results show that pre-stress has a clear influence on the width of the pass/stop band, increasing or decreasing depending on the type of pre-stress applied. This thesis gives a deep understanding of how waves propagate in quasiperiodic structures, giving broader options for designers of acoustic devices like waveguides and acoustic filters.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Engineering
Uncontrolled Keywords:	1). Periodic Structure 2). Quasiperiodic Structure 3). Fibonacci Sequences 4). Kohmoto’s Invariant 5). Periodic orbits 6). Pre-stress
Date of First Compliant Deposit:	16 February 2024
Last Modified:	16 Feb 2024 10:00
URI:	https://orca.cardiff.ac.uk/id/eprint/166302

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