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Quasicrystalline-generated phononic crystals for advanced engineering applications

Chen, Zhijiang ORCID: 2022. Quasicrystalline-generated phononic crystals for advanced engineering applications. PhD Thesis, Cardiff University.
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Quasicrystalline phononic crystals structures have attracted intensive attention due to their outstanding capability in manipulating acoustic and elastic waves. They are rationally designed composites made of tailored building blocks, which are composed of one or more constituent bulk materials. As a main contribution to the research field, the concept of canonical configuration is here introduced as a novel tool to design quasicrystalline-generated structures. A periodic one-dimensional quasicrystalline-generated rod can be used to minimise system noise and vibration acting as a wave filter. It can be composed of repeated elementary cells devised by adopting generalised Fibonacci substitution rules. We apply the concept of canonical configuration into it, for which the orbits predicted by the trace map at the specific frequencies, which we call canonical frequencies, are periodic. This theory reveals that (i): the frequency spectrum is periodic and symmetric, (ii): a set of multiple periodic orbits exist at frequencies, and (iii): scaling exists in the frequency spectra that can be explained rigorously. Negative refraction effect can be used for wave focusing as a perfect lens. This effect in quasicrystalline laminate is governed by three particular frequencies. Canonical configurations for laminates and canonical frequencies can be used as a rule to investigate the effect of variation of those frequencies with different phases of the laminate. Three main conclusions can be drawn: (i): the effects of pure negative refraction following variation of canonical ratio and two-phase material are analysed, (ii): the three mentioned frequencies show some local peaks that can be analysed, in some cases analytically, (iii): under certain conditions, the expression of the Poynting vector can be simplified to calculate explicitly the transmission angle and to formulate an ‘inverse problem’ to design the laminate to achieve a particular pair of frequency and wavenumber. The interface state in periodic structures is formed in the interfacial region at two one-dimensional structures with different surface impedance, which can be determined by the symmetric properties of band-edge mode on lower or upper bandgap or, otherwise, properties of the Zak phase. It can be used as an amplifier leading an increasing of sensitivity at the target frequency. Three results are obtained: (i): the surface impedance of band-edge mode is periodically associated with canonical frequencies with canonical configuration, (ii): the representation based on the universal torus can be used as a new tool for designing quasicrystalline waveguides with the sign of surface impedance determined without Zak phase integral, (iii): the frequency of interface state is determined under two particular configurations.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Engineering
Uncontrolled Keywords: Metamaterials Quasicrystalline structures Bloch technique Topological interface state Wave shield Transfer matrix
Date of First Compliant Deposit: 25 April 2023
Last Modified: 25 Apr 2023 15:42

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