Use this URL to cite or link to this record in EThOS:
Title: Filtering and localisation effects for elastic waves in periodic composite structures
Author: Tallarico, Domenico
ISNI:       0000 0004 6495 6407
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2017
Availability of Full Text:
Access from EThOS:
Access from Institution:
This PhD thesis is primarily concerned with the study of propagation - either enhanced or inhibited - of elastic and electromagnetic waves in composite structures governed by coupled equations. The introductory chapter of the thesis provides scientific and technological motivations of the aforementioned problems by means of a literature review. Chapter 1 is concerned with the mathematical methodologies and illustrative examples useful in the subsequent chapters. In particular, the governing equations for piezoelectric materials are discussed. Quasi-periodicity Bloch-Floquet conditions are presented and used to study periodic isotropic and piezoelectric layered structures as well as structured discrete lattices in one and two dimensions. In chapter 2, we formulate and solve the scattering of shear elastic and TM electromagnetic waves from a finite stack of piezoelectric layers via a recurrence procedure approach. The reflectance and transmittance are evaluated for pass- and stop-bands of the corresponding periodic problem. Particular attention is given to the so called “cross-term” transmittance, i.e. to the quantification of the conversion efficiency of electromagnetic energy into elastic energy and vice versa. Chapter 3 is dedicated to the analysis of the dispersive properties of a doubly-periodic piezoelectric composite material. Different frequency regimes are identified: a low-frequency regime where the material behaves isotropically, and a higher frequency regime in which the material exhibits dynamic anisotropy. Attention is given to the role of the piezoelectricity on the aforementioned phenomena. Chapter 4 introduces a triangular lattice whose unit cell contains a geometrically chiral inclusion, i.e. a triangular resonator which is tilted by an angle ϑ0 with respect to the hosting unit cell. The Newton equations for the structured unit cell are solved together with Bloch-Floquet boundary conditions. The physical implications of the geometric chirality are identified and discussed both via the analysis of the dispersion diagram and through illustrative examples, including Bloch-Floquet displacement fields and forced problems of elasticity. Chapter 5 is devoted to several applications of the lattice structure introduced in chapter 4: focussing of elastic waves through a “flat lens” is achieved using the novel tunable dispersive properties of the triangular lattice with tilted resonators; structural interfaces containing tilted resonators are implemented and analysed in the context of edge wave-guiding and wave-defect interaction; finally the role of resonators on the initiation and advance of a crack in a thermoelastic lattice is investigated. In chapter 6 we provide our conclusions and outline future work.
Supervisor: Movchan, N. V. ; Movchan, A. B. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available