Keywords:
Waves--Mathematical models.
;
Electronic books.
Description / Table of Contents:
Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.
Type of Medium:
Online Resource
Pages:
1 online resource (259 pages)
Edition:
1st ed.
ISBN:
9781498782104
Series Statement:
Chapman and Hall/CRC Monographs and Research Notes in Mathematics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5143499
DDC:
531/.1133015118
Language:
English
Note:
Cover -- Half title -- Published Titles -- Title -- Copyright -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Bloch-Floquet waves -- 1.2 Structured interfaces and localisation -- 1.3 Multi-physics problems and phononic crystal structures -- 1.4 Designer multi-scale materials -- 1.5 Dynamic anisotropy and defects in lattice systems -- 1.6 Models and physical applications in materials science -- 1.7 Structure of the book -- Chapter 2 Foundations, methods of analysis of waves and analytical approaches to modelling of multi-scale solids -- 2.1 Wave dispersion -- 2.2 Bloch-Floquet waves -- 2.3 Asymptotic lattice approximations -- 2.4 Transmission and reflection -- 2.5 Wave localisation and dynamic defect modes -- 2.6 Dynamic localisation in a biatomic discrete chain -- 2.7 Asymptotic homogenisation -- Chapter 3 Waves in structured media with thin ligaments and disintegrating junctions -- 3.1 Structures with undamaged multi-scale resonators -- 3.2 Singular perturbation analysis of fields in solids with disintegrating junctions -- 3.3 Structures with damaged multi-scale resonators -- Chapter 4 Dynamic response of elastic lattices and discretised elastic membranes -- 4.1 Stop-band dynamic Green's functions and exponential localisation -- 4.2 Dynamic anisotropy and localisation near defects -- 4.3 Localisation near cracks/inclusions in a lattice -- Chapter 5 Cloaking and channelling of elastic waves in structured solids -- 5.1 A cloak is not a shield -- 5.2 Cloaking as a channelling method for incident waves -- 5.3 Boundary conditions on the interior contour of a cloak -- 5.4 Cloaking in elastic plates -- 5.5 Singular perturbation analysis of an approximate cloak -- Chapter 6 Structured interfaces and chiral systems in dynamics of elastic solids -- 6.1 Structured interface as a polarising filter.
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6.2 Vortex-type resonators and chiral polarisers of elastic waves -- 6.3 Discrete structured interface: shielding, negative refraction, and focusing -- References -- Index.
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