Keywords:
Waves--Mathematical models.
;
Electronic books.
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.
,
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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