Alexander B. Movchan, Natasha V. Movchan, Ian S. Jones

Mathematical Modelling of Waves in Multi-Scale Structured Media

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Chapman and Hall/CRC
• Seitenzahl: 258
• Erscheinungstermin: 8. November 2017
• Englisch
• Abmessung: 240mm x 161mm x 19mm
• Gewicht: 555g
• ISBN-13: 9781498782098
• ISBN-10: 1498782094
• Artikelnr.: 50248313

Autorenporträt

Alexander Movchan is a Professor at the University of Liverpool, Natasha Movchan is a Professor at the University of Liverpool, Ian Jones is a Professor at Liverpool John Moores University and an Honorary Fellow at the University of Liverpool, and Daniel Colquitt is a Lecturer at the University of Liverpool. The authors have worked on wave propagation in multi-scale elastic media over many years and have developed novel modelling approaches, which have opened efficient ways to design and study the dynamic response of multi-scale structures known as elastic metamaterials introduced within the last decade.

Inhaltsangabe

Introduction and literature survey. Foundations, methods of analysis of
waves and analytical approaches to modelling of multi-scale solids. Linear
differential operators and distributions. Waves in 1D, 2D and 3D media.
Fundamental solutions. Integral transforms and their applications in
modelling of waves. Dispersion. Periodic systems, Floquet-Bloch waves.
Lattice dynamics. Asymptotic analysis and singular perturbations. Waves in
structured media with thin ligaments and disintegrating junctions.
Multi-resonator systems. Singular perturbation analysis of fields in solids
with disintegrating junctions. Floquet-Bloch waves in periodic
multi-resonator systems. Standing waves. Asymptotic estimates for their
frequencies. Tuneable multi-resonator systems. Transmission of waves by
structured interfaces containing multi-scale resonators. Negative
refraction and localisation of waves in structured solids with thin
ligaments. Dynamic response of elastic lattices and discretised elastic
membranes. Lattice Green's functions in dynamics. Dynamic anisotropy and
localisation near defects. Stop-band Green's functions and strong
exponential localisation. Localisation near cracks/inclusions in a lattice
. Cloaking and channelling of elastic waves in structured solids. A cloak
is not a shield. Cloaking as a channelling method for incident waves.
Boundary conditions on the interior contour of a cloak. Cloaking in elastic
plates. Singular perturbation analysis of an approximate cloak. Example of
an "impossible cloaking" problem. Structured interfaces in dynamics of
elastic solids. Structured interfaces as filters and polarisers.
Vortex-type resonators and chiral polarisers of elastic waves. Coated
inclusions in dynamics, scattering and neutrality. Lattice approximations
of filters and polarisers. Electronic Appendix: Illustrative animations