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2013 | Book

Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism

Editors: Richard V. Craster, Julius Kaplunov

Publisher: Springer Vienna

Book Series : CISM Courses and Lectures


About this book

Properties of wave localization play a decisive role both in applications of engineered microstructures and in the detection of cracks and flaws. The papers in this volume give an introduction into a variety of interrelated dynamic localization phenomena occurring in elasticity, acoustics and electromagnetism. In particular, these involve surface and edge waves and also trapped modes localized near defects, shape changes and the edges of elongated waveguides. The effects of layering, prestress, anisotropy, periodic microstructures as well as various multi-field phenomena are addressed with reference to underlying industrial problems. The essential and up-to-date numerical, asymptotic, and analytical techniques are covered as well as relevant continuum theories that are required to make progress in, and understand wave localization and allied effects. A major focus is on a qualitative physical insight into the mechanisms of dynamic localization.

Table of Contents

Modelling microstructured media: periodic systems and effective media
My aim in these lectures is to give a broad overview of the Mathematics and Physics of perfectly periodic systems, drawing heavily upon the literature of solid-state physics: it is essential to understand how structure on a micro-scale affects longer scale macro-scale behaviour and periodic systems are a naturally place to begin. Periodic systems are, on one hand, quite special and the constructive interference created by periodicity leads to strong effects that we shall see later, but on the other hand many natural and man-made structures exhibit, at least some, general periodic structure. After developing the language of periodic systems we will turn our attention to the development of asymptotic “effective” media that are posed entirely upon the macro-scale. Importantly we will develop asymptotic theories valid at high frequencies. A general approach valid for continua, semi-discrete (frame) and fully discrete (mass-spring) systems will be developed. If time allows we will then look further into some of the remarkable physics that can be seen when waves move through structured media: defect states, all-angle negative refraction and ultra-refraction.
Richard V. Craster, M. Makwana
Multiscale models of electromagnetic and plasmonic metamaterials
In this chapter, we discuss paradigms central to electromagnetic metamaterials and their plasmonic counterparts. We start with a slab lens with unlimited resolution, which is made possible using the concept of negative refraction, when the permittivity and permeability of a medium change sign simultaneously. Pendry’s perfect lens heavily relies upon existence of surface plasmons that exist on its boundaries. Correspondences with acoustics are then investigated in light of spring-mass models which bridge the field of electromagnetic and acoustic metamaterials, which are composites within which light or other (e.g. elastic, liquid surface) waves experience inverted Snell-Descartes laws of refraction upon resonance of micro-scale resonators. Next, we explain how geometric transforms introduced for computational easiness in helicoidal fibres, were given a twist by Pendry’s team in 2006 in order to design invisibility cloaks. Finally, we apply these mathematical tools to the control of surface plasmons propagating at structured metal-dielectric interfaces. We illustrate transformational plasmonics with a broadband plasmonic invisibility carpet which has been experimentally validated by Quidant’s group in 2010 at near infrared frequencies.
Sébastien Guenneau
Explicit Models for Surface, Interfacial and Edge Waves
We derive explicit asymptotic formulations for surface, interfacial and edge waves in elastic solids. The effects of mixed boundary conditions and layered structure are incorporated. A hyperbolic-elliptic duality of surface and interfacial waves is emphasized along with a parabolic-elliptic duality of the edge bending wave on a thin elastic plate. The validity of the model for the Rayleigh wave is illustrated by several moving load problems.
Julius Kaplunov, D. A. Prikazchikov
Elastodynamic End Effects in Structural Mechanics
Current status of research on decay of dynamic end effects in elastic structures aiming at formulation of a dynamic analogue to Saint-Venant’s principle (DSVP) are critically reviewed. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. Nearly 200 references are examined in context of DSVP, starting with early ideas by Boley. Special attention is placed on available experimental findings on end effects and decay rate in dynamically excited structures. Current perception of possible versions of DSVP is classified into several categories, one of which, namely that of dynamic equivalence, is compatible with much of known experimental data and has been tacitly applied at various engineering situations. That observation, along with a perspective view on evolution of the traditional SVP, provides inspiring ground for renewed interest in both practical and theoretical aspects of DSVP formulation.
B. Karp, D. Durban
Trapped Modes and Edge Resonances in Acoustics and Elasticity
This chapter considers localized modes for acoustic and elastic waves. We first discuss trapped modes for acoustic scalar waves that are perfectly localized solutions near defects in waveguides with a real resonance frequency. Emphasis is given on the trapping mechanism coming from the evanescent nature of transverse modes in waveguides. We then study the case of quasi-trapped modes where the wave is strongly localized but can radiate energy. Complex resonance frequencies are shown to appear through approximate models and general principles. Eventually, we focus on elastic wave localization near traction free edges in plates and rods. The complicated polarization of the wave in elasticity is shown to increase the ability for trapping with very simple geometries.
Vincent Pagneux
Surface waves in elastic half spaces coated with crystalline films
A two-dimensional model of thin-film substrate interactions is obtained from three-dimensional elasticity theory for films having various kinds of crystalline symmetry. Extensions to electro-elastic behaviour are also discussed.
David J. Steigmann
Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism
Richard V. Craster
Julius Kaplunov
Copyright Year
Springer Vienna
Electronic ISBN
Print ISBN

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