Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism
June 11, 2012 — June 15, 2012
Coordinators:
- Richard Craster (Imperial College, London, UK)
- Julius Kaplunov (Brunel University, Uxbridge, UK)
A revolution is currently occurring in physics and engineering through the manufacture and application of smart structures with designer microstructure. Many of the applications: cloaking, invisibility, trapped and defect modes, resonances, ultra-refraction, all-angle-negative refraction, wave guiding along surfaces depend upon subtle properties of wave localization and are ubiquitous across several fields: examples will be drawn from elasticity, acoustics and electromagnetism. There are also numerous applications in more traditional fields such as the Non-Destructive Evaluation and Testing of structures. For example, prestresses or coatings on elastic media can be used to manipulate surface and edge waves, and localized modes arise in coated or deformed waveguides and are modified by fluid flow. In addition, surface and guided waves play a key role in crack and flaw detection and a knowledge of surface and resonant modes is invaluable. Recent work has highlighted how localized defect modes arise in microstructured media and new homogenization theories can be used to create continuum descriptions of micromechanical systems, even at high frequencies.
The aim of the course is to introduce an interdisciplinary audience into a variety of interrelated dynamic localisation phenomena occurring in elasticity, acoustic and electromagnetism. In particular, these involve surface and edge waves and also trapped modes localised 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 referencing to underlying industrial problems.
The course will provide a unique opportunity to learn simultaneously a wide range of subjects/techniques related to dynamic localisation phenomena. In particular, these include asymptotic and perturbation methods, modern homogenization
methodologies, variational methods, basics of non-linear elasticity, the general theory of surface waves, multimodal approach, and advanced applications of St Venant principle. The objective of the lectures is to cover the essential and up to date numerical, asymptotic, and analytical techniques as well as relevant continuum theories that are required to make progress in, and understand, wave localization and allied effects. A major focus will be on a qualitative physical insight into the mechanisms of dynamic localisation.
The lectures are chosen to appeal to researchers, primarily but not exclusively graduate students and postdoctoral researchers, from Mechanical, Aerospace and Civil Engineering programs and will naturally also be of interest to Physicists and Applied Mathematicians and will focus on recent work in localized modes and waves that are unlikely to appear in traditional university graduate courses; the lectures are also suitable for industrial researchers who encounter resonant or localised waves. The topics explore the applications in Engineering and Physics, notably in photonics, showing the interconnections with acoustics and elasticity that are normally treated independently. Both theoreticians and experimentalists are expected to gain useful knowledge from attending the course.
KEYWORDS: Smart Structures, Homogenization Methodologies, Cmposites and Laminates, Multimodal Methods.