Requiring no advanced knowledge of wave propagation, An Introduction to Metamaterials and Waves in Composites focuses on theoretical aspects of metamaterials, periodic composites, and layered composites. The book gives novices a platform from which they can start exploring the subject in more detail.
After introducing concepts related to elasticity, acoustics, and electrodynamics in media, the text presents plane wave solutions to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the plane wave expansion of sources as well as scattering from curved interfaces, specifically spheres and cylinders. The author then covers electrodynamic, acoustic, and elastodynamic metamaterials. He also describes examples of transformations, aspects of acoustic cloaking, and applications of pentamode materials to acoustic cloaking. With a focus on periodic composites, the text uses the Bloch-Floquet theorem to find the effective behavior of composites in the quasistatic limit, presents the quasistatic equations of elastodynamic and electromagnetic waves, and investigates Brillouin zones and band gaps in periodic structures. The final chapter discusses wave propagation in smoothly varying layered media, anisotropic density of a periodic layered medium, and quasistatic homogenization of laminates.
This book provides a launch pad for research into elastic and acoustic metamaterials. Many of the ideas presented have yet to be realized experimentally—the book encourages readers to explore these ideas and bring them to technological maturity.
Table of Contents
Elastodynamics, Acoustics, and Electrodynamics
A note about notation
Plane Waves and Interfaces
Plane wave solutions
Plane wave solutions in elastodynamics
Plane wave solutions in acoustics
Plane wave solutions in electrodynamics
Wave propagation through a slab
Sources and Scattering
Plane wave expansion of sources
Single scattering from spheres
A model for the permittivity of a medium
Negative permittivity materials
Artificial magnetic metamaterials
Negative refraction and perfect lenses
Acoustic and Elastodynamic Metamaterials
Dynamic mass density
Frequency-dependent moment of inertia
Negative elastic moduli
Band gaps, negative index and lenses
Willis materials in elastodynamics
A Milton-Willis model material
Transformation-Based Methods and Cloaking
Cloaking of electrical conductivity
Cloaking for electromagnetism
Inertial acoustic cloaking
Transformation-based cloaking in elastodynamics
Acoustic metafluids and pentamode materials
Waves in Periodic Media
Periodic media and the Bloch condition
Elastodynamics in the quasistatic limit
Electromagnetic waves in the quasistatic limit
Band gap phenomena in periodic composites
Waves in Layered Media
Wave equations in layered media
Piecewise-constant multilayered media
Smoothly varying layered media
Propagator matrix approach
Periodic layered media
Quasistatic homogenization of layered media
Biswajit Banerjee works at Industrial Research Limited in Auckland, New Zealand, where he researches and develops elastic wave control and deformation sensing technologies. He was previously a research professor of mechanical engineering and mathematics at the University of Utah.
… this book provides a thorough and modern introduction to a rapidly developing field of research with enormous potential for application.
—Chris Linton, Contemporary Physics, March 2012
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