By Biswajit Banerjee
Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites makes a speciality of theoretical elements of metamaterials, periodic composites, and layered composites. The booklet supplies newcomers a platform from which they could begin exploring the topic in additional detail.
After introducing techniques on the topic of elasticity, acoustics, and electrodynamics in media, the textual content provides aircraft wave options to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the aircraft wave enlargement of assets in addition to scattering from curved interfaces, in particular spheres and cylinders. the writer then covers electrodynamic, acoustic, and elastodynamic metamaterials. He additionally describes examples of ameliorations, facets of acoustic cloaking, and purposes of pentamode fabrics to acoustic cloaking. With a spotlight on periodic composites, the textual content makes use of the Bloch-Floquet theorem to discover the powerful habit of composites within the quasistatic restrict, offers the quasistatic equations of elastodynamic and electromagnetic waves, and investigates Brillouin zones and band gaps in periodic buildings. the ultimate bankruptcy discusses wave propagation in easily various layered media, anisotropic density of a periodic layered medium, and quasistatic homogenization of laminates.
This e-book presents a release pad for study into elastic and acoustic metamaterials. a number of the principles offered haven't begun to be learned experimentally―the e-book encourages readers to discover those principles and convey them to technological maturity.
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Additional resources for An Introduction to Metamaterials and Waves in Composites
We have also seen that the electromagnetic wave equations can be written as ¨ c2 ∇2 A = A ∇ f − ∇ × ∇ × Π e ) = Π¨ e ; c2 (∇ c2 ∇2 φ = φ¨ ; ∇ f − ∇ × ∇ × Π m ) = Π¨m . c2 (∇ At fixed frequency we have the electrodynamic wave equations c2 ∇2 E + ω2 E = 0 ; c2 ∇2 H + ω2 H = 0 c2 ∇2 φ + ω2 φ = 0 ; c2 ∇2 A + ω2 A = 0 . Notice that, at a fixed frequency ω, most of these equations are of the form of the Helmholtz equation. In this chapter we will explore plane wave solutions of the wave equation. We will also examine plane wave solutions for problems involving reflection and refraction 47 48 An Introduction to Metamaterials and Waves in Composites of waves at plane interfaces.
The orientation of the magnetic dipole is given by the direction of the magnetic flux density (B), also called the magnetic induction. Let us now consider the magnetic flux density produced by a current. A current is a motion of charges and is described by a current density (J). Consider an element of length dl carrying a current J. The Biot-Savart law relates the elemental magnetic flux density (dB) produced at a point x due to the current in the element located at point y and can be expressed as dB = k J dl × (x − y) x−y 3 where k is a constant.
65) For linear magnetic materials the relationship between H and B can be deduced in a manner similar to that for electric fields and electric displacements. 66) where µ is the magnetic permeability of the medium. For time-independent media the above relation becomes H(x) = µ −1 (x) · B(x) =⇒ B(x) = µ (x) · H(x) . A relation between the electric and the magnetic field can be obtained with the help of the generalized Ohm’s law which predicts the current density generated by an electric field, J(x) = σ (x) · E(x) where σ is the second-tensor electrical conductivity tensor.