By Biswajit Banerjee
Requiring no complicated wisdom of wave propagation, An advent to Metamaterials and Waves in Composites specializes in theoretical features of metamaterials, periodic composites, and layered composites. The e-book supplies beginners a platform from which they could commence exploring the topic in additional detail.
After introducing ideas with regards to elasticity, acoustics, and electrodynamics in media, the textual content provides aircraft wave recommendations to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the airplane wave growth 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 alterations, 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 potent 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 constructions. 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 offers a release pad for examine into elastic and acoustic metamaterials. some of the principles provided haven't begun to be discovered experimentally―the booklet encourages readers to discover those rules and produce them to technological maturity.
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Additional info for An Introduction to Metamaterials and Waves in Composites
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. In SI units k = µ0 /(4π) where µ0 is the magnetic permeability of free space and has units of henry/m (H/m). Linear superposition also applies for many magnetic phenomena.
If we plug in this solution into the governing equations we get (λ + µ) (s ⊗ s) · u + µ (s · s) u = ρ u . Now [(s ⊗ s) · u] × s = 0 and [(s ⊗ s) · u] · s = (s · s)(u · s). Taking the vector and scalar products of the above equation with s leads to ρ− µ (u × s) = 0 c2 and ρ− λ + 2µ (u · s) = 0 c2 where we have used the relation s · s = 1/c2 . , u and s are perpendicular) and with phase velocity cs = µ/ρ. An elastodynamic plane wave in a homogeneous and isotropic medium cannot have both P- and S-wave components.
We will then proceed to calculate the reflection and transmission through flat slabs, first for acoustics (and the associated impedance tube calculations) and then for electromagnetism. 1 Plane wave solutions Ideally we would to find the most general solutions u(x,t) to the wave equations ∇2 u − 1 u¨ = 0 . , the solution varies in the x1 -direction but not in the x2 and x3 directions. Waves that have this property are called plane waves. The general solution of the equation for a plane wave propagating in the x1 -direction is u(x,t) = f1 (x1 − ct) + f2 (x1 + ct) .
An Introduction to Metamaterials and Waves in Composites by Biswajit Banerjee