By Biswajit Banerjee
Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites specializes in theoretical features of metamaterials, periodic composites, and layered composites. The ebook supplies rookies a platform from which they could begin exploring the topic in additional detail.
After introducing suggestions concerning elasticity, acoustics, and electrodynamics in media, the textual content offers aircraft wave ideas to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the airplane wave enlargement of resources in addition to scattering from curved interfaces, particularly spheres and cylinders. the writer then covers electrodynamic, acoustic, and elastodynamic metamaterials. He additionally describes examples of modifications, features 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 booklet presents a release pad for study into elastic and acoustic metamaterials. a number of the rules offered have not begun to be discovered experimentally―the ebook encourages readers to discover those principles and produce them to technological maturity.
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Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites specializes in theoretical features of metamaterials, periodic composites, and layered composites. The ebook offers newbies a platform from which they could begin exploring the topic in additional element.
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Additional info for An Introduction to Metamaterials and Waves in Composites
The free current density (J f ) arises only from conduction currents arising from the response of the medium and not from beams of charged particles. 2. In the far distant past (t = −∞) all fields are zero. 3. The media are at rest. Define Z t D(x,t) := D(x,t) + −∞ J f (x, τ) dτ . 81) and using Maxwell’s equation connecting the magnetic field to the total current, we have ∂D ∂D = +Jf = ∇ ×H . 67) and Maxwell’s equation relating the electric displacement to the free charge density, we get ∇ ·D = ∇ ·D+ Z t −∞ ∇ · J f dτ = ∇ · D − Z t ∂ρ f −∞ ∂t dτ = ∇ · D − ρ f = 0 .
38 An Introduction to Metamaterials and Waves in Composites or µ−1 E1,2 ,2 + µ−1 E1,3 ,3 + ω2 εE1 = 0 . 6 we can write the above equation as ∇· 1 ∇ E1 + ω2 ε(x2 , x3 ) E1 = 0 . 27) for antiplane shear with the substitutions E1 ↔ u1 , 1 ↔µ, ε↔ρ. µ Let us now consider the case where the permeability and permittivity are anisotropic. In that case we can write these second-order tensors in matrix form as µ11 0 0 ε11 0 0 µ = µ (x2 , x3 ) ≡ 0 µ22 µ23 and ε = ε (x2 , x3 ) ≡ 0 ε22 ε23 .
3 Electromagnetic transparency and opacity of a material as a function of µ and ε. 92) where ε 0 is the real part of the permittivity tensor and σ is the electrical conductivity tensor. The above relation for the permittivity tensor can be obtained as follows. Recall that Z t D(x,t) = D(x,t) + J f (x, τ) dτ . −∞ Differentiation with respect to time gives ∂D ∂D = + J f (x,t) . ∂t ∂t 37 Elastodynamics, Acoustics, and Electrodynamics Assuming harmonic solutions of the form D(x,t) = D(x) exp(−iωt) ; D(x,t) = D(x) exp(−iωt) J f (x,t) = J f (x) exp(−iωt) ; E(x,t) = E(x) exp(−iωt) and plugging into the differential equation, we get (−iω)D(x) = (−iω)D(x) + J f (x) .