An Introduction to Metamaterials and Waves in Composites by Biswajit Banerjee

By Biswajit Banerjee

Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites specializes in theoretical facets of metamaterials, periodic composites, and layered composites. The e-book supplies rookies a platform from which they could commence exploring the topic in additional detail.

After introducing recommendations regarding elasticity, acoustics, and electrodynamics in media, the textual content offers aircraft wave recommendations to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the airplane wave growth of resources 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 variations, elements of acoustic cloaking, and functions 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, provides 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 ebook presents a release pad for examine into elastic and acoustic metamaterials. the various rules awarded have not begun to be discovered experimentally―the booklet encourages readers to discover those principles and convey them to technological maturity.

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Example text

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.

C : ∇ u] = (λ + µ)∇ Let us look for a forward-propagating plane wave solution to the above equation of the form u(x,t) = u(k · x − ct) . Researchers in elastodynamics prefer to work with a quantity called the “slowness vector,” defined as s := k/c, instead of the wave vector k. Note that s · s = 1/c2 and that the general plane wave solution in terms of the slowness vector is u(x,t) = u(s · x − t) . Since c = ω/ k , the time-harmonic plane wave solution can be written as u(x,t) = u eiω(s·x−t) .

For an isotropic material C = λ 1 ⊗ 1 + 2µ I and we have ∇ · u)1 + µ(x)[∇ ∇u + (∇ ∇u)T ] . C : ∇ u = λ(x)(∇ ∗ Our discussion of plane wave solutions in elastodynamics is based on Aki and Richards (1980). 50 An Introduction to Metamaterials and Waves in Composites If the material is also homogeneous, the governing equations become ∇(∇ ∇ · u) + µ ∇ · (∇ ∇u)T = ρ u¨ . ∇ · [C : ∇ u] = (λ + µ)∇ Let us look for a forward-propagating plane wave solution to the above equation of the form u(x,t) = u(k · x − ct) .

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