An Introduction to Metamaterials and Waves in Composites by Biswajit Banerjee

By Biswajit Banerjee

Requiring no complex wisdom of wave propagation, An creation to Metamaterials and Waves in Composites makes a speciality of theoretical features of metamaterials, periodic composites, and layered composites. The ebook provides rookies a platform from which they could commence exploring the topic in additional detail.

After introducing strategies regarding elasticity, acoustics, and electrodynamics in media, the textual content provides airplane wave ideas to the equations that describe elastic, acoustic, and electromagnetic waves. It examines the aircraft 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 changes, 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, 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 booklet offers a release pad for learn into elastic and acoustic metamaterials. a few of the principles provided have not begun to be learned experimentally―the publication encourages readers to discover those principles and convey them to technological maturity.

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Acoustic power over a surface area Γ with outward unit normal n is then given by Z P= Γ I(x) · n dA = 1 Z T /2 Z dt dA [p(x,t) v(x,t)] · n . T −T /2 Γ For a simply connected region Ω of which Γ is the boundary, the divergence theorem yields 1 Z T /2 Z P= dt dV ∇ · [p(x,t) v(x,t)] T −T /2 Ω or Z 1 Z T /2 ∇ p · v + p∇ ∇ · v) . 56) where the dependence on x is implicit. If p = pr + i pi and v = vr + ivi , we may write these as p(t) = pr cos(ωt) + pi sin(ωt) and v(t) = vr cos(ωt) + vi sin(ωt) . 47) that, for isotropic media, ∂p =− ∂t Z ∞ −∞ κ(t − t ) ∇ · v(t ) dt and ∇ p = − Z ∞ ρ(t − t ) −∞ ∂v dt .

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. In SI units k = µ0 /(4π) where µ0 is the magnetic permeability of free space and has units of henry/m (H/m).

The primary variables in the above equations are E and B. 70) where µ 0 (x,t) is the magnetic permeability tensor of free space, µ is the magnetic permeability of the medium, ε 0 (x,t) is the permittivity tensor of free space, ε is the permittivity of the medium, M(x,t) is the magnetization vector, and P(x,t) is the polarization vector. The magnetization vector M measures the net magnetic dipole moment per unit volume. This dipole is associated with electron or nuclear spins. The polarization vector P measures the net electric dipole moment per unit volume and is caused by the close proximity of two charges of opposite sign.

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