By Biswajit Banerjee
Requiring no complex wisdom of wave propagation, An advent to Metamaterials and Waves in Composites specializes in theoretical points of metamaterials, periodic composites, and layered composites. The ebook offers newbies a platform from which they could begin exploring the topic in additional detail.
After introducing innovations regarding 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 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 modifications, points 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 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 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 offers a release pad for examine into elastic and acoustic metamaterials. the various rules offered haven't begun to be discovered experimentally―the publication 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
2 Plane Waves and Interfaces Owing to the extraordinary complexity of the investigation when written out in Cartesian form (which I began doing, but gave up aghast) some abbreviated method of expression becomes desirable. O LIVER H EAVISIDE, On the electromagnetic wave-surface, 1885. In the previous chapter we have seen that the dynamics of elastic, acoustic, and electromagnetic waves can be expressed in the form of wave equations. In classical linear elastodynamics without body forces we have the wave equations ∇ψ )T = ψ¨ .
In general, the direction of plane wave will not be oriented with one of the coordinate axes. Let k be a unit vector in the direction of propagation of the wave, also called the wave vector. Then the general solution of the wave equation is u(x,t) = f1 (k · x − ct) + f2 (k · x + ct) . This solution is not particularly useful because the functions f1 and f2 remain to be found. The problem that we face can be resolved by appealing to the Fourier transform, finding a particular solution for a fixed frequency, and summing up the solutions at all frequencies to arrive at the general solution.
3 Therefore the TM wave equation for the isotropic case has the form ∇· 1 ∇ H1 + ω2 µ(x2 , x3 ) H1 = 0 . 97) where R⊥ ≡ 0 1 −1 0 and E ≡ ε22 ε23 . ε23 ε33 The general solution independent of x1 is a superposition of the TE and TM solutions. 98) where the first term represents the TE solution. 99) implying that H2 = H3 = 0 which is the TM solution. 7 Maxwell’s equations in elasticity form Interestingly, Maxwell’s equations can be reduced to the form of the equations of elastodynamics at fixed frequency (Milton, 2006).