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 e-book offers rookies a platform from which they could begin exploring the topic in additional detail.
After introducing strategies relating to elasticity, acoustics, and electrodynamics in media, the textual content provides airplane 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, particularly spheres and cylinders. the writer then covers electrodynamic, acoustic, and elastodynamic metamaterials. He additionally describes examples of adjustments, elements 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, provides 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 presents a release pad for study into elastic and acoustic metamaterials. a number of the principles offered have not begun to be learned experimentally―the e-book encourages readers to discover those principles and produce them to technological maturity.
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Additional resources for An Introduction to Metamaterials and Waves in Composites
45) Similarly the acoustic potential equation in curvilinear coordinates is 1 ∂2 φ 1 ∂ √ ji ∂φ gg = 2 2 . 1 we will show that periodic and stratified structure can have an anisotropic dynamic density. 42) in the form ∂v +∇p = 0 ∂t where ρ 0 is now a second-order anisotropic mass density tensor. 32) we have ∂p +κ ∇ ·v = 0 . ∂t Combining the two equations gives us a single equation for p which is ρ0 · ∂2 p − κ ∇ · ρ −1 0 ·∇p = 0 . 43)2 for a medium with anisotropic density. If we also allow the mass density to be frequency dependent we can write Z ∞ −∞ ρ 0 (x,t − t ) · ∂v dt + ∇ p = 0 .
0 = ρ0 1, then the acoustic wave equation at fixed frequency is 1 ω2 ∇· ∇p + p=0. 51) where k2 = ω2 /c20 and c20 = κ/ρ. Here c0 is the phase velocity of the wave and must be real for a wave to propagate. 2. Proceeding in a similar manner, the acoustic equations in terms of a scalar potential (φ) can be expressed as ∇ϕ and v = −∇ p = −iωρ0 ϕ . The acoustic wave equation becomes the Helmholtz equation ∇2 ϕ + ω2 ϕ=0 c20 or ∇2 ϕ + k2 ϕ = 0 . 2 Acoustic transparency and opacity of a material as a function of ρ and κ.
4 An electrically conducting region Ω with boundary Γ. A potential φ = φ0 has been specified on the boundary. where n is the outward unit normal to the surface Γ, qtot is the charge inside Ω, q is the charge density, and t is the time. Assuming continuity of the quantities involved, we can use the divergence theorem and the Leibniz rule to get Z ∇ · J dΩ = − Ω Z ∂q dΩ. Ω ∂t Since the volume under consideration is arbitrary, we can use the continuum hypothesis to get the differential form of the conduction equation σ · ∇ φ) = − ∇ · J(x) = ∇ · (σ ∂q .