By Richard V. Craster, Sébastien Guenneau
About the publication: This booklet is the 1st finished assessment on acoustic metamaterials; novel fabrics which may control sound waves in wonderful methods, which come with collimation, focusing, cloaking, sonic screening and amazing transmission. It covers either experimental and theoretical points of acoustic and elastic waves propagating in dependent composites, with a spotlight on powerful houses linked to destructive refraction, lensing and cloaking. so much comparable books within the box tackle electromagnetic metamaterials and concentrate on numerical equipment, and little (or no) experimental part. each one bankruptcy can be authored via an stated professional, among the subjects lined could be experimental effects on non-destructive imaging, cloaking via floor water waves, flexural waves in skinny plates. purposes in scientific ultrasound imaging and modeling of metamaterials can be emphasised too. The publication can function a reference for researchers who desire to construct a pretty good beginning of wave propagation during this classification of novel materials.
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Extra resources for Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking
E. μη = η2 μr where μr denotes the shear modulus inside a rod before scaling. The time-harmonic displacement field satisfies the following governing equation ∇ · (μη ∇uη ) + k 2 uη = 0. 43) When the acoustic wave penetrates the structured cloak Ωf , it undergoes fast periodic oscillations: Ωf (a ≤ |xi | ≤ b, i = 1, 2), is evenly divided into a large number N(η) ∼ η−2 of small sectors ηY , where η is a small positive real parameter. The smaller η, the larger the number of small sectors ηY . 43) remains fixed.
5 in panel (c). [From ] that is it separates into a standing wave solution on the fast scale U0 (ξ ; k0 ) modulated by a long-scale function f (X). 77) where the spatially constant tensor Tij incorporates the short-scale information associated with the standing wave frequency k0 . This tensor is composed of integrals of the standing wave displacements are related quantities, , these are no longer simple averages, that act to capture the influence of the short-scale upon the longscale. 78) for r a positive constant, an exact solution is readily obtained.
The density is 1 everywhere of a series. 74) that the larger the inclusion, the larger the negative values of the homogenized density upon resonance. 5 Dispersive Effective Parameters and Negative Refraction An important application of the dispersive nature of the effective density for such high-contrast phononic crystals is the possibility to achieve negative refraction and 1 Fundamentals of Acoustic Metamaterials 33 Fig. 5 (c, d) corresponding to a negative group velocity in Fig. 17. The density is 1 everywhere.