By Pierre A. Deymier
This complete e-book provides all features of acoustic metamaterials and phononic crystals. The emphasis is on acoustic wave propagation phenomena at interfaces resembling refraction, specifically strange refractive houses and adverse refraction. a radical dialogue of the mechanisms resulting in such refractive phenomena contains neighborhood resonances in metamaterials and scattering in phononic crystals.
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Extra resources for Acoustic Metamaterials and Phononic Crystals
This later Green’s function is labeled with a “prime” sign to indicate that the spring constants and masses m0 and b0of the finite crystal may be different from those of the infinite crystal m and b. A. Deymier and L. 81). 105). 106), n and n0 refer to sites in the infinite crystals and the finite side branch, respectively. 95) to obtain the displacement field. For this we also need to assume a form for the reference displacement UðDÞ ¼ tn . This displacement corresponds to a wave propagating in the infinite crystal and launched from n ¼ À1 .
1 (Eq. 5)). 18a) remains purely real. 18a). We will denote this term hÆ ðoÞ. 19) is zero. A trivial solution exists for k0 ¼ 0. However, in this case, the function hÆ ðoÞ is always negative and one cannot find a corresponding value for k00 . 20) is positive and the other negative. In the former case, the displacement is representative of an exponentially decaying evanescent wave. In the latter case, the displacement grows exponentially. This second solution is unphysical. , k) for a 1-D monoatomic crystal.
This example clearly illustrates the contribution of local resonance to wave propagation as well as the contribution of scattering by a periodic array of scatterers. The former mechanism is the foundation of locally resonant structures that determines the properties of acoustic metamaterials. The latter is associated with Bragg’s scattering, which is the fundamental mechanism underlying the properties of phononic crystals. References 1. N. Economou, Green’s Functions in Quantum Physics (Springer, New York, 1990) 2.