By Pierre A. Deymier
This entire ebook provides all elements of acoustic metamaterials and phononic crystals. The emphasis is on acoustic wave propagation phenomena at interfaces akin to refraction, particularly strange refractive houses and unfavorable 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
The case n ¼ 3 and other odd values are identical to the case n ¼ 1. 35). Â pThese Ã dispersion p relations are only valid in the interval of wave number: À 2a ; 2a . They are illustrated in Fig. 5. In the super-cell representation, the dispersion relation consists of two branches that can be obtained graphically by folding the dispersion curve of Fig. 2 about p p two vertical lines at wave numbers À 2a and 2a . The super-cell representation of the band structure of the monoatomic crystal is a purely mathematical representation.
The dynamical operator for the cleaved crystal is written as ! h0 "$ # $ hS1 0 ¼ $ $ 0 hS2 2 Á Á Á À3 6 b Àg 6 6 0 b 6 16 0 0 ¼ 6 0 0 m6 6 6 0 0 6 4 0 0 0 0 À2 b Àg b 0 0 0 0 À1 0 b Àg b 0 0 0 0 1 0 0 0 0 b 0 Àa 0 0 Àa 0 b 0 0 2 3 0 0 0 0 0 0 0 0 b 0 Àg b b Àg 3 . . .. 0 7 7 À3 0 7 7 À2 0 7 7 À1 : 0 7 7 0 0 7 7 1 0 5 2 .. b . A. Deymier and L. Dobrzynski Fig. 11 Schematic illustration of the 1-D mono-atomic harmonic crystal cleaved between atoms 0 and 1 ! 77), h0 is a block matrix composed of two independent matrices hS1 and hS2, corresponding to the two semi-infinite crystals on the left and right of the cleaved $ bond, respectively.
A. Deymier and L. Dobrzynski Fig. 4 Schematic representation of the 1-D mono-atomic crystal as a periodic structure with super-period Na Fig. 5) that was illustrated in Fig. 2. 5) translated along the wave number axis by pa . For n ¼ 2a and other even values, one obtains again the same result than for n ¼ 0. The case n ¼ 3 and other odd values are identical to the case n ¼ 1. 35). Â pThese Ã dispersion p relations are only valid in the interval of wave number: À 2a ; 2a . They are illustrated in Fig.
Acoustic Metamaterials and Phononic Crystals by Pierre A. Deymier