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Elastic superlattices with simultaneously negative effective mass density and shear modulus
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10.1063/1.4794314
/content/aip/journal/jap/113/9/10.1063/1.4794314
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/9/10.1063/1.4794314

Figures

Image of FIG. 1.
FIG. 1.

Phononic dispersion curves for transverse modes propagating along the growth direction of binary superlattices composed of one layer of rubber and the other one of solid polyurethane (curves A1-A2), conventional polyurethane foam (curves B1-B2), and auxetic polyurethane foam (curves C1-C5).

Image of FIG. 2.
FIG. 2.

Phononic dispersion curves for the longitudinal modes propagating along the growth direction of binary superlattices as in Fig. 1 : solid-polyurethane/rubber (curve F1), conventional-polyurethane-foam/rubber (curve G1), and auxetic-polyurethane-foam/rubber (curves H1-H3).

Image of FIG. 3.
FIG. 3.

(a) Second pass band (A2) of transverse phonon modes propagating in a solid-polyurethane/rubber superlattice. Frequency dependences for the effective dynamic density (panel b) and elastic constant (panel c).

Image of FIG. 4.
FIG. 4.

(a) Second pass band (B2) of transverse phonon modes propagating in a conventional-polyurethane-foam/rubber superlattice. Frequency dependences for the effective dynamic density (panel b) and elastic constant (panel c).

Image of FIG. 5.
FIG. 5.

(a) Second pass band (C2) of transverse phonon modes propagating in an auxetic-polyurethane-foam/rubber superlattice. Frequency dependences for the effective dynamic density (panel b) and elastic constant (panel c).

Image of FIG. 6.
FIG. 6.

Real (dashed curve with label 1) and imaginary (dotted curve withlabel 2) parts of the displacement profile u(z) for the eigenmode at kHz and in the band A2 shown in Fig. 3 . Solid line (curve 3): Profile of the magnitude . All the profiles are normalized to the magnitude . Gray regions correspond to rubber layers.

Image of FIG. 7.
FIG. 7.

Real (dashed curve with label 1) and imaginary (dotted curve withlabel 2) parts of the displacement profile u(z) for the eigenmode at kHz and in the band B2 shown in Fig. 4 . Solid line (curve 3): Profile of the magnitude . All the profiles are normalized to the magnitude . Gray regions correspond to rubber layers.

Image of FIG. 8.
FIG. 8.

Real (dashed curve with label 1) and imaginary (dotted curve withlabel 2) parts of the displacement profile u(z) for the eigenmode at kHz and in the band C2 shown in Fig. 5 . Solid line (curve 3): Profile of the magnitude . All the profiles are normalized to the magnitude . Gray regions correspond to rubber layers.

Tables

Generic image for table
Table I.

Component parameters (mass density ρ, Young E, and shear G moduli used in the calculations of dispersion curves and effective dynamic parameters).

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/content/aip/journal/jap/113/9/10.1063/1.4794314
2013-03-05
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Elastic superlattices with simultaneously negative effective mass density and shear modulus
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/9/10.1063/1.4794314
10.1063/1.4794314
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