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Speed of sound in periodic elastic composites
Arkadii Krokhin,Jesús Arriaga,Ludmila Gumen +2 more
- Vol. 2003
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TLDR
The low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals) is considered and exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived.Abstract:
We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.read more
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References
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Journal ArticleDOI
Acoustic metamaterials for new two-dimensional sonic devices
TL;DR: In this article, the elastic properties of cylinders are taken into account and a gradient index lens for airborne sound is proposed, whose functionality is demonstrated by multiple scattering simulations, and it is shown that metamaterials with perfect matching of impedance with air are possible by using aerogel and rigid cylinders equally distributed in a square lattice.
Journal ArticleDOI
Anisotropic mass density by two-dimensional acoustic metamaterials
TL;DR: In this paper, a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic is presented. But the analytical expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit, showing an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell and their multiple scattering interactions.
Journal ArticleDOI
Effective medium theory for elastic metamaterials in two dimensions
Ying Wu,Yun Lai,Zhao-Qing Zhang +2 more
TL;DR: In this article, an effective medium theory is developed which goes beyond the quasistatic limit to accurately predict the unusual properties of certain elastic metamaterials in two dimensions.
BookDOI
Homogenization and effective moduli of materials and media
TL;DR: In this paper, the effective dielectric coefficient of a composite medium is derived from the Darcy's constant, and the effect of the number of dielectrics on the overall response of an Inhomogeneous Nonlinear Dielectric.
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