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The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement

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Abstract

The work presented in this paper focuses on the reflection and transmission coefficients of an incident plane wave which impinges obliquely a plane of identical spheres arranged periodically in a homogeneous host with infinite extension. The Bloch theorem of periodic structure and the addition theorem of spherical wave functions are used to obtain the total scattering wave from all spherical scatterers periodically arranged in a plane. The total scattering wave in series form of spherical wave functions is then transformed into plane wave form in order to derive the reflection and transmission coefficients. Some numerical examples are given for different size, material constants and array patterns of spherical scatterers, and their influences on the reflection and transmission coefficients of a plane of spheres are discussed based on the numerical results. This study implies that a plane of spheres can be elaborately designed to serve as a sound barrier at a certain frequency range.

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Authors and Affiliations

  1. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing, 100083, China

    Qiang Zhao & P. J. Wei

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  1. Qiang Zhao
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  2. P. J. Wei
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Correspondence to P. J. Wei.

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Zhao, Q., Wei, P.J. The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement. Acta Mech 224, 1009–1018 (2013). https://doi.org/10.1007/s00707-012-0801-2

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  • DOI: https://doi.org/10.1007/s00707-012-0801-2

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