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Ray Tracing Method for a High-Frequency Propagation of the Ultrasonic Wave Through a Triple-Periodic Array of Spheres

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Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 59))

Abstract

The Ray method is applied to study the propagation of a high-frequency plane wave through a triple-periodic system of the spherical obstacles. The initial plane wave is taken as a superposition of spherical waves, which in discretization are reduced to a system of waves, each of them being studied by the Ray method in a local formulation. On the first step, we calculate the geometric parameters of the trajectory of each ray transmitted through the system of spherical obstacles, which is a spatial broken polyline. On the second step, we calculate the wave characteristics, by using methods of the short-wave diffraction.

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Acknowledgements

The authors express their gratitude to the Russian Science Foundation (RSCF), for its support by Project 15-19-10008.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Milchakova Street 8a, Rostov-on-Don, 344090, Russia

    Nikolay V. Boyev & M. A. Sumbatyan

Authors
  1. Nikolay V. Boyev
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  2. M. A. Sumbatyan
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Correspondence to Nikolay V. Boyev .

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Editors and Affiliations

  1. Insti. for Math., Mech. and Comp. Sci., Southern Federal University Insti. for Math., Mech. and Comp. Sci., Rostov-on-Don, Russia

    Mezhlum A. Sumbatyan

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Boyev, N.V., Sumbatyan, M.A. (2017). Ray Tracing Method for a High-Frequency Propagation of the Ultrasonic Wave Through a Triple-Periodic Array of Spheres. In: Sumbatyan, M. (eds) Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials . Advanced Structured Materials, vol 59. Springer, Singapore. https://doi.org/10.1007/978-981-10-3797-9_10

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  • DOI: https://doi.org/10.1007/978-981-10-3797-9_10

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  • Online ISBN: 978-981-10-3797-9

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