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Mathematical Models and Finite Element Approaches for Nanosized Piezoelectric Bodies with Uncoulped and Coupled Surface Effects Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Short-Wave Diffraction of Elastic Waves by Voids in an Elastic Medium with Double Reflections and Transformations

Author : Nikolay V. Boyev

Published in: Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials

Publisher: Springer Singapore

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Abstract

The classical diffraction problem of high-frequency waves emitted from a point source in an elastic medium with a void or a system of voids is considered. The voids are bounded by arbitrary smooth surfaces. Single reflection cases of longitudinal and transverse waves are studied by taking into account their transformations on the boundary surface. Double reflection cases are investigated for two different possibilities of transformations of elastic waves: the longitudinal wave transformed to the transverse one, and vice versa. The developed method of the research is based on the evaluation of diffraction integrals by means of multidimensional stationary-phase method. The novel approach allows us to obtain the leading asymptotic term of the diffracted displacement field as a closed-form expression in the cases of single and double reflections, which corresponds to the geometrical theory of diffraction (GTD).

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previous chapter Identification of Arrays of Cracks in the Elastic Medium by the Ultrasonic Scanning
next chapter Finite Element Modeling and Computer Design of Anisotropic Elastic Porous Composites with Surface Stresses
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Metadata
Title
Short-Wave Diffraction of Elastic Waves by Voids in an Elastic Medium with Double Reflections and Transformations
Author
Nikolay V. Boyev
Copyright Year
2017
Publisher
Springer Singapore
Book
Wave Dynamics and Composite Mechanics for Microstructured Materials and Metamaterials

Print ISBN: 978-981-10-3796-2

Electronic ISBN: 978-981-10-3797-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-981-10-3797-9_5

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