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On Anti-Plane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations Read chapter Read first chapter

2019 | OriginalPaper | Chapter

A Far-Field Asymptotic Analysis in the High-Frequency Diffraction by Cracks

Author : M. Y. Remizov

Published in: Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials

Publisher: Springer International Publishing

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Abstract

On the basis of recently obtained asymptotic solutions of integral equations by the Wiener-Hopf method for diffraction by a straight finite-length crack in a linear elastic medium, we study the properties of the far-zone scattered field at high frequencies for (1) - anti-plane problem in a homogeneous medium, (2) - anti-plane problem for an interface crack, and (3) - in-plane problem in a homogeneous medium.The method proposed is founded on a high-frequency solution of the basic integral equation of the scattering problem. Then we develop an explicit analytical representation for the leading asymptotic term, by estimating the far-field behavior of the relevant integrals with high oscillations by the method of stationary phase. This allows us to obtain the final form of the scattered field in an explicit analytical form as some quadratures.

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previous chapter Finite Element Study of Ceramic Matrix Piezocomposites with Mechanical Interface Properties by the Effective Moduli Method with Different Types of Boundary Conditions
next chapter 3d Propagation of Ultrasonic Waves Through a System of Defects in an Elastic Material, with Arbitrary Reflections and Transformations
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Metadata
Title
A Far-Field Asymptotic Analysis in the High-Frequency Diffraction by Cracks
Author
M. Y. Remizov
Copyright Year
2019
Book
Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials

Print ISBN: 978-3-030-17469-9

Electronic ISBN: 978-3-030-17470-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-17470-5_13