Reflection and transmission of elastic waves by the spatially periodic interface between two solids (theory of the integral-equation method)
type: Item
instance of: scholarly article
title: Reflection and transmission of elastic waves by the spatially periodic interface between two solids (theory of the integral-equation method)
zbMATH Open document ID: 0493.73023
DOI: 10.1016/0165-2125(80)90016-5
published in: Wave Motion
publication date: 1980-01-01T00:00:00Z
review text: In this paper, the author develops the linear theory of reflection and transmission of time-harmonic, elastic waves by the spatially periodic interface between two perfectly elastic media -- the interface being cylindrical in one direction and periodic in another direction. A given phase progression of the incident wave in the direction of periodicity induces a modal structure in the elastodynamic field and leads to the introduction of the so-called spectral orders. In accordance with this structure, the incident field is represented by the superposition of an infinite set of spectral orders, composed of P-waves and SV-waves. Then, outside the corrugations of the interface, the scattered field, can be represented by a superposition of the same kind, but of an outgoing nature. The main tools in the analysis are the elastodynamic Green-type integral relations which follow from the two dimensional elastodynamic reciprocity theorem wherein a suitable Green state is used. The author shows that, by adapting the Green state to the periodicity of the configuration, the scattering problem needs solution in a single cell only. To obtain results for specific configuration, a numerical implementation of the method is required involving the evaluation of the Green tensors, the numerical solutions of the coupled integral equations and the subsequent computation of the amplitude factors of the scattered field.
reviewed by: Mumtaz H. Kazi
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74S99
Mathematics Subject Classification ID: 74B99
zbMATH DE Number: 3776988
zbMATH Keywords: reflection
zbMATH Keywords: transmission
zbMATH Keywords: time-harmonic, elastic waves
zbMATH Keywords: spatially periodic interface
zbMATH Keywords: two perfectly elastic media
zbMATH Keywords: cylindrical in one direction
zbMATH Keywords: periodic in another direction
zbMATH Keywords: phase progression of incident wave
zbMATH Keywords: modal structure
zbMATH Keywords: elastodynamic field
zbMATH Keywords: incident field
zbMATH Keywords: represented by superposition of infinite set of spectral orders
zbMATH Keywords: P-waves
zbMATH Keywords: SV-waves
zbMATH Keywords: elastodynamic Green-type integral relations
zbMATH Keywords: scattering problem needs solution in single cell only
zbMATH Keywords: numerical solutions
zbMATH Keywords: coupled integral equations
zbMATH Keywords: amplitude factors
author: Jacob T. Fokkema
MaRDI profile type: Publication
full work available at URL: 0165-2125(80)90016-5
OpenAlex ID: W1972709600
cites work: Q3256163
cites work: Q3289624
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cites work: Q3883756
cites work: Scattering of elastic waves by elastically transparent obstacles (integral-equation method)
cites work: Q5685720
cites work: Elastodynamic diffraction by a periodic rough surface (stress-free boundary)
cites work: Diffraction of elastic waves by the periodic rigid boundary of a semi-infinite solid
cites work: Q5329071
cites work: Q4113454
cites work: Reflection and transmission of elastic waves by the spatially periodic interface between two solids (numerical results for the sinusoidal interface)
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description: scientific article; zbMATH DE number 3776988