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Diffraction by an Immersed Elastic Wedge : Lecture Notes in Mathematics - Jean-Pierre Croisille

Diffraction by an Immersed Elastic Wedge

Lecture Notes in Mathematics

Paperback Published: February 2000
ISBN: 9783540668107
Number Of Pages: 140

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This monograph presents the mathematical description & numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, & for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.

Introductionp. 1
Notation and results
Notation and resultsp. 3
Strategy of the studyp. 6
Outgoing solutionsp. 12
Translation operatorsp. 14
Main theoremsp. 16
Integral representation of the solutionp. 19
Asymptotics of the diffracted wave in the fluidp. 22
The spectral function
The integral system for the spectral functionp. 27
The equations solid-fluid coupled by a plane surfacep. 33
Some properties of the operators DM and TMp. 41
Decomposition of the spectral functionp. 50
The functional equation for the spectral functionp. 53
Proofs of the results
An isomophism theoremp. 57
Proof of Theorem 1. Existence and uniqueness of the spectral functionp. 74
Proof of Theorem 2. Structure of the spectral functionp. 75
Numerical algorithm
Introductionp. 79
The case of an incident wave in the fluidp. 80
The case of an incident Scholte-Stoneley wavep. 81
Approximation of the regular part of the spectral functionp. 85
Computation of the spectral functionp. 90
Practical issuesp. 91
Numerical results
Introductionp. 97
Presentation of the resultsp. 100
Iterates generated by the recursive formulap. 103
Numerical accuracy of the direct evaluationp. 104
Numerical diagrams of diffractionp. 104
Appendixp. 127
Subject Indexp. 129
Referencesp. 133
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540668107
ISBN-10: 3540668101
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 140
Published: February 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.81
Weight (kg): 0.22

Earn 112 Qantas Points
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