Diffraction by an Immersed Elastic Wedge, Issue 1723

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Springer Science & Business Media, Dec 15, 1999 - Mathematics - 134 pages
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This monograph presents the mathematical description and 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, and 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.
 

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Contents

1 Introduction
1
2 Notation and Results
3
22 Strategy of the Study
6
23 Outgoing Solutions
12
24 Translation Operators
14
25 Main Theorems
16
26 Integral Representation of the Solution
19
27 Asymptotics of the Diffracted Wave in the Fluid
22
43 Proof of Theorem 2 Structure of the Spectral Function
75
5 Numerical Algorithm
79
52 The Case of an Incident Plane Wave in the Fluid
80
53 The Case of an Incident ScholteStoneley Wave
81
54 Approximation of the Regular Part of the Spectral Function
85
55 Computation of the Spectral Function
90
56 Practical Issues
91
6 Numerical Results
97

3 The Spectral Function
27
32 The Equations SolidFluid Coupled by a Plane Surface
33
33 Some Properties of the Operators DM TM
41
34 Decomposition of the Spectral Function
50
35 The Functional Equation for the Spectral Function
53
4 Proofs of the Results
57
42 Proof of Theorem 1 Existence and Uniqueness of the Spectral Function
74
62 Presentation of the Results
100
63 Iterates Generated by the Recursive Formula
103
64 Numerical Accuracy of the Direct Evaluation
104
Appendix
124
References
130
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