Diffraction by an immersed elastic wedge / Jean-Pierre Croisille, Gilles Lebeau

Auteur principal : Croisille, Jean-Pierre, 1961-, AuteurCo-auteur : Lebeau, Gilles, 1954-, AuteurType de document : Livre numériqueCollection : Lecture notes in mathematics, 1723Langue : anglais.Éditeur : Berlin : Springer, 1999ISBN: 9783540668107.ISSN: 1617-9692.Sujet MSC : 76Q05, Fluid mechanics, Hydro- and aero-acoustics
78A40, Waves and radiation in optics and electromagnetic theory
78A45, Optics, electromagnetic theory - General, Diffraction, scattering
78Mxx, Optics, electromagnetic theory - Basic methods
35L20, PDEs - Hyperbolic equations and hyperbolic systems, Initial-boundary value problems for second-order hyperbolic equations
En-ligne : Springerlink | Zentralblatt | MathSciNet
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The main aim of this booklet is to study the diffraction of a plane acoustic wave by a wedge-shaped elastic body located in an infinitely large space filled with a homogeneous fluid. To this end one supposes that i) the boundaries of the wedge are fixed planes, ii) the incident wave is normal to the edge of the wedge, iii) the field in the elastic medium is represented by two components of the displacement vector, while in the fluid it is represented by the potential function of the velocity, iv) the linearized equations are valid in both the wedge and the fluid. Under these assumptions one writes first the basic differential equations and boundary conditions and, then, one defines their outgoing solution. The authors try to obtain an integral expression of the outgoing solution in terms of two vector-valued spectral functions having three components, which reduce the problem into a system of singular integral equations. One of the main two results of the paper (Theorem 1) guarantees the existence and uniqueness of the solution while the other (Theorem 2) reveals the analytical structure of it. Furthermore, a numerical algorithm for the approximations of the spectral functions in the high-frequency limit is also given. A large number of numerical diagrams obtained through this algorithm are presented. (Zentralblatt)

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