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A boundary method for elastic wave diffraction: Application to scattering of SH waves by surface irregularities

INSTITUTO DE INGENIERA UNIVERSIDA NACIONAL AUTONOMA DE MEXICO, MEXICO 20 DF Mexico
INSTITUTO DE INVESTIGACIONES EN MATHEMATICAS APLICADAS Y EN SISTEMAS UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO, MEXICO 20 DF Mexico

Abstract

A boundary method developed by Herrera is briefly explained in connection with wave scattering. The method is based on the use of complete systems of solutions of the homogeneous equations. A convenient criterion of completeness is the notion of c-completeness. The general method grants convergence of the approximating sequence when a least-squares fitting of the boundary conditions is used. As an illustration, the scattering and diffraction of SH waves by surface irregularities is treated here. It is shown that plane waves are c-complete in a bounded region of arbitrary shape. Scattering is formulated as a problem of connecting solutions in such a region with solutions in an unbounded one where Hankel functions are used. Numerical results for specific cases are reported.

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