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The scattering of plane elastic waves by a one-dimensional periodic surface

✍ Scribed by T. Arens

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 158 KB
Volume: 22
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19990110)22:1<55::aid-mma20>3.0.co;2-t

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✦ Synopsis

The two-dimensional scattering problem for time-harmonic plane waves in an isotropic elastic medium and an effectively infinite periodic surface is considered. A radiation condition for quasi-periodic solutions similar to the condition utilized in the scattering of acoustic waves by one-dimensional diffraction gratings is proposed. Under this condition, uniqueness of solution to the first and third boundary-value problems is established. We then proceed by introducing a quasi-periodic free field matrix of fundamental solutions for the Navier equation. The solution to the first boundary-value problem is sought as a superposition of single-and double-layer potentials defined utilizing this quasi-periodic matrix. Existence of solution is established by showing the equivalence of the problem to a uniquely solvable second kind Fredholm integral equation.

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