Babinet's principle for elastic waves: A numerical test

Babinet's principle states that the diffracted fields from complementary sc reens are the negative of each other. In electromagnetics, Babinet's princi ple for infinitely thin perfectly conducting complementary screens implies that the sum, beyond the screen plane, of the electric and the magnetic fie lds (adjusting physical dimensions) equals the incident (unscreened) electr ic field. A test of the principle for the elastodynamic case was made using numerical calculations, and the results demonstrate that Babinet's princip le holds quite well for complementary plane screens, with contrasting bound ary conditions; that is, the complementary screen of a stress-free screen i s a rigid screen with openings where the original stress-free screen existe d, and vice versa. The results are exact in an anisotropic SH case; for the P-SV case, the diffracted waves, PdP, SdS, PdS, and SdP satisfy the princi ple exactly, while the refracted waves, PdPrSc and SdPrSc, do not satisfy t he principle at all (these waves are generally much smaller than the PdS an d SdP waves). Diffracted surface waves also do not satisfy the principle. T he numerical method is based on a domain-decomposition technique that assig ns a different mesh to each side of the screen plane. The effects of the sc reens on wave propagation are modeled through the boundary conditions, requ iring a special boundary treatment based on characteristic variables. The a lgorithm solves the velocity/ stress wave equations and is based on a Fouri er/Chebyshev differential operator. (C) 1999 Acoustical Society of America. [S0001-4966(99)01403-4].