Babinet’s principle for elastic waves: A numerical test

Abstract

Babinet’s principle states that the diffracted fields from complementary screens are the negative of each other. In electromagnetics, Babinet’s principle for infinitely thin perfectly conducting complementary screens implies that the sum, beyond the screen plane, of the electric and the magnetic fields (adjusting physical dimensions) equals the incident (unscreened) electric field. A test of the principle for the elastodynamic case was made using numerical calculations, and the results demonstrate that Babinet’s principle holds quite well for complementary plane screens with contrasting boundary conditions; that is, the complementary screen of a stress-free screen is a rigid screen with openings where the original stress-free screen existed, 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 principle exactly, while the refracted waves, PdPrSc and SdPrSc, do not satisfy the principle at all (these waves are generally much smaller than the PdS and SdP waves). Diffracted surface waves also do not satisfy the principle. The numerical method is based on a domain-decomposition technique that assigns a different mesh to each side of the screen plane. The effects of the screens on wave propagation are modeled through the boundary conditions, requiring a special boundary treatment based on characteristic variables. The algorithm solves the velocity/stress wave equations and is based on a Fourier/Chebyshev differential operator.