Scattering of plane harmonic P, SV and Rayleigh waves by a completely embedded corrugated elastic inclusion

Scattering of a plane harmonic P, SV or Rayleigh wave by a corrugated elastic inclusion completely embedded in a two-dimensional isotropic half or full space is investigated by using a direct boundary integral equation method. The corrugated scatterer is generated by superimposing a sinusoidal perturbation of arbitrary amplitude and period to a smooth elliptical shape.Extensive testing of the numerical results is presented. The displacement fields are evaluated along the half space and rough inclusion surfaces for a wide range of frequencies and corrugation shapes. The results clearly demonstrate the importance of the inclusion roughness on the ensuing motion. The surface response is found to strongly depend upon the frequency and polarization of the incident wave and the shape of the inclusion. For both models and low frequency incident waves the difference between the rough and smooth inclusion response is small. Moderate differences between the two responses are obtained at a higher frequency for vertical P and SV incidences or an oblique incident P wave. However, at the higher frequency for an oblique SV or a Rayleigh wave incidence, the half-space surface response is very sensitive upon the inclusion roughness especially for shorter corrugation periods. Similarly, for the full-space problem the inclusion roughness may produce significant effects in the resulting motion for both P and SV incident waves even at moderate frequencies.