Scattering of plane harmonic SH waves by multiple inclusions

Abstract

SUMMARY Scattering of a plane harmonic SH wave by an arbitrary number of inclusions of general shape and placements within an elastic half-space is investigated by using a direct boundary integral equation approach. The integral equations have been reduced to a system of linear algebraic equations by using the linear elements. The structure of the resulting algebraic system is investigated and compared to the single-inclusion model. For convenience the multiple-inclusion models are assumed to consist of the reference and the auxiliary inclusions. The reference inclusion has the same shape, placement and the material properties as those of the corresponding single-inclusion model. The auxiliary inclusions then surround the reference inclusion assuming different patterns. Extensive testing of the proposed solution is performed. These tests include the transparency and the single-inclusion tests. In the former the material properties of the inclusions are assumed to be the same as those of the half-space and the surface response is found to be equal to the free field one. In the single-inclusion test the material properties of the auxiliary inclusions are assumed to be the same as those of the half-space while those of the reference inclusion are different. Then the resulting surface response is found to reduce to that of the single-inclusion model. For different number of multiple inclusions the surface motion atop the reference inclusion is compared with that of the corresponding single-inclusion model. In particular, a specific measure is introduced to assess accurately the importance of the multiple scattering upon the surface response. The effect of the auxiliary inclusion locations with respect to the reference inclusion upon the surface motion is investigated for two-, three- and nine-inclusion models. The results clearly show the importance of the interactions between the inclusions for a wide range of parameters present in the problem (e.g. nature of the incident wave, geometry of the model and the number of inclusions). For the problems considered here it appears that by ignoring these interactions, that is, using the single-inclusion model, will result in underestimation of the peak surface motion amplification.