Scattering of transmission SH-wave by elliptic inclusion in bi-material half-pace

In this paper we studied the scattering of the transmission SH-wave form by elliptic elastic inclusions in a bi-material half-space using mainly the Green function, the complex function, the conformal mapping and the polar coordinate. Firstly, by introducing the complex variables and using the conformal mapping, we mapped the elliptic boundary into a unit circle. Next, by dividing the double-phase medium along the vertical boundaries into two quarter-spaces and adding a force system on the subdivision surface to make the SH wave satisfy the displacement and stress continuity conditions in the vertical boundary, we constructed a quarter-space Green function of displacement field. Then, we established an additional force system of integro differential equations in the vertical interface using the "conjunction" technique, and solved the unknown additional force system using the effective truncation. Finally, we presented and discussed the distribution of the dynamic stress concentration factor around the elliptic inclusion under the conditions of different parameters. The results show that the SH-wave incident angle and frequency, and the media both have influences on the distribution of the dynamic stress concentration factor.