The scattering field of SH-wave in a half-space with a semi-cylindrical hill and a subsurface horizontal hole is studied in the present research by utilizing a complex function and the moving-coordinate method. Based on the concept of ‘conjunction,’ the domain considered is divided into two subdomains. The first subdomain is a cylindrical one which includes the surface of the hill, while the rest is the second subdomain. In the cylindrical subdomain, a standing wave function is constructed which automatically satisfies the zero-stress condition at the hill surface and arbitrary-stress condition at the other part of the circular subdomain. For the second subdomain, which contains a semi-cylindrical canyon and a subsurface hole, a scattering wave function is assumed, which satisfies the zero-stress condition on the horizontal surface. By employing the moving-coordinate method, the solutions of the mathematical model established for the SH-wave can be obtained with the satisfaction of the continuous conditions of stress and displacement across the junction interface together with the zero-stress condition at the surface of the tunnel. The solutions such obtained consist of a series of infinite linear algebraic equations, which can be solved numerically with consideration of the first finite terms corresponding to the frequencies of the wave. For demonstrating the application of the model developed, the displacements of the horizontal and semi-cylindrical hill surfaces are quantified with different properties of wave and geometry parameters.
A rationalized Newtonian mechanics through consideration on the relativity of space (2nd report, Generalization for curvilinear moving coordinate systems)
