On The Scattering Of SH-Wave By Single Shallow-embedded Circular Cavity Near An Isosceles Triangular Hill

In this paper, an analytic method is developed for the problem of scattering of steady SH-wave by single shallow-embedded circular cavity, which is near an interface isosceles triangular hill.To solve problem, at first, a steady wave function which satisfies the boundary condition of stress free at the isosceles triangular wedges is constructed in virtue of the concept of symmetry of the isosceles triangle and the character of the trigonometric function; secondly, based upon the symmetry of scattering of SH-wave and the method of multi-polar coordinate system, a scattered wave function which satisfies the condition of stress free at the horizontal surface by shallow-embedded circular cavity impacted by incident steady SH-wave is constructed as well. Furthermore, moving coordinate system is used to transform the problem to be solved into a "conjunction" problem. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of infinite algebraic equations.In the end, the scattering of SH-wave by single circular cavity near an interface isosceles triangular hill is studied and numerical examples are provided to show the effects of wave number, distance between the center of the cavity and the ground surface upon the dynamic stress concentration around the cavity edge and ground motion.