Axissymmetric circular shape opening in transversely isotropic half-space

A half-space containing transversely isotropic material with a circular shape opening in it is considered in such a way the surfaces of the opening to be subjected to a time harmonic tensile tractions. The material axis of symmetry is considered to be perpendicular to the free surface of the half-space. The solution of this kind of problem may be used as a basic for fault analysis in transversely isotropic rocks. In order to analyze the problem, the Hankel integral transforms are used, so that the involved mixed boundary value problem is changed to a system of dual integral equations, which itself is transformed to Fredholm integral equations of second kind via the method propose by Noble in 1963. A numerical scheme is needed to solve the Fredholm integral equations in the general dynamic case. The graphical forms of the solution are presented to illustrate the effect of different degree of anisotropy on the response of the medium