analytical solution for a two-layer transversely isotropic half-space affected by an arbitrary shape dynamic surface load

the dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. with the help of displacements and stresses green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface layer and the underneath half-space in frequency domain. special results are prepared for circular, ellipsoidal, square and recangular patch load. it is shown that the displacements and stresses due to circular patch load are colapesd on the existing solution in the literature. some new illustrations are prepared to show the effect of the shape of the patch on the responses of the domain specially near the load.