A Transversely Isotropic Stratum Bonded on the Top of a Half-Space Subjected to Surface Tangential dynamic Force

An analytical solution is presented for displacements and stresses of a three dimensional linear hyperelastic transversely isotropic layer bonded on the top of a transversely isotropic half-space subjected to an arbitrary, time-harmonic surface tangential force. The equations of equilibrium in terms of displacements are uncoupled by using a set of two potential functions introduced by Eskandari-Ghadi (2005) for electrodynamics problems of any convex transversely isotropic domain with respect to the axis of material symmetry. The Fourier expansion and Hankel transform in a cylindrical coordinate system are employed to solve the boundary value problems for the potential functions. The development includes a set of transformed displacement-potential relations that are useful in a variety of either static or dynamic problems. To verify the accuracy of the numerical evaluation of the present solutions, comparisons with existing solutions are given. Different numerical results are also included to demonstrate the influence of the degree of the material anisotropy and the frequency of excitation on the response. Solutions presented in this paper are important in development of boundary-integral-equations to analysis both dynamic anisotropic soil-structure interaction problem and seismic waves scattering in anisotropic soils.