Transversely isotropic elastodynamic solution of a finite layer on an infinite subgrade under surface loads

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 surface loads is considered. An analytical formulation is presented for the determination of the displacements and stresses in both regions in frequency domain. By means of a complete representation using two displacement potentials, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order and a second-order partial differential equation. Using Fourier expansions and Hankel transforms in cylindrical coordinates, the formulation includes a complete set of transformed displacement-potential and stress-potential relations. As illustrations, the cases of a finite layer bonded to (i) an identitcal underlying half-space, (ii) on a rigid half-space, and (iii) an elastic half-space of different material moduli are considered. Typical numerical results on the response characteristics as a function of material anisotropy, in both the frequency and spatial domains are included.