Axisymmetric time-harmonic response of a transversely isotropic substrate–coating system

By virtue of a method of displacement potentials, an analytical treatment of the response of a transversely isotropic substrate–coating system subjected to axisymmetric time-harmonic excitations is presented. In determination of the corresponding elastic fields, infinite line integrals with singular complex kernels are encountered. Branch points, cuts, and poles along the path of integration are accounted for exactly, and the physical phenomena pertinent to wave propagation in the medium are also highlighted. For evaluation of the integrals at the singular points, an accurate analytical residual theory is presented. Comparisons with the existing numerical solutions for a two-layered transversely isotropic medium under static surface load, and a transversely isotropic half-space subjected to buried time-harmonic load are made to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses are presented to portray the dependence of the response of the substrate–coating system on the frequency of excitation and the role of coating layer.