An Efficient and Accurate Green’s Function Solution of Time-Harmonic Responses in Elastic Layered Half-Spaces

Time-harmonic loading over layered elastic half-spaces has applications in various science and engineering fields. While various approaches have been proposed in solving the related boundary-value problems, in this paper, we propose a new approach, which is based on the novel Fourier-Bessel series system of vector functions and the dual variable and position method (DVP). While the DVP method was proposed recently and verified to be computationally stable and efficient, the Fourier-Bessel series system of vector functions is newly introduced. Similar to the cylindrical system of vector functions, the normal (dilatational) and shear (torsional) deformations (waves) can be separated and solved in terms of the LM- and N-types of the new vector function system. The new formulation is coded, and the corresponding algorithm/program is applied to a couple of cases. It is shown that, by comparing previous approaches, this new series system of vector functions is equally accurate, but much more computationally powerful. Since it is substantially time saving in calculation, it is hopeful that this new approach would have broad applications related to transient response and inverse problems in elastodynamics of layered systems.