This paper presents an analytical solution for the steady-state response of a homogeneous three-dimensional half-space subject to a time-harmonic point load. This expresion is of great importance in the formulation of three-dimensional elastodynamic problems in a half-space by means of boundary element methods which can be employed as a Fundamental Solution. The expressions are validated comparing the results with those obtained with the boundary element method solution, where the free surface is discretized. The solution is further compared to that of a 2.5D half-space, and with experimental results available in the literature. The asymptotic behaviour of the solution is explored for different limits of the distance, frequency and wave number, and the ensuing limits are compared to existing fundamental solutions.
Puertas, E., & Gallego, R. (2014). Función de Green para el problema elastodinámico armónico en un semiespacio con amortiguamiento histerético. Revista Internacional de Metodos Numericos Para Calculo y Diseno En Ingenieria, 30(4), 247–255. https://doi.org/10.1016/j.rimni.2013.09.002