A Semi-Analytical Solution for Responses of the Surface of an Elastic Half-Space Subjected to Vertical, Harmonic, Concentrated Forces

The dynamic response of a soil medium surface subjected to a vertical, harmonic, concentrated force is investigated. The half-space soil medium is considered to be elastic, isotropic and homogeneous. The expression of surface displacement is given analytically through a double Fourier transformation, integrals and Rayleigh functions. For numerical results of the surface response, the Modified Gaussian quadrature method is used. The in-phase and quadrature components of the displacements for any position on the surface of the unloaded half-space are illustrated for the Poisson’s ratio of 0.25 as a sample problem.