Analytic solution for dynamic loading on half-space medium

A systematic procedure for generating impedance matrices for foundations resting on an elastic half-space medium is presented. The prescribed harmonic loading due to the foundation is decomposed into an infinite Fourier series with respect to the azimuth. For each Fourier component an analytic solution is found. Then, provided that the interaction stresses due to excitation of the foundation can be assumed to be piecewise linear in the r-direction of the cylindrical coordinates, the impedance matrix of the foundation can be generated using the variational principle and the reciprocal theorem. A simple example of a rigid circular plate, rigidly attached to the half-space medium, and subjected to torsional, vertical, rocking, and horizontal exitation is used to demonstrate the effectiveness and efficiency of the procedure.