Vibration of rigid bodies on semi-infinite elastic media

This mixed boundary-value problem gives rise to a set of dual integral equations which have not hitherto been solved. Four cases are analysed: the vertical translation and rotation about an axis normal to the surface of a rigid circular body and the vertical translation and rocking of an infinitely long rigid rectangular body. The dynamic stress distributions under the rigid bodies are determined and are shown to reduce to the known static distributions for zero frequency factors. The dual integral equations are solved by a series of expansion procedures. The calculated response curves for translation and rotation of a rigid circular body are compared with the experimental results by Arnold, By croft & Warburton (1955) and are shown to be an improvement over other approximate theories. A suggestion is made for using the results of this analysis for the determination of the dynamic elastic properties of a soil in situ.