The Response of an Elastic Solid to Nonuniformly Moving Surface Loads

Abstract

Wave motion in an elastic half space subjected to nonuniformly moving surface loads is studied. The sudden application and subsequent motion of either a line load or a pressure step is considered. In each case the load is applied normal to the surface, the shear traction being zero, and the subsequent motion is such that the solid is in a state of plane strain. The motion of the load or step is allowed to be quite general, including acceleration or deceleration through the various characteristic speeds of the material. Both problems are formulated, and the line load problem is solved in detail. Properties of the solution are discussed, with emphasis on the determination of the wave fronts for any particular load motion. It is also shown that singularities in surface displacement are generated as the load accelerates or decelerates through the Rayleigh wave speed. On the other hand, if the load moves at the Rayleigh wave speed for any finite time, such singularities also appear. Finally, the application of the analytical technique to nonuniformly moving dislocation problems is discussed.