Dynamic Stresses Produced in an Elastic Half Space by Reciprocally Moving Surface Loads

Abstract

In studies of moving load problems, Galilean or Laplacian transformations have been commonly used by several previous investigators to construct the solutions. Meanwhile in this paper analytical techniques of superposition of harmonic vibrations are available because the elements composing an elastic half space are excited periodically by reciprocating surface loads. Formal solutions of the equation of motion described in terms of well known displacement potentials φ and ψ in the theory of elastodynamics, are decided from the theory of partial differential equations. Numerical calculations are carried out and we find out the differences between both stress distributions produced in the interior of the media by surface loads moving forward and by the Loads moving backward, even if both the loads coincide instantly with each other. That is one of the properties of the response of an infinite extended solid to reciprocating loads. These differences become large as the moving speed increases.