On the dynamic response of a half-space subjected to a moving mass

Abstract

The dynamic response of a homogeneous, isotropic elastic half-space under a moving time-varying inertial load with subsonic speed is investigated. The surface of the half-space, which is under the action of the moving load, is a thin frictionless layer. In order to study the influences of the inertia of loads, the problem was first solved for a moving load and, then, the procedure was extended to include the inertial effects. The Navier equations of motion for the two-dimensional half-space were transformed to a system of wave-type partial differential equations using the Stokes–Helmholtz resolution. A new moving coordinate system was used and a modified system of equation was derived. The solutions of the modified system are obtained by utilizing a concurrent two-sided and one-sided Laplace transformation. The transformed dynamic responses and stresses were inverted by the Cagniard–de Hoop method. The effects of the inertia of the moving load were included using a numerical procedure to obtain the vertical surface displacement. Numerical examples for a landing traversing object on a half-space are presented to illustrate the methodology for finding the dynamic stresses and displacements in the half-space for moving load and mass cases. The final results revealed the influences of the inertia of moving loads on the dynamic stresses and displacements in the half-space. A parametric study was carried out to clarify the effects of the magnitude of the load, the Poisson ratio, density and shear moduli of the half-space on the results.