Transient Vibrations of a Half-Space Under a Massive Line Loading

Abstract

Dynamic response of a half-space subjected to loads is of considerable practical interest for engineers and scientists. Recent investigations demonstrated that the inertial influences of moving loads are of importance in some cases. Although there are several works on moving inertial loads (masses), very few works were performed on the interaction of a half-space and a stationary inertial foundation on its surface. In this study, a new analytical–numerical method has been used to investigate the vertical interaction between a massive strip foundation and a homogenous, isotropic elastic half-space. Navier’s equations of motion were transformed to a system of wave-type partial differential equations using the Helmholtz resolution. The interactive tractions between the strip foundation and the half-space were imposed to the problem as boundary conditions. A concurrent two-sided and one-sided Laplace integral transform was used for the wave type partial differential equations subjected to the specific boundary conditions and eventually the solution in transformed form was obtained. In order to inverse the transformed solution, the Cagniard–De Hoop method accompanying a numerical procedure was implemented. Final results revealed the influence of the inertia of the massive strip foundation on the dynamic response of the half-space.