2.5D formulation and analysis of a half-space subjected to internal loads moving at sub- and super-critical speeds

Abstract

The 2.5D dynamic response of a half-space to an internal point load moving at sub- and super-critical speeds is studied in Cartesian coordinates both analytically and numerically. Firstly, the partial differential equations of waves are converted to the ordinary differential equations by the Fourier transformation. Then, a multiplying factor is derived and added to the stiffness matrix to account for the dissipation of the load moving at different velocities, with or without self-frequency. Finally, the displacements of the half-space induced by the waves propagating upward and downward are obtained analytically for the specified boundary conditions. For comparison, the half-space is also analyzed by the 2.5D finite/infinite element method. The findings of the paper include: (1) the 2.5D solutions for a point load moving extremely fast are same as those for the line load by the 2D approach, (2) the dissipation of the moving load can be considered by adjusting the multiplying factor, (3) the attenuation of the half-space above the load level is reduced by the dissipation of the moving load, and (4) the displacement of the half-space increases with the self-frequency of the moving load.