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

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 numerically. Firstly, the partial differential equations waves are converted ordinary by Fourier transformation. Then, multiplying factor derived added stiffness matrix account for dissipation different velocities, with or without self-frequency. Finally, displacements induced propagating upward downward obtained specified boundary conditions. For comparison, also analyzed finite/infinite element method. findings paper include: (1) solutions extremely fast same as those line 2D approach, (2) can be considered adjusting factor, (3) attenuation above level reduced load, (4) displacement increases self-frequency load.