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.

在笛卡尔坐标系中，以解析和数值方式研究了半空间对以亚临界和超临界速度运动的内部点载荷的2.5D动态响应。首先，通过傅立叶变换将波的偏微分方程转换为常微分方程。然后，得出一个乘数因子，并将其添加到刚度矩阵中，以考虑在有或没有自频率的情况下以不同速度移动的载荷的耗散情况。最后，对于指定的边界条件，通过解析获得了由向上和向下传播的波引起的半空间的位移。为了进行比较，还通过2.5D有限/无限元方法分析了半空间。本文的研究结果包括：（1）2。