On a 3D moving load problem for an elastic half space

The paper deals with 3D dynamic response of an elastic half-space loaded by a point force moving at a constant speed along a straight line on the surface. The problem is formulated within the framework of the asymptotic hyperbolic–elliptic model developed earlier by two of the authors. The validity of the model is restricted to the range of speeds close to the Rayleigh wave speed. Steady-state near-field solutions are derived in terms of elementary functions. Transient analysis of surface motion illustrates peculiarities of the resonance associated with the Rayleigh wave.

► An approximate solution of a 3D moving load problem is obtained in elementary functions.
► A significant distinction of the 3D case from the 2D one is revealed.
► Steady-state motion is considered for both sub and super-Rayleigh regimes.
► Transient surface dynamics is analysed.