The simulation of surface disturbances elastic semi-infinite medium caused by moving oscillating source

Abstract

This paper considers the problem of the motion at a constant speed over the surface of the elastic layer of the mobile source which oscillates. The problem is solved by means of Fourier integral transformations. The homogeneous boundary value problem is being considered in the moving coordinate system, connected with the source. It is assumed that there is a steady-harmonic oscillation. By using the direct method of contour integration, which is described in detail in the work, the elastic surface perturbation obtained by numerical integration of two-dimensional Fourier integrals. This method makes it possible to calculate the wave processes in the same manner as for the fixed sources. Due to its simplicity, the method of integration can be considered as engineering method, although it can be successfully used for scientific purposes. Examples of calculation of the surface perturbations of isotropic elastic layer in flat and three-dimensional problem are given, caused by moving source in a speed range from 0.5 values of Rayleigh waves velocity up to 1.16 of the longitudinal wave velocity, both in the presence of the oscillations and in the absence of oscillations. The method can be applied without any additional modifications for multilayer anisotropic and isotropic materials, as cushion base.