(untitled) (ADVANCED TECHNOLOGIES AND COMPUTER SCIENCE, 2021)
The problem of developing mathematical models of wave propagation with a base under the influence of a moving load in a layer of soft soil is considered. The soil is modeled by an ideal nonlinearly compressible and irreversible unloading medium, in which the relationship between pressure and volumetric deformation during loading and during unloading of the medium is linear and irreversible. The load is applied to the upper surface of the layer and moves at a super seismic speed. The problem of the effect of a moving load on a two-layer medium consisting of a soft layer of soil and an elastic-yielding gasket with different thicknesses and densities is considered. The solution of the problem is constructed analytically in both inverse and direct ways. There is no median plane in the present problem. Therefore, the displacement and deformation of the points of the plane, which under certain conditions passes into the median plane of the layer, are considered as the desired values. Methods of mathematical physics are used in the study of wave processes in deformable media or in solving problems of interaction of a layer with a deformable base.