Simulation of spatial perturbations of a two-layer elastic semibounded medium caused by an internal moving oscillating source

Abstract

This paper is devoted to numerical modeling of spatial perturbations in semibounded two-layer elastic isotropic media. The vibrations of the media are caused by a moving oscillating internal or surface mechanical stress source. Three variants of an elastic isotropic medium were investigated: the first is a two-layer laminate with a rigidly fixed base, the second variant is a two-layer laminate with a mechanically free base, the third variant is a single-layer half-space. The surface source moves at a constant velocity along the surface of the body, the internal source moves in the interface plane. Homogeneous boundary value problems are considered in a moving coordinate system that is related to the source. The solution of the spatial problem is based on the use of integral Fourier transforms, the method of direct contour integration, the algorithms for constructing the symbol of the block Green matrix for the media under consideration. Due to its simplicity, the method of direct contour integration can be considered an engineering method. Nevertheless, this method can be successfully used for research purposes. Variants of motion are considered for zero and nonzero frequencies at a velocity that exceeds the velocity of transverse waves in a half-space. For a single-layer half-space, two solutions are compared, one solution is obtained for a surface source, another solution is obtained for an internal source that performs oscillations.