Dynamic characteristics of inhomogeneous half-space, excited by a surface or internal moving source of oscillations

Abstract

The oscillations of a single-layer half-space excited by an oscillating moving source of oscillations are studied numerically. Layer and half-space have contrasting mechanical properties. The problem is considered in a flat formulation, the behavior of the amplitude of the oscillations of the stamp is investigated either on the surface of the layer or on the half-space level depending on the frequency of oscillations and the speed of movement. Surface, internal, vertical and horizontal sources, two components of displacements are considered. The speed varies from zero to the speed of the fastest longitudinal wave, the frequency varies from zero to several tens of hertz. Homogeneous boundary value problems are solved using the integral Fourier transform, the algorithm for constructing the symbol of the block Green matrix, and the numerical method for calculating Fourier integrals. The calculations of eighteen amplitude-frequency characteristics and amplitude-speed characteristics of the oscillations of the stamp are presented. Analysis of the calculations showed that for the region of low frequencies and velocity values that are less than the velocity of the transverse wave for the upper layer, the most dramatic changes in characteristics occur. The maximum amplitudes correspond to zero frequency and the Rayleigh velocity in the layer, somewhat smaller amplitude values are associated with the Rayleigh velocity in the half-space. The amplitudes of vertical displacements caused by a vertical source have the largest range of variation. Their range exceeds by several decimal orders the corresponding ranges for horizontal displacements.