Dynamic behaviour of a layer of discrete particles, part 1: Analysis of body waves and eigenmodes

This paper is one in a series of two, and discusses the body wave propagati on and the eigenmodes for a layer of discrete particles. This configuration is a representation for a ballast layer used in ordinary railway tracks. T he discrete nature of the ballast is simulated via an elastic nine-cell squ are lattice. After deriving the equations of motion for the lattice, the lo ng-wave approximation for the equations of motion is compared with the equa tions of motion for a classic elastic continuum. This comparison yields rel ations between the macroscopic continuum parameters and the microscopic lat tice parameters. Then, the dispersion curves that characterize the eigenmod es of the discrete layer are derived. The differences between these dispers ion curves and those of a continuous layer are elucidated. By means of a pa rametric study, the influence is shown of the particle diameter and thickne ss of the layer on the dynamic response. In an accompanying paper, the laye r response to a moving, harmonically vibrating load is analyzed, which is a representation for a ballast track that is subjected to an instantaneous t rain axle passage. (C) 2001 Academic Press.