The effect of initial stresses on dynamic (harmonic) stress fields within an elastic stratified half plane is investigated. It is assumed that the point-located harmonic force acting on the free plane of the layer by which the half plane is stratified causes this stress field. By employing displacement potentials and the exponential Fourier transform the governing system of partial differential equations of motion is solved. The necessary inverse transformations including rigorous mathematical complexity is performed numerically. The analysis of the numerical results, which shows the influence of the homogeneous initial stresses on the distribution of the stresses on the inter-medium plane, is made. These analyses are examined for various problem parameters and it is assumed that the material of both the layer and the half plane is homogeneous, isotropic, compressible and linearly elastic. It has been observed that the initial stresses may change significantly the values of the superimposed harmonic stresses. ο 2001 Γditions scientifiques et mΓ©dicales Elsevier SAS harmonic force / initial stress / stratified half plane / stress distribution
1. Introduction
The investigations of the dynamical problems for a pre-stressed elastic medium have are highly significant. A considerable number of these investigations, such as those carried out by Stroh (1962), Barnett et al. (1985), Chadwick and Jarvis (1979-a, 1979-b), Dunwoody (1989), Dowaikh andOgden (1990, 1991), Bagno and Guz (1997) and others have been related to the influence of initial stresses on the speed of various types of waves in an elastic medium.
Other investigations have been related to wave propagation (dispersion) problems and reviews have been carried out by Guz (1978) and Babich et al. (1975). The systematic presentation and analysis of the above mentioned results which were obtained before 1986 were made in the monographs by Guz (1986Guz ( -a, 1986-b)-b). Recently published investigations by Rogerson and Fu (1995), Rogerson andSandiford (1997, 2000) and Rogerson (1997) also relate to the dispersion problems of the elastic waves in the pre-stressed rubber-like elastic medium.
However, up till now a lot of investigations as reviewed by Guz (1999Guz ( -a, 1999-b) -b) had been carried out on the dynamical contact and crack problems for a pre-stressed elastic medium. In these investigations it is assumed that either the crack or the punch moves with constant speed, and the influence of the initial stresses on the stress field in the vicinity of the crack or punch is studied.
The analysis of the investigations shows that they were made under the following two basic assumptions: 1. The pre-stressed state (or initial stress-state) is purely homogeneous and static.