THE RESPONSE OF AN INFINITE ELASTIC MEDIUM WITH INHOMOGENEOUS INITIAL STRESSES TO MOVING LOAD ACTING IN A CYLINDRICAL CAVITY

Abstract

In this paper, we studied on the response of an infinite elastic medium with inhomogeneous initial axisymmetric stresses to the moving ring load acting in a cylindrical cavity contained with this medium. It is assumed that in the initial state the infinite elastic medium contained the cylindrical cavity is compressed with the uniformly distributed radial normal forces acting at infinity and these forces cause the known inhomogeneous initial stresses. It is required to determine the response of the elastic medium to this moving load and the influence of the inhomogeneous initial stresses on this response. Mathematical formulation of the problem is made within the framework of the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses and the discrete-analytical method is developed for the solution to this problem. Numerical results on the critical velocity and on the stress distribution in the elastic medium caused with the moving load and on the influence of the initial stresses to these distributions and on the critical velocities are presented and discussed. In particular, it is established that the initial radial compression of the elastic medium causes to increase the critical velocity.