Response of an Infinite Elastic Medium to Traveling Loads in a Cylindrical Bore

Abstract

A line load applied along a transverse circle travels in the axial direction along the interior of a circular bore in an infinite elastic medium. The line load has an arbitrary distribution in the angular coordinate along the circumference of the circle and moves with a constant velocity V which is greater than the propagation velocities of the dilatational and equivoluminal waves in the elastic medium. Disregarding initial conditions at far distances, steady-state solutions which do not change in a coordinate system which moves with the velocity V of the moving load are obtained for the stresses and displacements at points in the medium. The components of the applied line loads are expanded into a Fourier series in terms of the angular coordinate. Expressions for the stress and displacement components at points in the medium are derived for each term of the series as a function of the radial distance from the cavity axis and the longitudinal distance behind the wave front. Numerical results are presented for the axisymmetric case for both the stress and displacement components on the cavity boundary. Corresponding results are also given for the case in which the applied boundary tractions have step distributions in the longitudinal direction behind the wave front.