Three-dimensional dynamics of the moving load acting on the interior of the hollow cylinder surrounded by the elastic medium

Abstract

This paper studies the non-axisymmetric 3D problem on the dynamics of the moving load acting in the interior of the hollow cylinder surrounded with elastic medium and this study is made by utilizing the exact equations of elastodynamics. It is assumed that in the interior of the cylinder the point located with respect to the cylinder axis moving forces act and the distribution of these forces is non-axisymmetric and is located within a certain central angle. The solution to the problem is based on employing the moving coordinate method, on the Fourier transform with respect to the spatial coordinate indicated by the distance of the point on the cylinder axis from the point at which the moving load acts, and on the Fourier series presentation of the Fourier transforms of the sought values. Numerical results on the critical moving velocity and on the distribution of the interface normal and shear stresses are presented and discussed. In particular, it is established that the non-axisymmetricity of the moving load can decrease significantly the values of the critical velocity.