1. Introduction

A widespread source of wave generation in continuous media is transport loading, i.e., moving loads whose form does not change over time. The velocity of a transport load has a large effect on the type of differential equations describing the dynamics of the medium. The equations depend parametrically on the Mach numbers, i.e., on the ratio of the speed of motion to the propagation speeds of perturbations in the medium (sound speeds). It is well known [1] that, in an isotropic elastic medium, there are two sound speeds (c1,c2), which determine the

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

velocities of dilatational and shear waves propagation. This has a large effect on the type of equations and leads to systems of elliptic, hyperbolic, or mixed equations. For transport problems, typical factors are shock effects generated by supersonic loading. At shock fronts, the stresses, displacement rates, and energy density are discontinuous. A convenient research method for such problems is provided by the theory of generalized functions (distributions), which makes it possible to significantly expand the class of processes amenable to study by using singular generalized functions in the simulation of observed phenomena. In this chapter, methods of this theory are used to solve boundary value problems using motion equations of the theory of elasticity in cylindrical domains under the action of transport loads, moving at supersonic and supersonic speeds.
