Green function of curved rail-beam

In this article, we study the dynamic behavior of the rail under inclined loads. The rail is modeled as a curved beam under lateral loads. When a train enters a curve, two sources lead to these lateral forces that have rarely been studied by previous researchers: the forces of action of the train result from the forces of the drawbar (due to centrifugal forces) and forces that develop due to the dynamic interaction of the vehicle and the rail. The rail is modeled as an infinite beam according to the Euler-Bernoulli theory. The use of a curved elementary section, allows to establish the solicitations that act the beam, and to write the differential equation of the system. The use of the residue theorem allows determining the Green function associated with the differential equation governing the vibration behavior of the rail system of the free beam.