Moving Mass Problem—Analytical Approximation of Transient Solution on Infinite Two-Layer Model

Abstract

The problem of moving inertial objects traversing simplified models of railway tracks has an analytical solution in the transformed domain under the assumptions of linearity and longitudinal homogeneity of the model. However, the time-domain response usually requires numerical integration, which could only be avoided if the inverse Laplace transform could be evaluated by contour integration as a sum of residues. Such approach relies on the assumption that the function to be integrated is analytic except for isolated poles and vanishes asymptotically along the infinite contour. Unfortunately, this function exhibits step discontinuities that, in addition to violating the previous assumption, prevent, in several cases, the existence of poles, or there are poles that are not related to the dominant frequency, or the associated deflection is incorrect. This contribution presents a way of dealing with such situations. A new technique for the determination of dominant frequencies is proposed and validated. We show how to estimate deflections with acceptable accuracy not only at the contact point, but also along the structure without numerical integration. The technique is new and, to the author’s knowledge, has not been previously published. Additionally, it is explained why the response in undamped cases resembles that of damped systems.