Calculation of force distribution for a periodically supported beam subjected to moving loads

In this study, a novel model for a periodically supported beam subjected to moving loads was developed using a periodicity condition on reaction forces. This condition, together with Fourier transforms and Dirac combs, forms a relation between the beam displacement and support reaction forces. This relation explains the force distribution at the supports, and holds for any type of support and foundation behaviors. Based on this relation, a system equivalence for a periodically supported beam is presented in this paper. An application to non-ballasted viscoelastic supports is presented as an example and the results clearly match the existing model. Next, an approximation of real-time responses was developed for the moving loads as periodic series. The comparison shows that this approximation can be used for a limited number of loads if the distances between loads are sufficiently large. The system equivalence for a periodically supported beam is efficient for supports with linear behavior, and could be extended to other behaviors.