Semi-analytical approaches to vibrations induced by moving loads

With the evolution of the computational power, there is a tendency to overlook analytical and semi-analytical solutions, despite their inherent obvious advantages. One should, however, be aware of the fact, that these solutions provide the necessary insight into the relevant physical phenomena and are accompanied by highly precise results, quickly obtainable without the necessity of additional numerical convergence tests. The objective of this contribution is to fill the gap in available semi-analytical solutions related to wave propagation induced by moving loads, with practical applications of high-speed rails. The structures that will be considered are composed of a beam and a supporting medium. The beam represents the interface between the structure and the moving object and will be simplified in conformity with the Euler-Bernoulli theory. In this paper the supporting structure will be considered as a two-parameter viscoelastic foundation and the moving object will be simplified by masses carrying constant forces with harmonic components, under assumption of tight contact. Special attention is paid to the proximity of moving masses.