This contribution deals with the vibrational response of Euler-Bernoulli beams equipped with tuned mass dampers, subjected to random moving loads. The theory of generalised functions is used to capture the discontinuities of the response variables at the positions of the tuned mass dampers, which involves deriving exact complex eigenvalues and eigenfunctions from a characteristic equation built as the determinant of a 4 x 4 matrix, regardless of the number of tuned mass dampers. Building pertinent orthogonality conditions for the deflection eigenfunctions, the stochastic responses, under Poissonian white noise, are evaluated. In a numerical application, a beam with multiple tuned mass dampers, acted upon by random moving loads, is consideredThe research presented in this project was carried out as part of the H2020-MSCA-ETN-2016. This project has received funding from the European Unions H2020 Programme for research, technological development and demonstration under grant agreement number 72149
