Stochastic response of beams equipped with tuned mass dampers subjected to Poissonian loads

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 considered.