Vibration of damaged beams under a moving mass: Theory and experimental validation

A theoretical and experimental study of the response of a damaged Euler-Bernoulli beam traversed by a moving mass is presented. Damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. The analytical solution is based on the series expansion of the unknown deflection in a basis of the beam eigenfunctions. The latter are calculated using the transfer matrix method, taking into account the effective mass distribution of the beam. The convective acceleration terms, often omitted in similar studies, are considered here for a correct evaluation of the beam-moving mass interaction force. The analytical solution is then validated through a series of experimental tests. An adequate small-scale model is designed to satisfy both static and dynamic similitude with a prototype bridge structure, thus providing data of practical engineering relevance. It is shown that experimental results are in good agreement with the theoretical predictions. Moreover, it is observed that the percentages of variation in the beam response due to damage are, generally, larger than those induced in the structural natural frequencies; that is, an increase in structural damage sensitivity is noticed under the effect of a moving interacting load.