Optimisation of the Parameters of a Vibration Damper Installed on a Historic Bridge

The paper presents theoretical analyses of renovating a historical bridge in order to decrease stresses. The installation of additional equipment, including a vibration absorber, is relatively easy to perform if such a need is indicated by the current bridge diagnostics or the monitoring of the structure’s vibrations. Moreover, absorbers could be mounted in such a way as not to alter the appearance of the historic structure. The authors focused on the problem of optimising the cooperation between a dynamic vibration absorber (DVA) and a structure under dynamic load moving with constant velocity. A simple degree of freedom (SDOF) system – as a model of the absorber and a multi-degree of freedom (MDOF) system – as the primary structure, were adopted in the calculations. Every force is regarded as a random variable, as well as interarrivals of moving forces. Two different situations and solutions were presented. The first case is when the stream of moving forces with a constant velocity is modelled as the filtered Poisson process. The second one when one of the forces is located in the point of the beam in which the response of the beam has the maximum value.