Optimization of multiple tuned mass dampers for a two-span continuous railway bridge via differential evolution algorithm

The study aims at proposing a methodology for optimization of multiple tuned mass dampers (MTMD) in reducing the multi-resonance vibrations of continuous bridges due to moving train loads. The equations of motion for time-domain analysis are derived for obtaining train-induced vibrations of a two-span continuous railway bridge with equipped MTMD-1 and MTMD-2 devices when the vehicle-bridge interaction (VBI) is considered. The bridge and the train are modeled as a Bernoulli-Euler beam with constant section and a series of moving sprung masses of identical length, respectively. To reduce the multiple resonance vibrations of a two-span continuous railway bridge, the MTMD-1 and MTMD-2 are tuned to the first mode and the second mode of the bridge, and they are attached to the midspan of each span, respectively. The optimum parameters of the both MTMD systems are investigated using the differential evolution (DE) method. The criterion chosen to obtain the optimum parameters is the minimization of the first two resonance peaks of the bridge. The influence of the different mass ratios and the number of TMD units in the MTMD system on the optimum parameters of the both MTMD systems and corresponding displacement responses of the bridge are also investigated. The results show that the VBI effect does not have much effect on the resonant train speeds and the control performance of TMDs. Therefore, the optimum parameters of TMDs can be obtained quickly by modeling the train as a series of moving forces for the vibration control of railway bridges.