Structural modification formula and iterative design method using multiple tuned mass dampers for structures subjected to moving loads

Passive vibration control based on multiple tuned mass dampers is widely used in structural dynamics. They consist of a series of single tuned mass dampers with closely spaced frequencies attached to a primary structure and have the advantage of a wider effective frequency band. In this paper an iterative design method based on updating the receptances of a primary structure by controlled modifications introduced at every step by an individual tuned mass damper is proposed. There are some similarities between this method and the system control theory which allow the modifications to be represented as feedback elements. The implementation of the method is based on an approximate modification formula which is proposed and applied to continuous structures modelled as Euler–Bernoulli beams. The method is exemplified and used to improve the vibration response of a bridge-like structure induced by a train of masses moving independently at random speeds in the same direction. ► Multiple tuned mass dampers for reducing vibration caused by moving masses. ► An iterative design approach that adds one tuned mass damper a time and require less computing time. ► Analogy of this passive control approach to closed-loop control. ► Simulation of excitation by a random number of moving masses of random quantity arriving at random time at random speed.