Robust design optimization of TMDs in vehicle-bridge coupled vibration problems

Optimal design of Tuned-Mass-Dampers (TMD) and Multiple-Tuned-Mass-Dampers (MTMD) for vibration control has been a popular research theme. In most applications, one observes that uncertainty in dynamical excitations is considered (e.g., for earthquake or wind loading). However, a literature survey shows that parameter or system uncertainties are seldom taken into account. Moreover, we could not find applications of robust design optimization to coupled vehicle-bridge systems. Hence, this paper presents a novel application of robust design optimization of TMD and MTMD applied to vehicle-bridge coupled vibration problems. Robust optimization looks for designs which are less sensitive to uncertainties in system parameters and in parameters of excitation models. Parameters of the TMD, of pavement irregularity models and of the bridge-vehicle models are considered as random variables. The principle of maximum entropy is employed to obtain the probability distributions of these random variables. The robust optimization problem is solved by means of the Firefly Algorithm. Results show that the use MTMDs allows decreasing the expected value and the variance of the maximum vertical displacement of central bridge node when compared to solutions with single TMDs. The numerical solution developed herein is also compared to classical techniques of Den Hartog and Warburton. The paper shows that the classical analytical techniques can also be successfully employed in robust optimal design of single TMD devices.