Tuning Moving Vehicle Suspensions for Vibration Mitigation of Damped Bridges

It has been widely recognized that traversing vehicles can dampen bridge vibrations. This work clarifies the efficacy of different vehicle suspension tuning approaches for bridge vibration mitigation using an equivalent tuned mass damper (TMD) model and presents a parametric analysis of the key physical factors governing vehicle-bridge interaction. The vehicle-bridge system is modelled as a TMD traveling on an elastically supported beam. A finite element model is developed to numerically validate the analytical model. Transmissibility functions, obtained using the time-freezing technique, and complex eigenvalue loci are employed in the tuning process. For an undamped bridge, the optimal stiffness and damping ratio of the vehicle suspension are obtained from an extended fixed-point principle, under which the analytical model is equivalent to a smooth bridge coupled to a TMD and subjected to a harmonic transverse excitation at the contact point. For a damped bridge, the optimal vehicle suspension parameters are determined from the intersection of the eigenvalue loci of the system. Vehicle damping can induce curve veering of the instantaneous coupled eigenvalues during the vehicle passage, and this phenomenon is further examined through a perturbation analysis. In the parametric analysis, the root-mean-square values of the kinetic and potential energy of the bridge are used to quantify the vibration mitigation performance. Tuning at bridge midspan generally achieves the greatest bridge energy reduction under both sinusoidal and stochastic excitations, since the maximum bridge displacement occurs at that position. Among the considered tuning methods, the optimal parameters determined by enforcing a zero gradient at the fixed point of the fundamental bridge frequency and equal transmissibility magnitudes at the other two fixed points are shown to be the most effective. Based on the midspan tuning strategy, a parametric study of the sprung mass, vehicle speed, excitation frequency, surface roughness class, bridge damping, and bearing stiffness is performed, which reveals the importance of frequency match and phase lag between the bridge and the vehicle in mitigating the bridge responses. The present study also shows that bridge surface roughness can significantly influence the efficacy of vibration mitigation.