Optimization and sensitivity of TMD parameters for mitigating bridge maximum vibration response under moving forces

In order to effectively reduce the vertical vibration response of the bridge, this paper proposes a frequency-domain analysis method of bridge vibration that can consider the influence of the tuned mass damper (TMD) device. In this method, the time-domain motion equation of bridge-TMD under moving concentrated loads' excitation is first established. Then, the equation of motion is Fourier transformed to obtain the displacement response spectrum of the bridge with the TMD device installed. Further, the 2-norm of the displacement response spectrum of the bridge is optimized by the augmented Lagrangian optimization method to obtain the optimal TMD parameters. Finally, numerical simulations verify the superiority of this method over the traditional optimization method (Den Hartog's method) in terms of maximum displacement control. And, the effects of bridge damping ratio, moving load number, and axle-span ratio and moving load speed on the optimal parameters of TMD to control the maximum displacement response of the bridge were studied. The results show that using the augmented Lagrangian optimization method to optimize the 2-norm of the displacement response spectrum of the bridge can not only effectively analyze the influence of each bridge and load parameters on the selection of TMD optimal parameters, but also it can reasonably configure TMD parameters for all kinds of simply supported beam bridges, which can provide references for practical engineering applications.