Dynamic Response of Suspension Bridge to Typhoon and Trains. II: Numerical Results

The field measurement results of the Tsing Ma suspension bridge under cross winds and running trains during Typhoon York have been presented in Part I of this study. The field measurement results are used in this paper (Paper II) to verify, to some extent, the finite element based framework developed by the writers in the time domain for predicting dynamic response of coupled train and bridge systems in cross winds. In this regard, a three-dimensional finite element model is used to model the Tsing Ma suspension bridge. Wind forces acting on the bridge are generated in the time domain using a fast spectral representation method and based on the field measurement results and wind tunnel test results. Each coach in a train running on the bridge is modeled by a $27\text{degree}$ -of-freedom dynamic system. The dynamic interaction between the bridge and the train is realized through the contact forces between the wheels and the track. Track irregularity is simulated using a high-order multivariate autoregressive model, whereas wheel hunting is assumed to be a sinusoidal function with a random phase. The acceleration and displacement responses of the bridge under cross winds and running trains are computed and compared with the responses measured from the field for four cases. The comparison is found to be satisfactory in general. The dynamic response and performance of trains on the bridge is also computed and evaluated. The proposed framework is found to be feasible and practical.