基于模态叠加法和直接刚度法的列车-轨道-桥梁耦合系统高效动力分析混合算法

AN EFFICIENT HYBRID METHOD FOR DYNAMIC ANALYSIS OF TRAIN-TRACK-BRIDGE COUPLED SYSTEMS BASED ON THE MODAL SUPERPOSITION METHOD AND DIRECT STIFFNESS METHOD

为提高列车-轨道-桥梁耦合系统(Train-Track-BridgeCoupledSystem,TTBS)动力分析的计算效率,该文基于作者之前提出的TTBS动力分析混合模型,结合模态叠加法和直接刚度法,提出了一种改进的混合方法(Improved Hybrid Method,IHM)。该方法中,列车动力方程通过多刚体动力学方法建立;轨道结构动力方程通过直接刚度法建立以准确求解其高频局部振动响应,桥梁结构动力方程通过模态叠加法建立以降低其自由度数目。列车和轨道结构通过轮轨线性Hertzian接触关系耦合为列车-轨道耦合时变子系统,轨道与桥梁间通过轨-桥相互作用力的平衡迭代实现耦合。首先以朔黄重载铁路32 m简支梁桥现场试验数据验证了该文方法的正确性。然后,以CRH2型高速动车组通过万宁系杆拱桥为例,探究了桥梁振型数量对动力响应指标计算精度的影响规律,最后,对比三种不同的列车-轨道-桥梁耦合系统动力分析方法的计算结果及耗时,结果表明:同样的计算精度下,该文方法具有更高的计算效率。

To improve the computational efficiency for analyzing the vibration of train-track-bridge coupled systems (TTBSs), an improved hybrid method (IHM) is proposed by combining the direct stiffness method (DSM) and the modal superposition method (MSM) based on the hybrid method. The vibration equations of the train are established by applying multi-body dynamics. The vibration equations of the track are established by using the DSM, which can effectively display the local dynamic behavior with high frequency. The vibration equations of the bridge are established by using the MSM, a method that can efficiently reduce the degrees of freedom. The train and track are coupled as a train-track subsystem through the linear wheel-rail Hertz contact model. The train-track subsystem and the bridge subsystem are coupled by enforcing the compatibility of forces at the contact points between the track and the bridge. The proposed method is validated by the field measurement data collected from a 32 m simply supported girder bridge on the Shuo-Huang heavy-haul railway line. A numerical example of a CRH2 high speed train passing the Wan-Ning Bridge is provided to investigate the effects of the number of bridge modes on the accuracy of the dynamic responses. The computation time of the three different methods for analyzing the vibration of the TTBS is compared and the results show that the IHM has the most computational efficiency than the other two methods.