Dynamic Analysis On Train-bridge Coupled Vibration Under The Action Of Earthquake Based On Duhamel Integral

With the rapid development of our country's economy, the increase of the national economy is dependent on the development of transportation industry. Above all, the development of the rail transportation industry plays a huge role in the development of the national economy and the improvement of people's living standard. As we know, China is an earthquake-prone country, and the rail lines and Bridges take a higher percentage of in China transportation system. Besides, many Bridges were built in earthquake-prone areas, so the study of the car bridge coupling under of seismic action has very important significance. But traditional Newmark-? integration method has a high demand of precision time, and the records of the seismic wave is also longer as well as the interval time. Compared with it,Duhamel integral can significantly increase the integral step length, thus it can solve the problem effectively.According to the principle of D'Alembert, this paper has deduced equations of motion of the single section with 6 DOF vehicle system , and take the finite element method for the bridge system discretization, select the appropriate bridge unit to establish its quality and stiffness matrix. The Rayleigh damping is adopted to establish the damping matrix. Use the Hermite interpolation method to calculate the inside dynamic response of the bridge. In this paper, I have also introduced the relevant theories of track irregularity, contrasted second filtering method and trigonometric series method, and compared several kinds of commonly used to input earthquake excitation method, so as to combine the two coupling of the systems which include equations of motion of the vehicle system and bridge system through coordinate displacement equation and associated with interaction force. And then this paper has introduced the traditional Newmark-? method for solving train-bridge coupling vibration, and the Duhamel integral analytical solution is also deduced, as well as to introduce the analysis method for the structural natural vibration characteristics. The subspace iteration method is adopted to solve the natural frequencies and mode shapes of the system. Using modal superposition method, it works out the natural frequency of vibration and mode of vibration.Using modal superposition method, I change the original coupled train-bridge equation with generalized coordinates into the modal coordinates of the corresponding coupling equation. And then take each order modal independent calculation through Duhamel integration. Each order modal superposition of the dynamic response of generalized coordinates is obtained under the dynamic response. Finally, according to the above ideas,the MATLAB program comes out to compare the method with the traditional Newmark-?method validation.Taking a set of eight-carriage train go across a three-span continuous girder bridge under the action of earthquakes as an example, this paper analyzes different system models,different earthquake waves as well as different levels, different speeds of train, the influence of different cross-section bending stiffness on the bridge, in order to obtain some conclusions which are helpful to engineering application.