Vibration Modelling of Railroad Beam Under Moving Load Using New Moving Macro -Element

One of the important issues in the vibration analysis of rail structures is to investigate the effect of train movement and the variable location of the load. This research introduces a new model to provide the ability to investigate 3D stress during analyzing a linear model. This model includes 6 degrees of independent transitional and rotational freedom, and one dependent degree of freedom as Warping to analysis the effect of moving loads. So, the interaction of the independent degrees of freedom has been considered due to the asymmetry of the cross section, especially in the earthquake load conditions. Finally, using a numerical Mathcad programing model, some of the parameters that are effective in modelling and vibrational analysis of rails have been examined. One of the important achievements of this study is to prove the effect of rail vibration acceleration on the characteristics of the analysis model as well as the need to determine the length of the computational model based on the results of the rail vibrational acceleration and its processing at the end of the rail. According to the formulation performed, stiffness and damping matrix are asymmetric, because of the velocity and acceleration vector effect of the load, however the mass matrix remains symmetrical. Also, by creating initial sinusoidal displacement conditions on the system, the conditions of corrugation phenomena can be expressed. The seismic acceleration applied to the model to evaluate the relevant freedom degrees and determinate the permanent deformation is considered in the model. It indicates the presence of permanent twisting and warping values in the rail-beam model, is about 40-50% of the maximum value. According to this investigation, the determination of the boundary conditions based on the damping of the acceleration at the end of the rail is very effective in calculating the results more accurately.