Probability Analysis Of Vibration Response Of Ballasted Track Structure

The slab ballastless track is one of the main types of the ballastless track. Since the random characteristics of the track random irregularity on the train-slab track system, the probability analysis of the dynamic response will have reference value in the structural design of the slab ballastless track. This paper completed the following main contents:1.To consider the reference of the vehicle, front and rear bogie and wheel,this paper finished the vehicles-track system model.The vehicle with 10 degrees of freedom is modeled as a few multi-rigid body connected by springs and dampers. It is assumed that the wheel and rail keep in contact.The degree of freedom of the wheel can be represent by the degree of freedom of the rail.There fore, the degree of freedom of the wheel is not independent one.The rails are modeled as a uniform elastic Bernoulli-Euler upper beam.The slab and the concrete bearing layer are modeled as a uniform elastic short beam. The rails and the slab tracks are represented by continuous springs and dampers.The slab tracks and the concrete bearing layer, the concrete bearing layer and the subgrade are all represented by continuous springs and dampers.2.Train and track are considered as an entire system.The vertical equations of motion for a train-track system are formulated by the principle of total potential energy with stationary value in elastic system dynamics and the "set-in right-position" rule for formulating matrices.The equations of motion are solved by the Wilson-θmethod to obtain the dynamic responses. The corresponding program has been compiled.3.The random vertical irregularity samples are formulated by trigonometric progression method and the corresponding computer program is compiled with MATLAB.4.On the basis of the track vertical free vibration model,the dynamic responses of the ICE-2 model train running on the A-slab track are calculated.The calculated results of this paper be compared with the QINSHEN, WUGUANG passenger line.The equation and the programs are proved to be right.5.The random irregularity of the rail has been considered.Attention is focused on the dynamic response of train at five different speed (60,70,80,90,and100m/s)levels excited by the irregularity of track. The maximum dynamic response of each speed is considered a sample observation of the random variable. The samples are regarded as random variable which is used probability analysis.The results indicate that the Wheel-rail contact force and the Wheel and rail acceleration,the maximum displacement and acceleration of train rails and rail panels all defer to normal distribution under the same condition.It has also been obtained that the mean of the maximum dynamic response of random variables, mean and three times standard deviation increases with the increasing speed.