Stochastic Track Vibration Analysis in Consideration of Log-Normal Type Spatial Variation of Rail Material Parameters and Shape Dimensions

We investigate the influence of random variables selection on spatial variation of rail material parameters and shape dimensions to the expected value and the standard deviation of the simulated track dynamic response.The spatial variation is considered about Young's modulus, density, cross-sectional area, moment of inertia and surface profile on a rail, using the Karhunen-Loève expansion.The random variables in the Karhunen-Loève expansion are chosen from the standard normal-or the standard lognormal random variables.The dynamic response in a probability space is evaluated using the polynomial chaos and the stochastic collocation method Through numerical tests, we investigate the expected value and the standard deviation of the three kinds of dynamic forces, the wheel-rail contact force, the railpad force and the sleeper-ballast force for several running speed of a wheel.The expected value and the standard deviation of the wheel-rail contact force increase with rise of the wheel running speed c, due to existance of rail surface profile.The dynamic behavior on the expected value and the standard deviation tends to be independent of the choice of the standard normalor the standard log-normal random variables in Karhunen-Loève expansion.