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This paper presents the dynamic response of an Euler-Bernoulli beam supported on two-parameter Pasternak foundation subjected to moving load as well as moving mass. Modal analysis along with Fourier transform technique is employed to find the analytical solution of the governing partial differential equation. Shape functions are assumed to convert the partial differential equation into a series of ordinary differential equations. The dynamic responses of the beam in terms of normalized deflection and bending moment have been investigated for different velocity ratios under moving load and moving mass conditions. The effect of moving load velocity on dynamic deflection and bending moment responses of the beam have been investigated. The effect of foundation parameters such as, stiffness and shear modulus on dynamic deflection and bending moment responses have also been investigated for both moving load and moving mass at constant speeds. Numerical results obtained from the study are presented and discussed.

Wheel flats can create high-magnitude impact forces at the wheel/rail interface, these can induce high levels of local stress leading to fatigue damage, and failure of various vehicle and track components. With demands for increased load and speed levels, the issue of a strategy for effective maintenance and in-time replacement of defective wheel-flatcontaining wheels has become an important concern for heavy haul operators. A comprehensive coupled vehicle/ track model is generally used to predict the impact forces and the resulting component stresses in the presence of multiple flats. This paper considers the dynamic impact responses due to the presence of multiple flats. The characteristics of the bounce, pitch, and roll motions of the bogie due to a flat on a single wheel are investigated. The effect of multiple flats on the peak acceleration of a wheel is investigated for different sizes and relative positions of the flats, i.e. inphase and out-of-phase conditions. This paper further presents the development of a smart wheelset for the detection of wheel flats for two different load conditions; it is based on a derived relationship between the peak wheel acceleration, vehicle speed and flat size.

The movement of the liquid cargo within a partly filled tank car is known to impose additional slosh forces and moments that may adversely affect the dynamic responses of the vehicle. This study is aimed at analyzing the liquid cargo slosh in a partly filled tank car and its effects on vehicle responses during a switch-passing maneuver. A two-dimensional analytical liquid slosh model is formulated for the analyses of the liquid load shift in the roll plane, lateral slosh force, and roll moment through summation of first four antisymmetric modes of the liquid. The analytical slosh model is integrated to a 114 degrees-of-freedom multibody dynamic model of the railway tank car comprising nonlinear wheel–rail contact and contact pairs of the suspension system. The validity of the slosh model is illustrated by comparing the responses with those reported in other studies and those obtained from a nonlinear computational fluid dynamic model. The coupled fluid–vehicle model is subsequently used to study the effects of fluid slosh during switch-passing maneuvers on different response measures, namely roll motion of the tank car, lateral and vertical wheel–rail contact forces, and derailment ratio. The significance of the liquid cargo slosh in the partially filled state is demonstrated by comparing the responses with those of the car with equivalent rigid cargo. The results show that liquid sloshing within the partly filled car can lead to higher magnitudes of car body roll angle and thereby the unloading ratio compared to the conventional rigid cargo car. Switch-passing critical speeds are further identified for different fill ratios and switch geometries. For fill ratios below 80%, the switch-passing critical speeds of the partly filled car are substantially lower compared to those of the equivalent rigid cargo car. Neglecting the contributions due to dynamic slosh force and roll moment arising from a partially filled railway tank car may thus lead to underestimation of the critical speed in switch-passing maneuvers.

The dynamic impact forces due to the wheel defect such as a flat is a main concern for a heavy freight train operating at high speed. The present investigation employs a pitch plane vehicle model coupled with a comprehensive three-layer track system model to study the impact force generated in the wheel-rail interface due to the presence of wheel flats. The wheel-rail contact is modeled using nonlinear Hertzian contact theory. Responses in terms of wheel-rail impact load and forces transmitted to bearings, pad and ballast are evaluated in an attempt to identify desirable design and operating factors. Wheel-rail impact loads due to the presence of multiple flats either in single or different wheels in-phase or out-of-phase conditions are evaluated and analyzed. A detailed parametric study is carried out that includes the variations in selected vehicle, track, operational as well as flat parameters. The results show that the effect of multiple flats is insignificant if they are more than 45° apart. The impact due to single wheel flat can be larger than in-phase flats at each wheel due to the presence of pitch dynamics. The parametric study shows that other than speed, depth and length of the flats are most sensitive parameters, and there exists a critical length at each flat depth that leads to the largest impact load.