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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.

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The dynamic impact forces caused by wheel defects such as a flat have been of primary concern for freight trains operating at high speeds. A pitch plane model of a railway vehicle coupled with a comprehensive three-layer track system model is developed to study impact forces generated at the wheel-rail (W-R) interface in the presence of wheel flats. The W-R interaction is described by the non-linear Hertzian contact spring, while the rail is represented by a continuous Euler beam. The Rayleigh-Ritz method is used to solve the coupled partial and ordinary differential equations of the vehicle-track system. An idealized haversine wheel flat with the rounded corner is included in the W-R contact model. The W-R interface forces are evaluated under single or multiple flats on a single as well as multiple wheels. The forces transmitted to the bearings, pads, and the ballast are also evaluated under impacts due to single as well as multiple wheel flats. The results obtained through parametric analyses are discussed in view of a desirable design and operating condition to reduce the magnitude of impact loads. The results suggest that the rail mass, rail pad stiffness and damping, bending stiffness of rail, and ballast mass affect the W-R impact force considerably, apart from the flat size and vehicle speed. The influence of phase between the multiple flats on the resulting magnitudes of impact forces is also evaluated. The results suggest that the impact loads due to two flats are comparable with those due to a single flat when the spacing between the two flats exceeds 45 • . Furthermore, the magnitude of impact force due to a single wheel flat could be greater than that due to in-phase flats on both wheels, which can be attributed to the pitch dynamics of the bogie.

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.