Analytical and finite-element solutions to the problem of a vibrating beam, fully or partly supported by an elastic foundation, are presented. An application example is the vertical (transverse) vibration of a concrete railway sleeper embedded in an elastic medium (the ballast). The sleeper is also elastically connected to the rails. Eigenfrequencies are calculated and vibration modes are discussed. The beam (sleeper) is divided into sections where each section may or may not be supported by the elastic foundation. Outside the voids (the non-supported parts of the sleeper) the sleeper is assumed fully attached to the support. Some conclusions are that the foundation stiffness influences the (almost) rigid-body vibration modes of the sleeper the most, whereas the lowest bending-mode eigenfrequencies are just slightly influenced by the foundation stiffness; higher eigenfrequencies are affected very little by the foundation. The influence of railpad (and rail) stiffness on the sleeper bending-mode eigenfrequencies is negligible.

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation may be very large within a short distance. One example is when an unsupported sleeper is hanging in the rail. Track stiffness is then, locally at that sleeper, very low At insulated joints the bending stiffness of the rail has a discontinuity implying a discontinuity also of the track stiffness. A third example of an abrupt change of track stiffness is the transition from an embankment to a bridge. At switches both mass and stiffness change rapidly The variations of track stiffness will induce variations in the wheel/rail contact force. This will intensify track degradation such as increased wear fatigue, track settlement due to permanent deformation of the ballast and the substructure, and so on. As soon as the track geometry starts to deteriorate, the variations of the wheel/rail interaction forces will increase, and the track deterioration rate increases. In the work reported here the possibility to smooth out track stiffness variations is discussed. It is demonstrated that by modifying the stiffness variations along the track, for example by use of grouting or under-sleeper pads, the variations of the wheel/rail contact force may be considerably reduced.

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation may be very large within a short distance. One example is when an unsupported sleeper is hanging in the rail. Track stiffness is then, locally at that sleeper, very low. At insulation joints the bending stiffness of the rail has a discontinuity. A third example of an abrupt change of track stiffness is the transition from an embankment to a bridge.

The variations of track stiffness will induce variations in the wheel/rail contact force. This will intensify track degradation such as increased wear, fatigue, track settlement due to permanent deformation of the ballast and the substructure, and so on. In the work reported here the possibility to smooth out track stiffness variations by use of under-sleeper pads is discussed. It is demonstrated that the wheel/rail contact force variations can be made small by modifying the stiffness variations along the track.

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation may be very large within a short distance. One example is when an unsupported sleeper is hanging in the rail. Track stiffness is then, locally at that sleeper, very low. At insulated joints the bending stiffness of the rail has a discontinuity implying a discontinuity also of the track stiffness. A third example of an abrupt change of track stiffness is the transition from an embankment to a bridge. At switches both mass and stiffness change rapidly.

The variations of track stiffness will induce variations in the wheel/rail contact force. This will intensify track degradation such as increased wear, fatigue, track settlement due to permanent deformation of the ballast and the substructure, and so on. As soon as the track geometry starts to deteriorate, the variations of the wheel/rail interaction forces will increase, and the track deterioration rate increases. In the work reported here the possibility to smooth out track stiffness variations is discussed. It is demonstrated that by modifying the stiffness variations along the track, for example by use of grouting or under-sleeper pads, the variations of the wheel/rail contact force may be considerably reduced.

     This book provides the latest scientific research regarding the importance of infrastructure charges in establishing competitive conditions in the railway market. The current charging regimes applied throughout the EU member states are analyzed as well as the planning and scheduling that determine how and when the company's resources will be used in the case of railway organizations. Railway noise emission and its reduction are considered among the most important topics in the future development of transportation systems. This book gives an overview on the noise emitted by wheels and rails from the basic emission mechanisms up to noise attenuation by means of passive/active control. The importance of the vertical track stiffness as a means to guide railway track bed design for high speed railway lines are discussed as well. A rational approach to substructure design is described, which it is hoped will further an understanding of the process of appropriate track design and enable the adaptation of existing design procedures to provide a realistic design for the conditions at hand.

Teoretisk analys av vågutbredning i kontaktledning modellerad som en spänd sträng med böjstyvhet (eller axialbelastad balk) belastad med rörlig kraft.

An analytical Solution to the problem of a vibrating beam on an elastic foundation is presented. An application example of a concrete railway sleeper embedded in an elastic medium (the ballast) is provided. The sleeper is also elastically connected to the rails. The Rayleigh-Timoshenko (R-T) beam theory for a beam on an elastic foundation is used and eigenfrequencies are calculated. The beam (sleeper) is divided into three sections that have piecewise constant properties. The central portion of the beam is slightly thinner than the outer parts, and each one of the three parts may or may not be supported by the elastic foundation. The elastic connections to the rails are situated at the two joinings of the three sleeper sections.

Conclusions drawn are that the Euler-Bernoulli beam theory can be used to calculate two, or maximum three, eigenfrequencies of the sleeper. For higher frequencies, the R-T beam theory should be used. The foundation stiffness influences the lowest bending-mode eigenfrequency the most; higher eigenfrequencies are practically unaffected by the foundation stiffness. The influence of railpad (and rail) stiffness on the sleeper eigenfrequencies is negligible.

[No abstract available]