Keywords: high-speed trains, induced vibration, foundation stiffness abrupt changes, dynamic analysis, transient analysis, vehicle-rail-track interaction, methods of integral transformations, analytical solution, numerical analysis, commercial software.

This paper concerns with excessive ground and track vibrations induced by high speed trains, when crossing regions with abrupt changes in vertical stiffness of the track and, or subsoil. These vibrations have been observed and recorded, they degrade rolling equipment and track; and raise questions related to the vehicle stability and passengers comfort. Vertical stiffness changes can be caused by foundation inhomogeneity or by modification of structural solutions. In the latter case, covering passage from bridge or tunnel to regular line and transition from ballasted to concrete slab track and vice versa, the vertical stiffness change can be quite sharp and representative values can differ by several orders of magnitude.

Analytical transient solutions of the dynamic response of one-dimensional systems with sudden change of foundation stiffness are derived. Further development includes, cantilever dynamic response, expressed in terms of vertical displacement, and extended to account for elastic foundation and then two cantilever solutions, corresponding to beams clamped on the left and right hand side, with different values of Winkler constant, which are connected together by continuity conditions. The internal forces, as the unknowns, can be introduced by the same values in both clamped beam solutions and solved. Assumptions about the time variation of internal forces at the section of discontinuity must be adopted and originally analytical solutions will have to include numerical procedures.

Results are expressed in terms of vertical displacement. Although related to the one-dimensional case, this study can give insights into the problem of excessive ground vibrations induced by high speed trains in regions with vertical stiffness abrupt changes. In these preliminary solutions only a moving constant force is implemented, therefore the structure response is not always in accordance with what is experienced by real rail vehicles. The reason is that the interaction of spring-mass-damper system of the vehicle with the track structure cannot be omitted. This is subject for further research.

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