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The dynamics of un-isolated and isolated ballast tracks have been analysed by multi-beam models for the track and by a layered half-space model for the soil. The solution is calculated in frequency-wavenumber domain and transformed back to space domain by a wavenumber integral. This is a faster method compared to other detailed track-soil interaction methods and almost as fast as the widely used Winkler-soil method, especially if the compliances of the soil have been stored for repeated use. Frequency-dependent compliances and force transfer functions have been calculated for a variety of track and soil parameters. The ballast has a clear influence on the high-frequency behaviour whereas the soil is dominating the low-frequency behaviour of the track. A layering of the soil may cause a moderate track-soil resonance whereas more pronounced vehicle-track resonances occur with elastic track elements like rail pads, sleeper pads and ballast mats. Above these resonant frequencies, a reduction of the excitation forces follows as a consequence. The track deformation along the track has been analysed for the most interesting track systems. The track deformation is strongly influenced by the resonances due to layering or elastic elements. The attenuation of amplitudes and the velocity of the track-soil waves change considerably around the resonant frequencies. The track deformation due to complete trains have been calculated for different continuous and Winkler soils and compared with the measurement of a train passage showing a good agreement for the continuous soil and clear deviations for the Winkler soil model.

Ground vibrations created by running high-speed trains at speeds between 100 and 320 km/h are calculated in detail using transfer functions to model the effects of the moving loads. These transfer functions for layered soils are obtained by integration in the wavenumber domain. The train-induced vibrations in a soil that is considered to consist of single layers of two slightly different soils are analysed for different excitations: for their spectra, attenuation laws and amplitude-speed relations. An important mid-frequency component is shifted through the cut-on region of the layered soil with an increase in the train speed. The cut-on frequency divides the response of the layered soil into a low-frequency low-amplitude range and a high-frequency high-amplitude range. This leads to completely different train speed dependencies for the two soil layers with strongly increasing amplitudes around the cut-on frequency and almost constant amplitudes beyond this frequency. All calculated results closely agree with ground vibration measurements at two corresponding sites, especially if the mid-frequency component is calculated by axle impulses.

The soilstructure interaction of elastic plates on homogeneous or layered soils excited by horizontally propagating waves is analysed. Large plates are modelled by a combined finite-element boundary-element method (FEBEM), whereas the response of infinitely long plates is calculated by a numerical integration in the frequencywavenumber domain. The finite-element boundary-element method yields the complete soilplate transfer function of frequency and distance whereas the frequencywavenumber solution of the infinitely long plate can serve as an approximation for long distances on a finitely long plate. The soilplate transfer function starts to decrease strongly at the coincidence frequency, where the bending stiffness equals the plate inertia. A strong decrease follows at mid frequencies and a strong reduction of less than 0.1 of the ground vibration is reached at high frequencies. Rules for the characteristic frequencies are derived from the numerical results clearly indicating the strongest influence of the soil stiffness and the weaker influence of the bending stiffness of the plate. The influence of the mass, length and width of the plate are shown to be limited in case of realistic parameters, but it should be noted that the reduction effects are less effective for layered soils and for nearer observation points.