RTR 4/2010 11 Frequencies of the ballasted track n of the sleepers. As this mass seams to be small, the moved ballast mass (in the equations) seams to be hidden somewhere behind the relation between ground spring and sleeper mass. For frequency calculations a small deviation of this relation is of little influence, as it is standing under the square root. Consequently the mass of the ballast was not considered for the loaded and the unloaded track up to now. The smallest eigenfrequency of the ballasted track of about 80 Hz is mainly determined by the bedding stiffness of the ground. In order to have a better survey over the characteristic of the modes between 80 can be obtained by including the full ballast mass. This is true for all calculated eigenfrequencies with more than 80 Hz and of less than 135 Hz in chapter 4. A homogeneous distribution of the sleeper load by the ballast is possible only if the whole volume in the frustum of a pyramid below the sleeper is filled with ballast. In practice the lower side of the sleepers show that they have been supported by a few ballast stones only, where the discrete formation of small but deep craters can be observed. So just the small moved ballast mass in the few pyramids below the big craters should be considered dynamically together with mass sleepers are vibrating in the same sense and with almost the same amplitude. The length of the model is that of the unloaded track between the two bogies of an ICE 1 passenger vehicle. The ends of the rails are free to rotate and deflect, though there is no displacement at the ends of the rail section. On the right side of the Fig. 8 and 9 the important construction and calculation parameters are printed. The results of chapter 4 were obtained without considering the ballast mass. That is caused by investigations in this chapter. Calculating with the parameters of table 1 no coincidence with the measured results Fig. 10-2: Essential modes of the unloaded, ballasted track-system. Track section 1300 cm long. Stützpunktabstände = Suppor t distances [cm]
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