PSI - Issue 36

S. Panchenko et al. / Procedia Structural Integrity 36 (2022) 231–238 Sergii Panchenko, Oleksij Fomin, Glib Vatulia, et al./ Structural Integrity Procedia 00 (2021) 000 – 000

236

f e =2.7 Hz; k vd =0.35; ψ σ /K σ =0.2.

100 150 200 250 300 350 St ress, MPa

0 50

l, mm

Fig. 6. The stress state of the hopper car frame

Fig. 7. Distribution of stresses along the length of the spine beam

The calculations showed that the project life cycle of the hopper car frame was 16% higher than the life cycle of the prototype wagon. However, it is important to say that the obtained value of the project life cycle should be specified taking into account the additional studies of the vertical loading of the frame. Modal analysis of the hopper car frame was also conducted in the study. The calculation was performed according to the scheme shown in Fig. 6 in the SolidWorks Simulation software package. The values of the natural frequencies of oscillations of the hopper car frame are given in Table 1.

Table 1. Values of the natural frequencies of oscillations of the hopper car frame. Mode Frequency, Hz Mode Frequency, Hz 1 59.7 6 99.2 2 74.2 7 122.6 3 74.6 8 124.0 4 82.4 9 173.8 5 97.4 10 194.5

Some forms of oscillations of the hopper car frame are shown in Fig. 8.

Fig. 8. Forms of oscillations of the hopper car frame (deformation scale 10:1) (a) the first mode (b) the second mode (c) the third mode (d) the fourth mode