PSI - Issue 22

E. Georgievskaia / Procedia Structural Integrity 22 (2019) 229–234 E. Georgievskaia/ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. Normalized stress intensity: (a) skew-symmetric bending mode; (b) torsional mode; (c) symmetric bending mode.

Fig. 5. Normalized summary displacements: (a) skew-symmetric bending mode; (b) torsional mode; (c) symmetric bending mode.

Fig. 6. The effect of the crack on the blade (a) and runner (b) eigenvalues.

6. Discussion Analysis of the calculation results showed the following:

 the modes of natural oscillations can be divided into three groups (bending skew-symmetric, bending symmetric and torsional), characterized by the distribution of dynamic stresses and the possibility of their identification by diagnostic systems;  due to the structure symmetry, the first and second frequencies are paired; they have the same eigenvalues and identical shapes, differing only by 90 degrees rotation;  purely torsional vibrations do not cause linear displacements and force effects in the support nodes, but can be detected by the angle of the shaft twist or the created torque load on the support; with torsional vibrations, all blades are in the same stress-strain state;