PSI - Issue 35

10

6

A. Bovsunovsky et al. / Procedia Structural Integrity 35 (2022) 74–81 Author name / Structural Integrity Procedia 00 (2019) 000 – 00

79

2 c

8

a

6

Fig. 6. Design of the cross-section of blade in the plane of crack.

2 For comparison, Table 2 shows the results of spectral analysis of vibration response at the principal and super harmonic resonances. As can be seen, the non-linearity of vibration response at the principal resonance is extremely low even in the presence of a rather dangerous crack. At the same time, at super-harmonic resonance, the second harmonic in the spectrum of vibration response ( A 2 ), even in the case of minimal crack, is comparable to the amplitude of the first harmonic ( A 1 ). Therefore, such non-linearity can be quite reliably revealed in the test. At this, the non-linearity of the spectrum of acceleration vibration response is several times higher than that of the spectrum of strain vibration response, which corroborates the results of numerical investigation of Bovsunovskii (2001). 4 Y Axis Title

Table 2. Results of tests by the method of higher harmonics (  a =5 MPa).

0

A 2 /A 1

Material of blade

0 2c , mm

2

4

6

8

10 Superharmonic resonance

a , mm

Resonance

S с /S

f с /f

Strain - 0.004

Acceleration

Strain

Acceleration

X Axis Title

VT-3-1

1.6 9.7 1.3 7.5

(0.3) 1.8 (0.3)

(0.004) 0.12 (0.002)

0.9981 0.9937 0.9991 0.9978

- 0.024

0.91 2.09 0.27 1.71

1.87 4.31 0.71 3.27

EI-961

-

-

1.8

0.063

0.003

0.013

The problem of higher harmonics method is that, according to Bovsunovsky (2001), the super-harmonic resonances are much narrower than the principal resonance. Calculations performed by the Newmark method made it possible to obtain the frequency dependence of the second harmonic of spectrum of acceleration vibration response for the second level of damage, that is, at 2 c =9.7 and 7.5 mm, respectively (Fig. 7). In this case, the sharpness of the resonance peak is also due to the low level of damping in the material of blades. In calculations, the logarithmic decrement of vibration for the VT-1-3 alloy was taken to be  =0.0017, and for the EI-961 alloy -  =0.0013, which corresponds to the damping characteristic of the cracked blades at amplitude  a =5 (see Section 4).

6

4

( A 2 /A 1 ) a

2

0

0.490 0.495 0.500 0.505 0.510

p/  Fig. 7. Frequency dependence of the second harmonic of acceleration spectrum at super-harmonic resonance of order of 2/1 for the blades