PSI - Issue 61

Rachid Azzi et al. / Procedia Structural Integrity 61 (2024) 241–251 Rachid Azzi and Farid Asma / Structural Integrity Procedia 00 (2023) 000 – 000

244

4

with defect are compared with those of the blade without defect, and the influences of the inserted defect with its different characteristics on the modal parameters are estimated and analyzed in the following paragraphs. The natural frequencies of the healthy blade are compared with those of a blade that carries damage on the leading edge by using the percentage Reduction in natural Frequencies defined as follows (Sinou and Lee (2005)):

f

f

f −

(1)

*100%

RF

0

=

r

0

Where f r is the Eigen frequency of the damaged blade and f 0 is the Eigen frequency of the healthy blade. RF is the reduction frequency.

Fig.3. Geometric model of an intact propeller blade with embedded blade root.

To examine the influence of damage length on the reduction of natural frequencies, the percentage reduction of the natural frequencies for the first, second, and fourth orders in terms of damage length for the different damage positions is presented in Fig. 4. For small damage length (1mm), the percentage reduction of the natural frequencies is weak and increase in value as the damage length increase. For damage developed near the blade root, damage positions ((S2) and (S5)) the percentage reduction of natural frequencies increases rapidly as the damage length increases. The fourth natural frequency is more affected by the presence of damage compared to the first and second natural frequencies for any damage length. It is seen that the percentage reduction of the first frequency is null for the damage that is near the tip blade (S17), this is due to the shape of the first mode where the damage will not appear on the blade i.e. the width of damage is null.

a

b

c

0

0

0,1

0

-0,1

-0,5

-0,1

-0,2

-0,2

-0,3

-1

S2, V S5, V S8, V S12, V S17, V

-0,3

S2,V S5, V S8, V S12, V S17, V

S2, V S5,V S8, V S12,V S17,V

-0,4

-0,4

-1,5

-0,5

-0,5

Frequency reduction of the first mode (%)

Frequency reduction for the forth mode (%)

Frequency reduction of the second mode (%)

-0,6

-2

-0,6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Damage length (mm)

Damage length (mm)

Damage length (mm)

Fig. 4. Frequency reduction versus damage length for different damage positions. (a) First mode, (b) Second mode, (c) Fourth mode.