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

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The reduction frequency is different from one position to another and from one mode order to another. We can conclude that the more the damage length increases more the reduction frequency is significant. It is necessary to calculate more than one natural frequency to detect the presence of damage at any position on the entire length of the leading edge. Fig. 5 shows the percentage frequency reduction of the first, second, and fourth-order as a function of the damage positions along the leading edge for different damage lengths. It is seen that the more the damage moves away from the embedded base, the more the percentage frequency reduction decreases. The reduction frequency percentage of the fourth mode is significant compared to the two other modes and especially remarkable for the positions S2, S5, and S8 and can reach up to 2%. The reduction percentage of the first and the fourth frequencies is null for the case of damage length 1mm to 2mm, which is on the positions S12 and S17, on the other hand, the reduction of the second frequency is remarkable for all damage. Thus, the damages that are close to the blade tip will not appear on the first and the fourth natural frequencies. The percentage frequency reduction depends on damage length, damage position, and mode order. This analysis relates to a “V” geometrical damage form shape.

a

b

c

0

0

0,1

0

-0,1

-0,5

-0,1

-0,2

-0,2

-0,3

-1

-0,3

L=1mm L=2mm L=3mm L=4mm L=5mm

L=1mm L=2mm L=3mm L=4mm L=5mm

L=1mm L=2mm L=3mm L=4mm L=5mm

-0,4

-0,4

-1,5

-0,5

-0,5

Frequency reduction for the first mode (%)

Frequency reduction for the fourth mode (%)

Frequency reduction for the second mode (%)

-2

-0,6

-0,6

S2

S5

S8

S12

S17

S2

S5

S8

S12

S17

S2

S5

S8

S12

S17

Damage positions

Damage position

Damage position

Fig. 5. Frequency reduction versus damage position for different damage lengths (a) first mode, (b) second mode, (c) fourth mode.

Fig. 6. Shows the reduction percentage of the first, second, and fourth natural frequencies as a function of the damage length for different geometrical damage shapes. It is seen that the reduction percentage of the three frequencies versus the geometrical damage shapes is different from one frequency to another. The damage shape "I" which is at position "S2" causes a percentage frequency reduction superior to that caused by the shape "V" unlike other positions, and this is valid for the three frequencies. The percentage frequency reduction in terms of geometrical damage shapes is clear in the first and the second frequencies more than in the fourth.

a

c

b

0,1

0,5

0,1

0

0

0

-0,1

-0,1

-0,2

-0,2

-0,5

-0,3

-0,3

S2, V S2, I S8, V S8, I S17, V S17, I

-0,6 S2, V S2, I S8, V S8, I S17, V S17, I Frequency reduction for the first mode (%) -0,5 -0,4

-1

-0,4

-0,6 S2, V S2, I S8, V S8, I S17, V S17, I Frequency reduction for the second mode (%) -0,5

-1,5

Frequency reduction for the fourth mode (%)

-0,7

-0,7

-2

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. 6. Frequency reduction versus damage length for different damage shapes. (a) First mode, (b) Second mode, (c) Fourth mode.