PSI - Issue 70

Arpit Singh et al. / Procedia Structural Integrity 70 (2025) 580–587

586

of 1.5 cm and 3.0 cm (D1 to D12). Results showed that the deeper cracks resulted in more reduction in stiffness than for the undamaged beam, validating that greater depth of damage heavily compromises structural integrity.

-1100 -600 -100 400 900 1400

-100 400 900 1400

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Real part (x)

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Imaginary part (y)

Frequency (in Thousands)

Frequency (in thousands)

Fig. 5(a): Frequency vs real part(x)

Fig. 5(b): Frequency vs imaginary part(y)

Specifically, the stiffness displayed a more drastic reduction in the early (incipient) damage phase, whereas later damage phases (moderate to severe) exhibited a gradually diminishing rate of stiffness degradation. This indicates that the sensitivity to the change in stiffness reduces with enhanced damage severity. Notably, stiffness decrease was observable even at the initial damage stage, evidencing the high sensitivity of the EMI method in detecting small structural deteriorations.

2.95E+01 3.05E+01 3.15E+01 3.25E+01 3.35E+01 3.45E+01 3.55E+01

Stiffness(in millions)

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D2

D3

D4

D5

D6

D7

D8

D9

D10

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D12

Healthy

Incipient damage

Moderate damage

Severe damage

Controlled damage (D1 to D12)

Fig. 6: Stiffness vs Frequency

As seen in the plot of stiffness against damage (Fig. 6), the trend is distinctly one of declining stiffness with rising damage intensity. The levels of damage, D1 to D12, signify a sequential development of degradation in the structure. During the early stage (D1 to D3), there is an immediate loss of stiffness of around 4%, signaling the beginning of incipient damage. During the intermediate damage range (D3 to D9), loss of stiffness persists but at a gradual rate, with cumulative loss between 4% and 15%. Outside of D9, the degradation rate of stiffness is negligible, indicating a shift to a severe damage state, in which additional damage has a very small effect on structural stiffness.

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0 5

% Change RMSD

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10D11D12 Incipient Moderate Severe

Controlled Damage

Fig. 7: % change RMSD with controlled damage