PSI - Issue 72
Niki Tsivouraki et al. / Procedia Structural Integrity 72 (2025) 141–148
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experimental results show no variation, while the numerical model predicts a slight variation, which follows a polynomial trend similar to the curve in Fig. 4(a). In contrast, for the 3.5 kHz eigenvalue, both experimental and numerical methods indicate a significant decrease. The polynomial trendline of the numerical data exhibits strong convergence with the curve in Fig. 4(a). The discrepancy between the experimental and numerical results is attributed to the idealized environment of the numerical model, in which fatigue damage is more clearly defined, and vibration loading remains undisturbed by external factors. This controlled setting allows for a more accurate representation of the impact of damage on eigenvalues.
(a)
(b)
Fig. 4. (a) Fatigue damage evolution and stiffness degradation of composite laminates and (b) normalized frequency ratio versus normalized number of cycles of composite laminates.
Table 1. Empirical residual frequency models influenced by residual stiffness models from literature. Models Residual stiffness models Residual frequency models Yang et al. (1990) 0 0 1 1 v n N f E E n E E N 2 2 2 2 0 0 emp 1 1 v n cr f f f n f f N
b a
b a
n
n
2
2
E E
E
f f
f f
WFQ, Wu et al. (2010)
1 1
1 1
1 1
1 1
n
N
n
cr
2
2
f N
f N
E
0
0
0
0
a
E E
E
n
n
a
1
2 2 0 n f f
2
f f
n
n
1 1
1 1
q
q
n
rc
ZJD, Zong et al. (2019)
1
1 1
1 1
q
q
cr
E
N
N
2
N
N
0
0
f
f
0
f
f
emp
0 / n f f with the empirical residual frequencies
Fig. 6 compares the variation of the experimental residual frequency 2 2
2 of Table 1. The WFQ model, Wu et al. *(2010) shows the best correlation with the tests, while the other two show a steeper degradation of residual frequency. In Fig. 6, the polynomial trendlines were added. From all trendlines, only that of the WFQ model has the same form as the curve of Fig. 4(b). 2 0 emp n f f
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