PSI - Issue 57

Sven Maier et al. / Procedia Structural Integrity 57 (2024) 731–742

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S. Maier et al. / Structural Integrity Procedia 00 (2023) 000±000

was visually detected, a shift of the modes to lower frequencies due to a loss of sti ff ness caused by the crack initiation could also be observed at the same time. The results of the experimental vibration test are listed in Table 5. For all specimens, the first perceived damage occurred at hotspot 1 as predicted in the simulation, except for sample S9, for which a damage was also detected at hotspot 2 at the same test interval. The results show that the durability of the samples and their scatter are significantly lower than expected from the simulation with assumed scatter limits. For all samples, a failure was detected within only three inspection intervals. The variants with increased mass and thinner plates turned out be more critical. This observation is consistent with the simulation results of Figure 4, although the simulation with the assumed scatter limits for the input parameters significantly overestimated the durability and did not even predict fatigue within the 90% quantiles, except for variant 3, which also overestimated durability in general.

Table 5. Results of the experimental vibration test. Percentage values for structural durability refer to the target duration of 720 hours.

Variant 1

Variant 2

Variant 3

Specimen

S1

S2

S3

S4

S5

S6

S7

S8

S9

S10 S11 S12

Durability [%]

33.33 33.33 35.42 31.25

18.75 12.5 16.67 12.5

14.58 14.58 14.58 16.67

Durability range [%]

31.25 - 35.42

12.5 - 18.75

14.58 - 16.67

4. Comparison of simulations and experiments

For comparison of the deterministic numerical model (nominal variant as reference) and the experiment, the struc tural dynamics behaviour is focused first. A comparison of the modes shows a very low deviation for the eigenfre quencies and high Modal assurance criterion (MAC) values, displayed in Table 6. The measured eigenfrequencies are slightly higher than the simulated ones. The MAC value is formed by the scalar product between two normalised eigenvectors. It is a criterion for the correlation of the eigenvectors. While a value of 1 indicates a perfect match of the modes, a value of 0 denotes that the modes are not consistent. In this case the MAC value indicates a high correspondence for the first three modes between the eigenvectors of the simulation and the experiment.

Table 6. Comparison of the modal characteristics between experiment results and nominal simulation of variant 1.

Eigenfrequency f n [Hz]

Modes

Simulation

Experiment

Relative deviation [%]

MAC-Value

Mode 1 Mode 2 Mode 3

40.97 76.12 81.42

41.02 76.21 83.77

-0.12 -0.12 -2.81

0.81 0.98 0.94

Additionally, the frequency response functions in z direction of the simulation and the experimental modal analysis for the four sensor positions on the mounting are presented in Figure 7. The excitation force is normalised to 1 N to achieve a good comparability of experimental and simulation results. The frequency range investigated is limited to 100 Hz since only the first three eigenmodes are of significant influence (Figure 3). The comparison shows also an excellent correspondence of all curves. However, the 3rd mode shows minor di ff erences between simulated and measured eigenfrequencies. Similar good comparisons are also observed in x and y direction. In the experimental curves, the third mode appears at slightly higher frequencies and the magnitude is also slightly higher. The linear simulation model shows a very good correlation to experimental results.