PSI - Issue 54

Jakub Gorski et al. / Procedia Structural Integrity 54 (2024) 264–270 J. Gorski et al. / Structural Integrity Procedia 00 (2023) 000–000

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4.1. Analysis of spectrum components

Figure 5 shows the part of the spectrum near the frequency of the probing wave for point 11. Figure 5(a) presents the results for the undamaged structure and 5(b) of the damaged one. Both graphs include the identified frequency components. The component of the probing wave is indicated by a blue circular marker. The magenta square markers represent the components associated with the pumping wave that modulates the probing wave. These components are related to the VAM phenomenon. Green rhomboid markers represent MT-related components. The cyan triangular markers represent components related to the frequency that modulates the pumping wave. By comparing graphs between structures, it is easy to determine which spectrum was recorded for the damaged specimen. It is characterised by the higher number of frequency components and amplitudes.

Fig. 5. Overview of amplitude spectrum in the vicinity of probing frequency for (a) undamaged beam; (b) damaged beam.

4.2. Analysis of damage index trends

The damage index trends were derived using the algorithms outlined in Section 2. Figure 6 presents the results obtained from the response signals, with each graph illustrating the trends for both the damaged and undamaged structures. These indices were computed for MT phenomenon components. The results e ff ectively indicate which specimen is damaged and at which specific location. Notably, the trend for damaged beam attains a global maximum at the nearest point to the damage. This prominent maximum value stands out from the other values, facilitating accurate and precise damage localisation. The findings presented in the previous section unveil the presence of other nonlinear phenomena during MT exper iments. The results clearly demonstrate that VAM phenomena can coexist simultaneously with MT. This observation suggests the involvement of diverse nonlinear mechanisms during MT tests. One potential mechanism could be associated with the local nonlinear stress-strain relationship, which is induced by damage and may exhibit variations based on the modal form of structure. Several models presented by Pecorari and Solodov (2006) and Klepka et al. (2018) have been proposed to describe the local material sti ff ness in the presence of damage. 4.3. Result discussion