PSI - Issue 78

Antonio Sánchez López-Cuervo et al. / Procedia Structural Integrity 78 (2026) 1791–1798

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2.61Hz 18.70 Hz Fig. 3: Flexural mode shapes along weak axis and identified frequencies: (a) first mode; (b) second mode; (c) third mode; (d) fourth mode; (e) fifth mode. 8.08Hz 12.88Hz 16.40Hz

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Fig. 4: E ff ect of damage on modal frequencies: (a) first mode; (b) second mode; (c) third mode; (d) fourth mode; (e) fifth mode.

D.S.8, corresponding to damage in the third-story columns (see Fig. 2). Table 1 presents the percentage variation of frequencies, relative to D.S.0, as measured by each sensor system. Modes 3 and 4 show the most significant reductions, with the largest variation exceeding 6% in Mode 4 at D.S.11. It is worth noting that the frequency data obtained from accelerometers and SGs are highly consistent, with an average di ff erence of only 0.13%. The greatest discrepancies appear in Mode 3 and in D.S.7, and are attributed to the limited precision of the low-cost sensors used and the inherent uncertainties of the dynamic identification process. In addition, not all five modes could be identified from the accelerometer data in D.S.6, D.S.7, and D.S.8, where Modes 1 and 5 could not be extracted. This is attributed to a lower signal-to-noise ratio (SNR) in the acceleration signals. Damage also a ff ects the mode shapes. The evolution of each mode across the damage scenarios was analysed using the MAC matrix, as defined in Eq. (2). For brevity, only results for the fourth mode—the one showing the largest frequency variation—are reported here (Fig. 5). In general, the MAC values vary more significantly in the strain mode shapes than in the displacement mode shapes. For instance, the minimum MAC obtained from accelerometer-based identification is 0.950 (Fig. 5(a)), while