PSI - Issue 84

Fulvio Busatta et al. / Procedia Structural Integrity 84 (2026) 797–804

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Table 2. Selected statistics of the modal parameters tracked from 31/05/2024 to 31/05/2025. Mode # Mode type f mean (Hz) σ f (Hz) ζ mean (%) σ ζ (%) Tracking Ratio (%) 1 B1 – Bending 0.828 0.02 0.89 0.21 100 2 B2 – Bending 1.20 0.04 1.19 0.24 99.9 3 B3 – Bending 1.64 0.03 1.28 0.27 100 4 B4 – Bending 2.65 0.07 1.36 0.34 97.8 5 B5 – Bending 3.05 0.08 1.70 0.32 99.8 6 B6 – Bending 3.63 0.07 1.54 0.19 99.7 7 T1 – Torsion 3.89 0.11 1.72 0.22 85.7 8 T2 – Torsion 3.91 0.10 1.52 0.23 44.1 9 B7 – Bending 4.09 0.08 1.77 0.20 93.9 10 T3 – Torsion 4.17 0.09 1.45 0.20 81.3 11 B8 – Bending 4.34 0.09 2.21 0.26 98.7

As shown in Table 2, the bending modes of vibration denoted as B1-B8 are those showing the smallest variation of the modal parameters (natural frequency and damping ratio, where σ denotes the standard deviation) and the highest tracking ratio, approximately in the range 94-100%. Conversely, the torsion modes of vibration denoted as T1-T3 show the largest variation in terms of modal parameters and the lowest tracking ratio, with the mode 8 denoted as T2 being tracked about 44% only. Fig. 6 shows the correlation between natural frequency and temperature for each mode. The R-squared (R 2 ) coefficient of determination spans from 0.65 to 0.77 highlighting a slight non-linear variation of the natural frequencies due to temperature changes. a) b) c) d)

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Fig. 6. Vibration modes of the bridge deck: (a-k) correlation natural frequencies vs. temperature and linear regression.