PSI - Issue 62

Andrea De Flaviis et al. / Procedia Structural Integrity 62 (2024) 871–878 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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damping ratios and mode shapes through MAC), both in frequency domain, through Frequency Domain Decomposition (FDD, see Brincker et al. (2001)), and in time domain, through Stochastic Subspace Identification (SSI, see van Overschee and De Moor (1996)). With these two algorithms modal properties are obtained not only for modes related to bridge deck, but also for those coupled between deck and piers, which are not considered in this work. About deck modes, since those of FDD are the same of SSI, only one of them is reported. In Table 1 results are resumed and there is a good matching between OMA and GBT with distributed restraints. In Fig. 5 and in Fig. 6 deck mode shapes obtained with OMA and GBT respectively are illustrated, while in Fig. 7 a convergence analysis shows that only 5 deformation modes (in addition to the 4 rigid modes) are enough to get good results.

Table 1. Modal properties obtained with OMA and GBT Mode (type) OMA

GBT (distributed restraints)

GBT (punctual restraints)

f (Hz) 2.701 6.978 8.849

ξ (%) 1.263 0.699 1.551

f (Hz) 2.375 7.202 8.768

Δ (%) -12.07

MAC 0.988 0.814 0.904

f (Hz) 2.344 7.227 8.232

Δ (%) -13.22

MAC 0.948 0.081 0.598

1 (1° bending mode) 2 (1° torsional mode) 3 (2° bending mode)

3.21 -0.91

3.57 -6.97

Fig. 5. Deck mode shapes obtained with OMA. (a) 1° bending; (b) 1° torsional; (c) 2° bending.

Fig. 6. Deck mode shapes obtained with GBT. (a) 1° bending; (b) 1° torsional; (c) 2° bending.

Fig. 7. Convergence analysis for natural frequencies.