PSI - Issue 62

E. Tomassini et al. / Procedia Structural Integrity 62 (2024) 903–910 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Following the methodology proposed in Section 2.2, the first step toward the definition of the subgroups of channels is the preliminary whole bridge modal identification through the FDD algorithm (Fig. 2). Since the aim of the analysis was that to evaluate the coupling between the different portions of the bridge, only the principal peaks in the frequency range between 0 and 8 Hz were picked in the spectrum. The bridge exhibits 3 transversal modes in the frequency range between 2.656 and 3.242 Hz (Modes 1 (M1), 2 (M2) and 3 (M3) in Fig. 2) involving mainly the 5th, 6th, 7th and 8th spans. The sequel peaks are predominantly associated to vertical modal displacements in the spans, defining bending mode shapes in different portions of the bridge. The coupling of the modal displacements between the 1st and 2nd spans can be noted in Modes 5 (M5) and 8 (M8). Nevertheless, the modal identification was not able to find mode shapes involving the 3rd, 4th and 9th spans alone. The results of the FDD identification are collected in Table 1.

Fig. 2. Modal results derived from the FDD analysis. Based on the outcomes of the preliminary modal identification, four distinct subgroups were defined, as illustrated in Fig. 3 (a). Note that the specific static arrangement of the structure influenced the subgroup segmentation, with interruptions occurring at the half-joints. The second step is the definition of the reference modal identifications for each subgroup using the SSI-cov algorithm. To enhance efficiency and effectiveness, the SSI-cov parameters, stability thresholds, and additional parameters were adjusted for each subgroup, as detailed in Table 2. Parameters also involved disregarding poles with Modal Phase Collinearity MPC < 60% and damping ratio > 10%. The threshold used in the Hierarchical Clutesring stage was equal to 0.03 for each subgroup. The results of the SSI-cov modal identification of each subgroup are collected in Table 1. In particular, it was possible to identify the presence of 1st and 2nd order mode shapes in the transverse direction below 4 Hz in Subgroup 3, 1st order bending modes in the vertical direction between 4 and 6 Hz in each subgroup. Additionally, 1st order torsional and 2nd order vertical modes between 6 and 13 Hz were observable. Modes near 18 Hz pertain to 2nd order torsional modes.

Fig. 3. (a) Modal geometry; (b) cross-correlation between the frequency of Mode 1 and 6 of Subgroup 3 and max. RMS of channels 32 and 48.