PSI - Issue 78

Anna Brunetti et al. / Procedia Structural Integrity 78 (2026) 1729–1736

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reliable induced vibration analyses and for designing the TMDs. High-sensitivity, low-noise wired accelerometers were used to measure bridge vibrations induced by ambient excitation. Overall, 23 measurement cross-sections were adopted in order to have a refined spatial resolution of the mode shapes; the cross-sections were instrumented with three accelerometers each, with two sensors measuring in the vertical direction and one in the transverse direction. In addition, a sensor measuring in the longitudinal direction was added at one cross-section. The sensors layout was designed to capture the flexural, transverse, longitudinal, and torsional dynamics of the entire bridge deck. Measurements were carried out using six distinct non-simultaneous configurations, employing 16 sensors, and considering 4 fixed sensors (the entire cross-section with the longitudinal sensor) for all the configurations. Dynamic identification of modal parameters was performed by using the well-known Subspace Stochastic Identification - Principal Component (SSI-PC) technique (Brincker 2014). To merge modal displacements obtained from each measurement configuration, the Post Separate Estimation Re-scaling (PoSER) method was employed (Parloo 2003). This involves performing modal identification separately for each configuration, followed by a posteriori scaling of the modal shapes. The identified frequencies of the vibration modes in the 0-5 Hz range are shown in Table 1.

Table 1. Comparison of the experimental results and the numerical models. Experimental Numerical Global Model

Numerical Model with fixed supports

Frequency (Hz)

Frequency (Hz)

Δf (%)

MAC (/)

Frequency (Hz)

Δf (%)

MAC (/)

1.30 1.38 1.64 1.94 2.30 2.89 3.15 4.07 4.35 4.94

1.08 1.31 1.47 1.88 2.13 2.78 2.87 3.78 4.39 4.62

-17.2

0.97 0.74 0.95 0.98 0.97 0.97 0.93 0.96 0.97 0.39

1.24 1.38 1.63 1.94 2.39 2.89 3.00 4.07 4.36 4.94

-5.27 -0.24 -1.06 -0.19 4.13 -0.22 -4.99 -0.05 0.36 -0.16

0.97 0.91 0.96 0.99 0.96 0.92 0.99 0.97 0.97 0.83

-5.4

-10.5

-3.4 -7.3 -4.1 -9.1 -7.2

0.9

-6.6

2.2. Finite element model and comparison with experimental results The vibrational analysis was evaluated numerically by using the SAP2000 software. In the initial phase, the global model developed for designing the pedestrian bridge, including the steel superstructure and reinforced concrete piers on piles, was used. Specifically, all structural elements were modelled as beam elements, except for the deck, which was modelled with shell elements. The supports were modelled by using linear link elements. To account for soil-structure interaction, Winkler springs were applied to the foundation piles with an appropriate range of stiffness variability. As expected, the modal analysis of the global model is strongly influenced by the flexural stiffness of the substructures and the soil-foundation system. On the contrary, vibrations measured from low amplitude ambient excitation are mainly due to the steel deck and arch, being reasonable to assume that modal deformations of piers and piles are negligible in view of the excitation intensity. Therefore, the model do not fully reflect the bridge dynamics induced by ambient excitation and by pedestrian traffic. In view of the above considerations, the substructure was neglected and fixed supports are assumed at both piers and abutments (Fig. 2), obtaining a very good correspondence between the results of the experimental tests and the numerical model (Table 1). Indeed, analysis results demonstrate that by assuming fixed support conditions, the percentage difference between experimental and numerical frequencies decreases, with a maximum of about 5%. The Modal Assurance Criterion (MAC) values also show improvement, with all values approaching unity. Fig. 3 shows the modal shapes obtained from the numerical model.