PSI - Issue 84

Tommaso Pivetta et al. / Procedia Structural Integrity 84 (2026) 1286–1293

1291

, = , ∙ ( , , ) 2

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T. Pivetta et al. / Structural Integrity Procedia 00 (2026) 000–000

(1) Where E i,old and f i,old are the elastic modulus and the natural frequency at the current iteration step, respectively. Considering the classical analogy with a simply supported beam, in which the natural frequency is proportional to the square root of the elastic modulus, it is therefore reasonable to update the elastic modulus at each iteration through a formulation depending on the square of the frequency ratio. 4. Results and discussion This section presents the results of the calibration and validation process. First, the dynamically calibrated model is assessed through the comparison between numerical and experimental modal properties. Subsequently, the model is further validated by comparing the numerical and measured deflections obtained under the transit of vehicles with known axle loads. 4.1. Dynamic Calibration Results Fig. 7 presents the mode shapes of the first two vibration modes, obtained both from the numerical model and the ambient vibration tests. As can be observed, an excellent agreement is achieved after the calibration process. The first mode is characterized by a predominantly flexural behavior of the deck, whereas the second mode is governed by a torsional deformation pattern.

a)

Mode 1

b)

Mode 2

Numerical

Numerical

Experimental

Experimental

Fig. 7. Mode 1 (a) and Mode 2 (b). Numerical and Experimental mode shapes.

The comparison between the experimental and numerical natural frequencies of the first two modes considered in the calibration process is reported in Table 3. The results indicate an excellent agreement, with a maximum error below 1%.