PSI - Issue 78

Andrea Gennaro et al. / Procedia Structural Integrity 78 (2026) 663–670

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Table 2: Summary of epistemic uncertainties and configurations investigated. Epistemic uncertainty Configurations examined

(i) Fully constrained; (ii) Vertical + Longitudinal fixed, Transverse released; (iii) Vertical + Transverse fixed, Longitudinal released; (iv) Only vertical fixed; (v) 3D abutment model (dimensions and typology were assumed based on a similar bridge). (i) All rotations released; (ii) Only longitudinal rotation released; (iii) Only transverse rotation released; (iv) Only vertical rotation released. (i) Fully constrained; (ii) Longitudinal displacement released; (iii) Transverse displacement released; (iv) Longitudinal + Transverse displacements released. (i) Fully constrained; (ii) Transverse rotation released; (iii) Vertical rotation released; (iv) Longitudinal rotation released; (v) All rotations released. (i) Fully constrained; (ii) Longitudinal displacement released; (iii) Transverse displacement released; (iv) Longitudinal + Transverse displacements released.

Abutment constraint

Half-joint constraint (rotation)

Half-joint constraint (translation, at on side of the drop-in)

Intermediate constraint – rotation

Intermediate constraint – translation

Once the epistemic uncertainties were defined, the aleatory uncertainties were evaluated. Aleatory uncertainties are associated with the mechanical properties, such as Young's modulus and material density. These uncertainties are treated as random variables by defining a plausible range of variation. The aleatory uncertainties were evaluated with the use of FEMtools 3.6 software ( FEMtools 2012) , performing a Bayesian Parameter Estimation (BPE) approach. 3. Results 3.1. Summary of AVT results Fig. 5 provides a 3D graphical representation of the eigenvector components of the first five modes identified. In detail, the first mode (f = 3.678 Hz) activates the transverse response in the Y-direction, the second (f = 5.082 Hz) and fifth (f=11.888 Hz) the vertical response in the Z-direction; the third mode (f=6.447 Hz) is torsional, and the fourth mode (f = 4.799 Hz) is transversal. Table 2 presents the comparison between the experimental modal characteristics, estimated using the p-LSFC method, and the numerical results from the initial FE model. The results show a weak correlation between the numerical and experimental frequencies, with a maximum discrepancy of 71.38%. Moreover, in the initial FE model, an inversion of modes 4 and 5 is observed compared to the experimental results.

Fig. 5. 3D graphical representation of the experimental modal shapes for the first five modes identified using the pLSFC method: (a) 1st Mode — f = 3.678Hz; (b) 2nd Mode — f = 5.082Hz; (c) 3rd Mode — f = 6.447Hz; (d) 4th Mode — f = 9.068Hz; (e) 5th Mode — f =11.888Hz.

Table 3. Comparison between experimental and numerical modal characteristics. Mode Mode type p-LSCF [Hz] Initial FEM [Hz] |Δf| [%] MAC [-] 1 I° Trans 3.678 5.116 39.10 0.927 2 I° Vert 5.082 6.213 22.26 0.975 3 I° Tors 6.447 8.164 26.63 0.965 4 II° Trans 9.068 15.541 71.38 0.972 5 II° Vert 11.888 10.645 10.46 0.868