PSI - Issue 84

F. Foria et al. / Procedia Structural Integrity 84 (2026) 645–652

649

Table 1. Natural frequencies of the tower. Mode number

Frequency ( Hz )

Mode 1 Mode 2 Mode 3

4.88

30.66 86.50

Table 2. Modal displacements of the four nodes located at the abscissas 2.3 m, 6.3 m, 10.3 m, 15.2 m, normalised with respect to the maximum component at the top of the tower (node 4). Node Mode 1 Mode 2 Mode 3 1 0.037 -0.191 0.435 2 0.244 -0.695 0.475 3 0.561 -0.388 -0.664 4 1.0 1.0 1.0

Then frequencies identification was performed applying the described algorithm to velocity histories obtained through a linear dynamic analysis of the tower subjected to white noise excitation, which simulates environmental conditions. The numerical velocities at the four nodes were used to simulate velocity readings acquired on a real structure. Figure 1 shows one stabilisation diagram where the alignments of the stable poles are clearly visible, with different multiplicities. Their highest occurrence identifies the structure's natural frequencies.

Fig. 1. Stabilization diagram: Number of poles vs frequency (Hz)

Table 3 shows the results obtained from the identification, using 20 fictitious recordings over various time windows to train the algorithm and a further 38 fictitious recordings to obtain the final results. Table 3. Average frequency values, normalised modal amplitudes at the 4 nodes, frequency multiplicity, and MAC correlation value Mode number Frequency ( Hz ) Node 1 Node 2 Node 3 Node 4 Multiplicity MAC Mode 1 4.88 0.037 0.244 0.560 1.0 2677 1 Mode 2 30.31 -0.144 -0.545 -0.291 1.0 2778 0.98 Mode 3 79.53 0.433 0.476 -0.674 1.0 2462 0.91 One hundred different analyses were performed on each recording, using the optimised pairs of parameters selected as described in step 9. The table show the average frequency values obtained from the analyses, the normalised modal amplitudes at the four nodes, the frequency multiplicity, and the correlation between the numerical value and that obtained by applying the algorithm to the fictitious data, based on the Modal Assurance Criterion.