PSI - Issue 77

Job S. Silva et al. / Procedia Structural Integrity 77 (2026) 550–558 Author name / Structural Integrity Procedia 00 (2026) 000–000

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a)

b)

Fig. 7. PSD of the vertical (Z-axis) acceleration measured on the two wagon platforms: (a) Platform 1 and (b) Platform 2.

The SSI method was applied to the same acceleration data to obtain a more complete set of modal parameters. The stabilisation diagram in Fig. 8 illustrates the identification of stable poles as the model order increases. Stable modes correspond to eigenvalues that remain nearly constant in frequency and damping across successive model orders, confirming their physical nature. The analysis revealed consistent modes at approximately 12.2 Hz, 53.3 Hz, 138.0 Hz, 171.5 Hz, and 328.0 Hz. The number of occurrences for each frequency, representing the stability of identification, is listed in Table 3.

Fig. 8. Stabilisation diagram obtained from SSI analysis, showing the identified stable modes.

Table 3. Number of occurrences as a function of frequency for the stable modes identified by SSI.

Frequency (Hz)Number of occurrences 12.19 82 53.33 8 137.95 16 171.53 16 328.04 22

The results of the constrained modal analysis performed on the finite element model are summarised in Fig. 9. The numerical model predicted natural frequencies of 12.2 Hz, 51.0 Hz, 133 Hz, 174.1 Hz, and 325 Hz. The corresponding mode shapes illustrate both rigid-body and structural deformation modes. A direct comparison between the numerical results and the experimentally identified frequencies obtained from PSD and SSI is presented in Table 4.

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