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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Fig. 9. Mode shapes obtained from the FE model: (a) first global mode at 12.2 Hz (b) fourth mode at 174.1 Hz.

Table 4. Comparison between natural frequencies obtained from numerical simulation, PSD, and SSI methods.

FE (Hz) PSD (Hz) SSI (Hz) Error FE vs PSD (%) Error FE vs SSI (%) Δf (SSI –PSD) [Hz] Rel. Diff SSI vs PSD (%) 12.2 12.0 12.19 +0.7 +2.2 -0.18 -1.5 51.9 55.0 53.33 -5.5 -2.5 -1.67 -3.0 133.0 138.0 137.95 +0.1 +0.3 -0.37 -0.3 174.2 170.0 171.53 +2.5 +1.4 +1.92 +1.1 325.0 331.0 328.04 -1.8 -0.9 -3.04 -0.9 The comparison shows that both experimental techniques successfully captured the main vibration modes observed in the scaled freight wagon. Deviations between the numerical predictions and experimental results were generally below 6%, which is acceptable for small-scale modal testing. Among the two experimental approaches, SSI exhibited slightly better agreement with the numerical model, with an average deviation of 1.8%, compared to 3.1% for PSD. The smallest discrepancies were observed for the higher-order modes, while the second mode (around 52 Hz) showed the largest difference, with PSD slightly overestimating the frequency. These results confirm that SSI, by considering the system dynamics in the time domain, is less affected by spectral leakage and provides more stable estimates. Overall, the finite element model was successfully validated against the experimental data, representing the dynamic behaviour of the scaled structure with sufficient accuracy up to 330 Hz. The combined use of PSD and SSI proved effective for identifying the global dynamic characteristics of the system, even under unmeasured excitation, demonstrating the robustness of the proposed approach. 5. Conclusions This study presented an experimental–numerical framework for analysing the dynamic behaviour of a scaled freight wagon model. The methodology combined laboratory modal testing with FE simulation to validate the structural response and identify the principal vibration modes. The PSD and SSI techniques were applied to extract natural frequencies and mode shapes under output-only conditions. The comparison between experimental and numerical results revealed good agreement, with deviations generally below 6%. Both methods successfully identified the dominant global modes, but SSI provided more consistent and robust results, particularly in the presence of measurement noise. The validated approach establishes a reliable basis for the subsequent evaluation of alternative damping strategies, including dry friction and viscoelastic systems, aimed at improving vibration control in freight wagon suspensions. Acknowledgements The authors gratefully acknowledge the support of the Agenda “Smart Wagons – Desenvolvimento de capacidade produtiva em Portugal de vagões inteligentes para mercadorias” , operation code 02-C05-i01.02-2022.PC644940527 00000048, funded by the Recovery and Resilience Plan (PRR) and the European Union – NextGenerationEU.

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