PSI - Issue 62

Fabrizio Scozzese et al. / Procedia Structural Integrity 62 (2024) 911–915 Fabrizio Scozzese / Structural Integrity Procedia 00 (2019) 000 – 000

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Figure 2. (a) bilinear elastic force-displacement law; (b) Bridge deflection time series.

In Figure 3 the instantaneous angular frequencies extracted via HHT are plotted (a) as a function of the time and (b) as a function of the response amplitudes. It can be observed how the first chart provide only a preliminary information on a possible response “anomaly” for the case of heavy vehicle but no insights on response nonlinearity can be detected; on the other hand, the second plot is a frequency-amplitude correlation chart from which deviations from the linear elastic behaviour under heavy track passage can be clearly identified (see the red dot pattern); in particular the system responds according to the its fist natural frequency 0 until the displacements are lower than 3.0 mm; once exceeded this threshold the natural frequency values modify and tend to the 1 values according to the reduced stiffness branch of the constitutive law. The 10 t vehicle is not sufficient to induce response beyond the crack threshold hence the natural frequencies maintain around the reference value 0 . It is worth noting the aforesaid trends can be appreciated in average terms because of the (sometimes strong) local variability of the results stemming from the HHT analysis.

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Figure 3. (a) instantaneous frequency variation over the time and (b) frequency-amplitude correlation chart for travelling loads with different weight. Conclusions The abilities of the Hilbert-Huang Transform (HHT) in extracting the instantaneous property of the dynamic response were investigated and a novel procedure to recover the nonlinear elastic response of these systems was presented and validated through a preliminary theoretical application on a simple dynamic system. According to these first outcomes the methodology shows an high potential in identifying nonlinear trends in the system response. The interested reader can found a wider discussion of both method and outcomes in the work of