Issue 78

F. Veschi et alii, Fracture and Structural Integrity, 78 (2026) 44-73; DOI: 10.3221/IGF-ESIS.78.04

1 k  ). The reference

Figure 16: Statistical comparison of the predictive models under SoR loading with a wide-band background ( RFC probability density function is depicted as a shaded grey histogram in the first panel.

Cross-case observations. The comprehensive analysis reveals that, as the bandwidth of the random component increases, Rice's PDF exhibits excellent fidelity when S r f f  , leading to highly accurate estimates. Conversely, under conditions of spectral separation, this method proves strictly conservative, consistently yielding positive errors that can reach up to 900%. This behaviour stems directly from the assumption that every local maximum belongs to the upper envelope, thereby ignoring the presence of small-amplitude cycles nested within larger ones – a dominant phenomenon in wideband signals. Consequently, the results suggest that while Rice's formulation represents a safe approach for preliminary sizing, its application for the structural optimisation of components subjected to SoR profiles is strongly discouraged, as it invariably leads to severely over-engineered designs. In this context, Equivalent PSD approaches (specifically Irvine, Lalanne, and RMS Eqv) seem to emerge as the most robust engineering solution for Wideband scenarios. Although these methods fail to faithfully replicate the bimodal morphology of the amplitude distribution, tending instead to 'smear' the harmonic energy across a fictitious frequency band, they benefit from a highly effective error cancellation mechanism:  The transformation of the deterministic tone into a random band inherently underestimates the probability density around the sine peak.  Simultaneously, this mathematical transformation artificially inflates the distribution tails compared to reality. The net result is that, upon integrating the damage curve, the underestimation at medium amplitudes and the overestimation at extreme amplitudes tend to balance out. This provides final Damage Index estimates that generally fall within an acceptable ±20% accuracy band. The sole exception is the WN Approximation method. By reducing the entire mixed spectrum to pure white noise, it fundamentally fails to capture the energy complexity of the actual signal, proving systematically too severe and entirely unsuitable for these loading profiles. MIL-STD-810 SoR profile For this analysis, a representative SoR loading profile was adopted from the MIL-STD-810 standard (specifically, the OH 58A/C helicopter specifications). For comparative purposes, the original acceleration amplitudes were numerically transposed into the stress domain. This was achieved by applying a direct 1:1 mapping (substituting m/s² with MPa) to evaluate the fatigue response while preserving the exact spectral morphology of the reference signal (Fig. 17).

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