PSI - Issue 75

Sébastien Boudevin et al. / Procedia Structural Integrity 75 (2025) 72–84 Author name / Structural Integrity Procedia (2025)

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3.5. Vibration Test Synthesis In vibratory environment, by considering any time signals, Gaussian or not, stationary or not, the generalized time based methodology outlined through scientific publications from Dr. A. Halfpenny (2006) and C. Lalanne (2002), it is possible to build average unit FDSs and average unit SRSs for each phase of the product's life and then combine them depending on exposure times or occurrences observed during the mission profiles schedule. The result of this overall process is to get a linear cumulative reference FDS and a reference envelope SRS. Then, by reverse method, a PSD can be generated from the reference cumulative FDS (i.e. target or synthesis), knowing the SN curve of the material and the linear damage summation according to Miner’s assumption (see Eq.9). ℎ ( ) = 2(2 . ) 3 [ ( ). ( ). . . . (1+ 2 ) ] 2/ (9) The step presented on following figure concerns all situations of the life cycle profile, which can be divided into various blocks with related specifications (see Fig.2).

Fig. 2. Vibration test synthesis flowchart with APSD generation based on FDS approach

Concerning time compression, a severity factor can be applied to reduce the test time T eq with equivalent fatigue damage, checking that the ERS derived from the synthesized PSD is consistent with the envelope SRS. Moreover, an uncertainty coefficient or safety factor k(f) can also be applied to consider the uncertainties associated with respectively the environment loads (VCE), the parts mechanical strength (VCR) but also the number of samples to be tested (Test Factor).