PSI - Issue 57

Sven Maier et al. / Procedia Structural Integrity 57 (2024) 731–742

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S. Maier et al. / Structural Integrity Procedia 00 (2023) 000±000

An analysis of the PSD stresses across the frequency range up to 200 Hz for the three hotspots shows that after the third eigenmode almost no noteworthy PSD stresses occur across the entire frequency range and thus the modes after the third mode are of minor interest for a simulative comparison with the experiment. The PSD stresses for the nominal variant 1, as a representative, as well as the used PSD load in z direction is shown in Figure 3. It is also clearly noticeable that the highest PSD stresses arise around the frequency range of the first mode which is the main reason for the fatigue failure.

Fig. 3. Applied PSD load and PSD stresses in z direction for the three hotspots for variant 1 (nominal).

The PSD load used in this study represents an envelope curve containing peaks of several PSD signals obtained from di ff erent vehicle measurements. Hence, an uniaxial PSD load in the z direction is applied. In order to take into account the scatter of the input parameters, a MCS is performed for the three variants with the assumed scatter bounds illustrated in Table 1. MCS is a widely used and popular uncertainty propagation method. However, the low convergence rate of MCS and the associated computational e ff ort can be a limiting factor, hence the more e ffi cient Latin hypercube sampling method is employed Janssen (2013). An estimation of the required number of sample points by means of a MCS for the assessment of the reliability of structural mechanical systems can be found in Broding et al. (1964). According to Melchers and Beck (2018), the formula has to be extended by the number of the independent variables considered:

− ln (1 − C ) P f

(2)

M > N s

Whereas M describes the required sample number, N s the number of independent variables, C the confidence level and P f the probability of failure. In this study C = 95% and P f = 0 . 01 are selected, resulting in a required sample number of 1200 simulations. The results of a performed MCS with the assumed scatter bounds for the input parameters for all three variants are illustrated in Figure 4. The simulation runs that signalise a calculated failure, are highlighted in red colour. Based on the reference simulations, it can be observed that an increased mass of the mounted component as well as a lower sti ff ness due to thinner plates are resulting in lower durability results compared to the nominal condition. It is obvious that variant 2 and 3 with the assumed distributions of the parameters are expected to have a higher probability of failure, which can also be seen clearly in the drawn 10% quantile. This is because the energy content of the PSD load increases with decreasing frequency, which in turn leads to higher stresses, compare Figure 3. As in variant 2 and 3 the eigenmodes shift to lower frequencies, the PSD stress increases and thus also the damage. It should also be considered that variant 3 (thinner plates) not only increases the load due