PSI - Issue 84

Andrea Mileto et al. / Procedia Structural Integrity 84 (2026) 829–836

834

[−]

0.5 0.6 0.7 0.8 0.9 1.0 100 96 92 88 84 80

1.1 1.2 1.3 1.4 1.5 76 72 68 64 60

2 [kN]

[kN] 120 120 120 120 120 120 120 120 120 120 120 [kN] 80 72 64 56 48 40 32 24 16 8 0

Fig. 2. Results of the sensitivity analysis for case 2.

3.3. Case 3 (reduced number of mode shapes) The proposed identification procedure is based on the Differential Evolution (DE) as search algorithm. This scheme is characterized by a high computational cost, due to the repeated solution of the structural dynamic problem for each individual of the population and for each generation of the DE algorithm. This aspect becomes particularly relevant when a modal representation with a high number of mode shapes is adopted. In order to improve the computational efficiency of the approach, a modal truncation strategy (Truncation Method) can be introduced by limiting the number of vibration modes used to compute the dynamic response. The behaviour of the identification procedure with modal truncation is here analysed considering different structural configurations, with particular reference to the role of the skew angle . The results are showed in Fig. 3, where the number of modes is reduced from 20 (results of Figs. 1 and 2) to 12; the same conventions of Fig. 1 are still adopted. Both the case with a constant load difference Δ = 2 − 1 = constand the one with a constant total load TOT = 1 + 2 = const are performed. The chosen objective function is simpler than those in Eqs. (1): =√ 2 + 2 (2) which only considers the frequency peaks and the crossing time, and this in order to more clearly highlight the contribution of the number of modes.