PSI - Issue 38

Amaury Chabod et al. / Procedia Structural Integrity 38 (2022) 382–392 Amaury CHABOD / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 3. Modal Superposition Process Therefore, a load reconstruction process, including modal stresses { } as independent load cases, produces an estimator on input modal coordinates ( ) applied to each modal stress, as in Fig. 4. This underlines an interesting aspect of this approach, where it is possible to reconstruct input load from strain gages responses {S}(t), even if the behavior includes dynamic resonances. From a set of strain gages measurements, a first set of modal coordinates are obtained. Finally, combining modal coordinates ( ) and modal stresses { } , the full stress response on the entire model is obtained according to equation (20). Thereafter, from stress time histories, a damage analysis may be performed on the full FE model.

Fig. 4. Load Reconstruction Process for Dynamic Analysis

5. Use case In this use case, we consider a turbine blade made of steel, where the behavior is assumed as fully elastic linear. The model consists of 18437 shell elements and 17911 nodes. The boundary conditions are purely clamped on the origin. That component exhibits a dynamic behavior, and it is subjected to unknown acceleration, which effect will be measured indirectly by load reconstruction. The purpose of this use case is to compute damage on the full structure, based on strain gage measurements and simple modal analysis, presenting the methodology along the way. A strong advantage of this methodology is that we avoid calculating complex and long transient FE analysis. FE modal analysis is achieved with FE element solver Nastran 2017 sol 103, and FE post-processing including strain gage optimization, load reconstruction and damage analysis are performed using nCode DesignLife 2021.0. 5.1. Strain gage optimization FE modal analysis counts ten modes between 0.55 Hz and 7.1 Hz, which constitute our modal basis of independent load cases. The list of resonant frequencies found in FE the modal analysis is listed below.

Table 1. Resonance frequencies obtained from FE modal analysis. Mode

Frequency (Hz)

1 2 3 4 5 6 7 8 9

0.55 0.83 1.58 3.29 3.40 5.22 5.79 6.10 6.78 7.10

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