PSI - Issue 57

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Ewelina Czerlunczakiewicz et al. / Procedia Structural Integrity 57 (2024) 743–753 / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. Schematic view of the substructure model The application of superelements was verified by means of the Modal Assurance Criterion. This is a tool used in modal analysis to quantify the similarity between two sets of mode shapes. In the MAC plot (Fig. 3a), red color (1) corresponds to perfect agreement between the mode shapes. The presence of a red diagonal in the MAC plot, which compares the fully represented model with the one represented by superelements, confirms that the superelement application was correct.

Fig. 3. (a) MAC plot for the ECM (b) Transfer function comparison

2.3. Calculation methods The next step concerns the choice of the calculation methods for the comparison. As previously indicated, calculation methods used in the industry should be able to handle large models. Additionally should be able to provide results within reasonable calculation time. FEA random load dynamic analysis can be performed either in the frequency domain or in the time domain. Frequency domain methods such as Steady Statedynamic (SSD) typically have much shortercalculation times compared to time domain methods. These methods are widely used in industry due to their efficiency. The main objective of the study was to compare the commonly used linear SSD approach with an analysis method that is capable of including non linear behavior, specifically a transient analysis. To facilitate the comparison between the significantly different approaches, two intermediate steps were undertaken. The first step, known as Modal Transient Dynamic (MTD), follows a similar concept to the standard approach, with modal behavior and linearity, but it is calculated in the time domain. The second step involves a linear analysis conducted in the time domain, but instead of relying on the modal superposition method used in mode-based analysis, it employs direct integration to describe the physics of the system. It is important to note that direct integration methods require different damping definitions that were compared and correlated as well. Introducing these intermediate steps, allowed us to adopt a step by step approach making the comparison more reliable, enabling a more accurate understanding of the behavior and performance. The diagram below (Fig. 4) illustrates the types of analyses considered for the comparison.