134 Nicholas Pomianek et al. Fig. 4 Comparison of nominal FE models with EJR method optimization results. Solid element simulation run in Abaqus using explicitly modeled joint geometry, contact interactions, and bolt forces. MSSF similarity metric, bolt tightening order 3-2-1. The effect of different FRF similarity metrics was also considered. With the exception of the RMSPE and FRFSF metrics, all considered similarity metrics performed well. Figure 5 shows the optimized EJR models generated using the eight similarity metrics analyzed in this work. The optimal number of frequency window divisions depended on the similarity metric but for the ILR2, FRAC, MFRAC, CSF, MSF, and MSSF optimized models the highest performing number of windows was four. The highest performing similarity metric overall was found to be MSSF. Fig. 5 Performance comparison of FRF similarity metrics, bolt tightening order 3-2-1. A repeatability study was performed to test the sensitivity of the EJR method to system variability due to assembly conditions. Experimental data was taken on the same BRB assembled with six bolt tightening orders, as shown in the upper plot of Figure 6. An EJR optimized model was then generated for each data set, showing minor sensitivity to joint repeatability. The lower plot of Figure 6 shows the EJR model results corresponding to each bolt tightening order. Because four windows were used to update the models shown in the previous figures, the EJR properties vary as a function of frequency. Figure 7 shows the variation in properties in the different frequency windows used for optimization. The upper and lower bounds of each variable available to the particle swarm optimization algorithm are shown by the vertical axis limits of each plot. While many of these results are non-physical, the resulting FRF is in good agreement with experimental data. The MSSF similarity metric between the EJR models and experimental data in Figure 6 ranges from 0.924 to 0.967 (its maximum value is 1). One of the inherent limitations of beam elements is their lower performance at
RkJQdWJsaXNoZXIy MTMzNzEzMQ==