180 C.L. Fisher et al. Fig. 19.3 Mesh refinement analysis (left) and resulting mesh discretization used for numerical analysis (right) Fig. 19.4 FEA modal analysis displacements Using this model, a modal analysis was performed in ANSYS assuming a rigid, fixed base. The modes of the structure were evaluated up to 4.6 kHz, which was well beyond the 2 kHz frequency range of the electrodynamic shaker used in physical testing. This analysis demonstrated the first modes of the test article contained no coupling between the arms or modes located in the center support cylinder in the frequency range analyzed. Because of this, it was expected that the arms of the structure would act independently from one another as desired. The results of the first 4 modes of the test article are illustrated in Fig. 19.4 with the color gradient representing displacement. As desired, these results show a range of natural frequencies in the arms ranging from 29 Hz located in the arm with the smallest diameter increasing sequentially through the arms with the 4th mode at 115 Hz located in the arm with the largest diameter. To better understand the experimental dynamic behavior of the test article, the part was subjected to a random transient wave using a 25 lbf. [111.2 N] electrodynamic shaker. Accelerometers were placed on each cantilever arm, the support column, and the base of the structure, as seen in Fig. 19.5. The acceleration input from the accelerometer located at the base of the test article was used as the base accelerations for the analysis of the results. Six random vibration tests were performed for 19 different test article for a total of 114 vibration tests. Test repeats were performed to help account for the manufacturing and material property variation that could have occurred from test article to test article to allow for characterization of the experimental uncertainty. From these results, a power spectral density was calculated for each arm with the results demonstrated in the left image of Fig. 19.6. The natural frequencies for each arm were taken as the frequency with the maximum peak and demonstrate a distinct frequency value for each cantilever arm, allowing the experimental tests to be tailored towards this frequency range. Unlike the FEA modal analysis, the PSD experimental results indicated potential coupling between some of the arms. This may not have been seen in the FEA analysis as the boundary conditions were modeled as a perfectly rigid, fixed condition whereas no connection is perfect in physical experiments. The experimental
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