12 Sean Magoffin et al. 10-2 10-1 100 101 102 103 Amplitude (g) - Peak Modal Amplitude (g) 10-3 10-2 Damping Ratio Damping vs. Velocity Amplitude Fig. 16 Comparison of damping vs vibration amplitude between FEM and test for Mode 2: (black dashed) FEM Prediction, (colored lines) Measurements would have the minimum influence from other modes (i.e. see [15]) and hence agrees best with the assumptions made in QSMA. It is surprising that the results agree this well. In [10] the authors found that one had to model the interface very carefully, including any lack of flatness, to accurately capture damping. The FEM analysis also noted that Mode 6 was likely to behave nonlinearly, with an opening-closing type nonlinearity. The measurements did not show significant nonlinearity in Mode 6. However, it should be noted that bilinear-type nonlinearities may not exhibit a significant change in the resonance frequency with vibration amplitude [16]. Further analysis would be required to see if the test data confirms any bilinear behavior of Mode 6. Conclusion The Box Assembly with Removable Component (BARC) was modeled using Abaqus FEA software in order to predict the linear mode shapes and natural frequencies. Then QSMA was performed on Mode 2, which was suspected to have nonlinear behavior, in order to predict the amplitude dependant damping ratio and natural frequency. These predictions from the FEM were complete before physical testing on the BARC structure was performed, thus giving blind predictions of the linear and nonlinear behavior based only on the nominal design of the components. Once the FEM predictions were well along, the BARC was manufactured and linear and nonlinear testing was performed on the physical BARC structure. Modal analysis was performed in MATLAB to extract the linear mode shapes and natural frequencies. The mode shapes were found to visually match those of the FEM and the linearized natural frequencies from the FEM matched the tests well with typical errors of less than 1% and a maximum of 1.7% error, except for mode 6, which had an error of 8.0%. Mode 6 involves opening and closing of the joint while the other modes do not have this behavior. The first six modes were examined for nonlinearity and Mode 2 was found to exhibit a typical joint-type nonlinear damping behavior while the other modes had minimal nonlinearity. The nonlinearity predicted by applying QSMA on Mode 2 agreed quite well with the measurements. This study demonstrates the feasibility of using finite element analysis and QSMA to predict the linear and nonlinear behavior of a component such as the BARC. The linear and nonlinear FEM predictions agreed very well with measurements in this study, but, as was cautioned earlier, research on other structures with joints [10] suggests that prediction may often be much more challenging. Still, these results are encouraging and motivate further use of these predictive tools.
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