8 Using Modal Projection Error to Predict Success of a Six Degree of Freedom Shaker Test 103 Fig. 8.13 Stress comparison between the removable component on a rigid fixture to the ninth field mode os the BARC where ¯qL are the modal coordinates or amplitudes of the laboratory mode shapes. Two field modes, seventh and ninth, are examined with corresponding MPEs of 6.8% and 37%, respectively. The seventh field mode and the corresponding laboratory modes used to reconstruct the field mode are shown in Fig. 8.13. From examination of the stress plots, it can be seen that there will be areas of the RC that will experience higher stresses and areas that will experience lower stresses due to the minimization of the least squared error nature of the pseudo inverse in Eq. 8.2. Even with these errors, some parts of the RC will be tested to the correct levels that could have similar stresses depending on the input. The ninth field mode and the corresponding laboratory modes used to reconstruct the field mode are shown in Fig. 8.14. The laboratory modes needed to reconstruct the field mode do not share much resemblance of the field mode when examining the stress. Because of the poor reconstruction, the stresses induced by the ninth field mode will not be properly represented in the laboratory test. 8.6 Conclusion and Future Work The MPE is shown to be able to predict if a shaker test using a rigid fixture can reproduce the response of a component field environment. This conclusion is drawn by calculating low MPE for a laboratory test with a rigid fixture that successfully reproduced a field environment. The high MPE calculated for the BARC structure also shows evidence that MPE can predict the success using a rigid fixture in a laboratory test. The high MPE supports this conclusion because the RC of the BARC is designed to have different mode shapes when attached to a rigid fixture. In order for the MPE to provide insightful results, it is shown that the DOFs chosen from the component is important as choosing only the connection DOFs for the RC provided misleading results. Using a full field DOFs to represent the modes of the RC along with a concatenation of rigid body shapes and fixed base shapes provides useful MPE values.
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