5 Prediction of Forced Response on Ancillary Subsystem Components Attached to Reduced Linear Systems 67 Reference System Freq. (Hz) SEREP Reduced System Freq. (Hz) % Difference Mode 1 16.8 16.8 0% Mode 2 37.5 37.5 0% Mode 3 68.1 68.2 0% Mode 4 84.6 84.6 0% Mode 5 102.1 102.1 0% Mode 6 129.1 130.2 1% Mode 7 210.0 211.5 1% Mode 8 282.0 283.2 0% Mode 9 343.0 351.2 2% Mode 10 396.2 396.6 0% Mode 11 477.3 2611.8 447% Mode 12 645.3 3023.1 369% System 2: 7 ADOF – 23, 31, 33, 41, 43, 55, and 63 System 1: 5 ADOF – 65, 117, 169, 199 and 206 Fig. 5.18 Comparison of SEREP reduced order model (12 DOF) frequencies with respect to (206 DOF) reference solution Fig. 5.19 MAC and TRAC bar plots showing the correlation of the expanded SEREP reduced model to the reference model system. Figure 5.17 shows a comparison of time response at the first node of the ancillary beam (from the expanded SEREP reduced model) with respect to the reference solution; while only one node is shown for brevity, all of the nodes on the ancillary component had similar agreement. The average MAC and TRAC were found to be 0.97 and 0.95 respectively. Figure 5.19 shows the MAC and TRAC bar graphs correlating the expanded SEREP reduced model to the reference solution. The SEREP reduction and expansion process resulted in high correlation using the same amount of DOF as the Guyan reduced model. Furthermore, the omission of the connecting DOF for the ancillary subcomponent did not yield additional error as will be shown in Case 6. Moreover, issues can only arise if the selected DOF do not yield full rank reduced mass and stiffness matrices but this issue was not encountered in the analytical models studied. Nevertheless, Case 4 discusses the KM_AMI Model Improvement which can alleviate any issues arising from the rank deficiency in the reduction process while preserving the accuracy of the SEREP reduction methodology.
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