24 S.E. Obando et al. Nodes 17-20 DOF 33,35,37,39 F Nodes 1-2 DOF 1 and 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 MAC Time [s] 0 5 10 15 20 25 30 35 40 45 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 TRAC NDOF 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Time (sec) Displacement Time Domain Response near Base Average TRAC: 0.76 Average MAC : 0.92 Exp. 6 ADOF Guyan Reference Fig. 2.7 Comparison and correlation of 6 ADOF Guyan reduced and reference cantilever beam models 2.4.3 Case A-3: SEREP Reduced Order Models Model reduction of the reference cantilever beam (unmodified) was performed using 4 and 6 ADOF as in the Guyan reduced models. SEREP reduced models were not affected by the poorly selected ADOF and because the mode shape vectors and frequencies are preserved exactly, good correlation was obtained from the predicted time response. 2.4.3.1 Case A-3.1 In similar manner to that of Case A-2.1, a SEREP reduced model of 4 ADOF was created using nodes 17–20. A comparison of the predicted time response from the expanded reduced order model can be seen in Fig. 2.8. All DOF were preserved accurately, even those not included in the reduction process. The MAC and TRAC show high correlation for the predicted time response. Thus, SEREP reduction overcomes the limitations encountered in the Guyan reduced models allowing for the accurate prediction of the dynamic characteristics of the system. 2.4.3.2 Case A-3.2 For this case, two additional DOF are included in the reduced model (as in Case A-2.2). The SEREP methodology for this case produces rank deficient matrices and care must be taken in the numerical processing of the models. Nevertheless, accurate results were obtained at all NDOF. Figure 2.9 shows a comparison of the time response near the base of the beam.
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