5 Prediction of Forced Response on Ancillary Subsystem Components Attached to Reduced Linear Systems 65 0 0.05 0.1 0.15 0.2 0.25 0.35 0.4 0.45 -6 -4 -2 0 2 4 6 x 10−4 Time (sec) Displacement at Node 1 Time Domain Response of Ancillary Beam at Node 1 Guyan Red. Model Reference Model 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (sec) Guyan Red. Model Reference Model Fig. 5.15 Comparison of time response at node 1 of the ancillary subcomponent from the expansion of a 12 DOF Guyan reduced model versus the 206 DOF full space reference solution. Zoomed in region shows the response for the first 0.05 s Note that there are no DOF from 1 to 22 since these are the ancillary subcomponent DOFs and moreover, DOF 37 and 49 connecting the top red beam to the ancillary beam were omitted as well. As discussed in the theory section, even with sufficient modes selected in the reduction process (according to the U12 contribution matrix) and a well placed selection of ADOF, Guyan reduced did not preserve the five modes of interest as seen in the table of Fig. 5.14. The error can be observed to increase quickly for modes higher than 3 and the predicted system response is not expected to yield accurate results. The forced response of the Guyan reduced order model was calculated and using the transformation matrix [T], the results were expanded back to full N-space (206 DOF). The ancillary subcomponent response was found from the expanded forced response of the system. Figure 5.15 shows a comparison of the displacement at the first node of the ancillary subcomponent with respect to the full space reference solution. The average MAC and TRAC were found to be 0.6 and 0.53 respectively. Figure 5.16 shows the MAC and TRAC for the expanded Guyan reduced model. From Fig. 5.16 and from the calculation of time response correlation tools, the response of the expanded Guyan reduced model showed low correlation to the reference solution. Clearly mode truncation does not allowed for the accurate characterization of the reduced system, let alone the characterization of the ancillary subcomponent from embedded system information. While addition of extra DOF may diminish the effects of mode truncation, there is always an intrinsic risk of error in the Guyan reduction process and ADOF selection. 5.4.4 Case 3: SEREP Reduced Model The goal of preserving the first five modes of the full 3 beam system requires the selection of five modes of System 1 and seven modes of System 2. The same ADOF selection from Case 2 was used during the SEREP reduction process. Figure 5.17 shows the resulting frequencies of the reduced system.
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