62 S.E. Obando and P. Avitabile 16.78 Hz 37.50 Hz 68.11 Hz 84.61 Hz 102.08 Hz 129.11 Hz 209.96 Hz 282.02 Hz 342.95 Hz 396.25 Hz 477.32 Hz 645.25 Hz 716.29 Hz 889.02 Hz 960.58 Hz Fig. 5.9 Mode shapes of full 206 N-space 3 beam system used as reference solution 5.4.2 Overview of Reduced Models Full N-space subcomponents were assembled into two systems (System 1 and System 2) as in the reference case. The two systems were reduced separately and then tied together. For System 2, containing the ancillary subcomponent, the reduction was made as to omit any active DOF in the ancillary beam. The idea is that the reduction process, if carried out successfully, should embed the necessary component information onto the reduced assembled system. Figure 5.11 shows the assembly sequence performed to reduce the system components and the extraction of the subcomponent response from the calculated reduced model forced response. Three reduction methods were used to highlight particular advantages of each procedure. Guyan reduction, as explained in the theory section, does not fully preserve the dynamics of the system if an optimal ADOF set is not selected. On the other hand, SEREP will accurately preserve the selected modes of the system but issues may arise regarding full rank of the reduced mass and stiffness matrices of the system. Lastly, a model improvement technique, KM_AMI, is used to update the mass and stiffness matrices of the Guyan reduced model by seeding target frequencies and mode shapes and therefore preserving the exact model information while preserving the full rank advantages of a Guyan reduced model. These issues will be covered in the three cases described below. 5.4.3 Case 2: Guyan Reduced Model As with the other reduced models covered in this study, the selected DOF for the reduction did not include DOFs of the ancillary subcomponent. As indicated by the U12 matrix in Figs. 5.10 and 5.12, there are 12 modes of the system’s components necessary to accurately span the space of the first five modes of the assembled 3 beam system. Figure 5.13 shows the layout of connection DOF of the 3 beam system. Figure 5.14 shows the reduced order model frequencies compared to the reference N-space solution.
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