64 S.E. Obando and P. Avitabile Range Color Min Value Max Value Red 0.90 1.00 Yellow 0.70 0.90 Magenta 0.50 0.70 Cyan 0.30 0.50 Green 0.20 0.30 Blue 0.10 0.20 Black 0.01 0.10 System 2 System 1 Comp. Modes Full 3 Beam System Modes 1 2 3 4 5 Sys2 - M 1 0.5 0.5 0.2 0.1 0 Sys2 - M 2 0.1 0.2 0.4 0.1 0 Sys2 - M 3 0 0 0.1 1 0 Sys2 - M 4 ### ### 0 ### ### Sys2 - M 5 ### 0 0 0 0 Sys2 - M 6 ### ### ### ### ### Sys2 - M 7 ### ### ### 0 0 Sys1 - M 1 0.9 0.3 0 0.1 0 Sys1 - M 2 0 0.8 0.4 0.1 0 Sys1 - M 3 0 0.1 0.8 0.1 0 Sys1 - M 4 0 0 0.1 0 0 Sys1 - M 5 0 0 0 0 0 Fig. 5.12 Selected portion of U12 mode contribution matrix from system components to first five modes of full 3 beam system Ancillary: 10 Elements – 22 DOF Top Beam: 20 Elements - 42 DOF Base Beam: 70 Elements – 142 DOF 65 DOF # 1 22 23 64 206 37 49 169 31 55 199 Connection DOF # Fig. 5.13 Summary of numbering of 3 beam system NDOF (206) and connecting DOF Reference System Freq. (Hz) Guyan Reduced System Freq. (Hz) % Difference Mode 1 16.8 16.8 0% Mode 2 37.5 37.7 0% Mode 3 68.1 69.9 3% Mode 4 84.6 86.4 2% Mode 5 102.1 129.9 27% Mode 6 129.1 220.6 71% Mode 7 210.0 347.9 66% Mode 8 282.0 663.8 135% Mode 9 343.0 731.0 113% Mode 10 396.2 1578.4 298% Mode 11 477.3 3073.4 544% Mode 12 645.3 3283.3 409% System 2: 7 ADOF – 23, 31, 33, 41, 43, 55, and 63 System 1: 5 ADOF – 65, 117, 169, 199 and 206 Fig. 5.14 Comparison of Guyan reduced order model (12 DOF) frequencies with respect to (206 DOF) reference solution
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