60 S.E. Obando and P. Avitabile 0 500 1000 1500 −130 −120 −110 −100 −90 −80 −70 Frequency (Hz) dB Force (lbf) FFT of Analytical Force Pulse 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 −10 −8 −6 −4 −2 0 2 4 Time (sec) - beginning portion Force (lbf) Analytical Time Domain Force Pulse Fig. 5.7 Time (left) and frequency (right) domain plots of input analytical force pulse Table 5.1 Frequencies of the first 15 modes of the 3 beam system and its components Mode Frequency (Hz) Beam A Beam B SubComponent System w/o A.C. System 1 0.0015 18.9 0.010 16.8 16.8 2 0.0024 45.9 0.014 37.6 37.5 3 87.6 80.9 224.5 68.2 68.1 4 241.4 161.4 619.0 86.9 84.6 5 473.2 299.7 1214.3 129.1 102.1 6 782.3 489.4 2010.4 210.5 129.1 7 1168.8 728.2 3011.1 282.8 210.0 8 1633.1 1015.5 4223.0 343.1 282.0 9 2175.4 1351.0 5653.7 477.1 343.0 10 2796.3 1734.7 7302.3 645.5 396.2 11 3496.7 2166.4 9071.4 716.4 477.3 12 4277.7 2646.2 12046.9 959.5 645.3 13 5140.7 3174.1 14493.9 1118.7 716.3 14 6087.4 3750.0 17502.7 1311.7 889.0 15 7120.0 4373.9 21038.3 1617.3 960.6 Yellow cells highlight similar frequencies after addition of ancillary subcomponent (AC) to the system therefore predicting its response from the information of the other two components (the red and blue beam). The test cases presented here are intended to show the results when a proper set of modes are selected such that no information is lost in the reduction process and an inappropriate reduced model where the modes do not span the space of the system. The cases presented here are summarized as: Case 1—Reference Model 206 DOF Total; System 1/Beam B 142 DOF; System 2—Beam A 42 DOF and Ancillary 22 DOF Case 2—Guyan Reduced Order Model 12 DOF Total; Beam B—ADOF 65, 117, 169, 199, and 205; Beam A—ADOF 23, 31, 33, 41, 43, 55 and 63
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