1 Experimental-Analytical Dynamic Substructuring of Ampair Testbed: A State-Space Approach 11 Table 1.1 Eigenfrequencies (Hz) and mass (g) for all the blades along with mean ( , Hz and g), standard deviation ( , Hz and g) and coefficient of variation (COV, %) of all the experimental blades Blades Statistics Component 841 722 819 FEA COV Error Mode 1 45:37 45:00 43:72 45:82 44:70 0:86 1:93 2.51 Mode 2 128:76 124:08 129:24 130:67 127:36 2:85 2:24 2.60 Mode 3 190:79 203:49 186:66 197:65 193:65 8:77 4:53 2.06 Mode 4 248:64 240:32 248:44 254:21 245:80 4:75 1:93 3.42 Mode 5 322:12 333:15 315:29 339:93 323:52 9:01 2:79 5.07 Mode 6 395:36 388:16 398:94 412:58 394:16 5:49 1:39 4.67 Mode 7 404:56 410:33 423:24 453:22 412:71 9:56 2:32 9.82 Mode 8 468:74 489:54 463:86 495:47 474:05 13:64 2:88 4.52 Mode 9 572:88 557:26 573:00 598:12 567:71 9:05 1:59 5.36 Mode 10 635:25 654:52 621:72 660:11 637:16 16:49 2:59 3.60 Mode 11 746:52 742:21 747:93 758:33 745:55 2:98 0:40 1.71 Mass 830:50 829:70 830:10 797:11 830:10 0:40 4.89e 04 3:97 The FE model eigenfrequencies (Hz) and mass (g) are also shown along with the relative error (%) between the measured mean and the FE element blade Table 1.2 Eigenfrequencies (Hz) for all the bracket mounted blades along with the error (%) between the measured mean and the experimentalanalytical synthesised components with the state-space method Set Blades/brackets Error Component SS841/FEA SS 722/FEA SS819/FEA Error 1 Error 2 Error 3 Mode 1 40:19 43:01 41:92 41:08 5:39 4:24 3:89 Mode 2 115:73 119:52 114:17 120:55 2:04 2:04 2:03 Mode 3 193:79 187:35 201:35 184:91 1:11 1:3 1:59 Mode 4 222:7 229:24 220:29 229:33 1:54 0:64 2:63 Mode 5 321:03 308:69 322:83 304:88 3:21 2:92 2:15 Mode 6 365:02 391:92 355:8 391:27 6:51 0:34 5:72 Mode 7 383:58 410:04 405:19 408:84 9:37 4:46 5:38 Mode 8 486:16 437:3 466:13 442:78 7:93 8:24 6:89 Mode 9 536:26 548:52 518:58 537:05 0:51 1:9 0:49 Mode 10 653:62 584:9 606:98 582:37 7:75 13:3 7:09 Mode 11 726:88 634:01 645:84 617:42 14:68 11:58 12:68 Error 1 stand for the relative error between SS 841/FEA and measured mean, Error 2 between SS 722/FEA and measured mean and Error 3 between SS 819/FEA and measured mean 1.6.1 Analytical and Synthesised Blade Models The 11 first eigenfrequencies for the three experimental blade models and the FE blade are shown in Table 1.1 along with themean ( , Hz), the standard deviation ( , Hz) and the coefficient of variance (COV, %) for the three experimental blades. Also, the relative error (%) between the measured mean relative to the FE blade is given. It can be seen that the spread between the blades is considerable and that the errors for modes 8 and 10 are considerably larger compared to the other modes. The mass (gramme) is also given in the table for the three blades and the FE blade along with the mean (gramme) of the three blades, the standard deviation (gramme), the coefficient of variance and the relative error with respect to the FE model. It should also be noted that the spread of the mass is very small. 1.6.2 Blade Bracket From Table 1.2 it can be seen that a relatively large spread is obtained for mode 7, 8, 10 and 11. In Fig. 1.9 the FRFs for the difference between the coupled models are shown for models coupled using frequency based and state space coupling. It can be seen that the two coupling procedures produces identical results. In Fig. 1.10 the difference between the individual measured FRFs of the blade bracket assemblies as well as the state space coupled systems becomes eminent.
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