284 Q. Fei and D. Jiang Table 27.5 Comparison of parameters: Incorrect initial model Parameter Real value (Nm2) Initial VALUE (Nm2) Initial errors (%) Updated value (Nm2) Updated errors (%) 1 4,560 4,500 1.33 5,860 30:2 2 4,560 4,500 1.33 2,153 52:2 3 4,560 4,500 1.33 2,612 42:0 4 4,560 4,500 1.33 4,071 0:10 5 4,560 4,500 1.33 4,394 0:02 0 2 4 6 8 101214161820 -10 -8 -6 -4 -2 0 2 Iteration Step Modal Frequency Errors (%) 0 5 10 15 20 25 0.88 0.9 0.92 0.94 0.96 0.98 1 Iteration Step MAC Fig. 27.5 Convergence curves for correct boundary case Table 27.6 Comparison of modal frequencies: correct initial model Mode order Experimental modal frequency (Hz) Initial modal frequency (Hz) Initial frequency errors (%) Updated modal frequency (Hz) Updated frequency errors (%) 1 37:5 33:9 9.6 37:5 0 2 236:8 220:6 6.8 236:8 0 3 657:6 613:9 6.6 657:6 0 4 1;256:3 1;155:0 8.1 1;256:3 0 5 1;996:6 1;819:8 8.9 1;996:6 0 6 2;889:7 2;687:1 7.0 2;889:7 0 Table 27.7 Comparison of parameters: correct initial model Parameter Real value Initial value Initial errors (%) Updated value Final errors (%) 1 4,560Nm2 4,500Nm2 1.3 4,560Nm2 0 2 1.0 105 Nm 1 5 104 Nm 1 50 1.0 105 Nm 1 0 3 4.0 107 Nm 1 2.0 105 Nm 1 50 4.0 107 Nm 1 0 27.4.2 Updating of Initial Model with Correct Boundary Condition In this case, three parameters are taken as updating objects, including stiffness of rotation and translation springs and EI of the beam. The same EI will be set to all the ten elements. Modal frequencies of the first four modes are employed in the updating. The other two modal frequencies of the fifth mode and the sixth mode are used in the updated model validation. The following figures (Fig. 27.5) show the convergence of modal frequencies and MAC. From the figures above, it’s obvious that updating converge in less than fifteen iterations. The errors of modal frequencies are really small after updating. MACs of all the modes reach 1 after updating. Modal frequencies, parameters and corresponding errors are listed in Tables 27.6 and 27.7. From the sixth column of Table 27.6, it could be seen that modal frequencies of the first four modes which are used in the updating are accurate after
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