524 D. Roettgen et al. Table 50.6 Elastic modal frequencies of CPB Mode Test frequency (Hz) FEM frequency (Hz) Error ( %) 1 134.2 133.83 0.28 2 171.2 171.30 0.06 3 430 435.15 1.20 4 511.2 497.42 2.70 5 975.7 954.60 2.16 6 1027 1038.14 1.08 7 1312 1301.33 0.81 8 1528 1535.62 0.5 9 1637 1589.17 2.92 10 1801 1846.45 2.52 11 1833 1859.75 1.46 Fig. 50.10 CPB model with additional mass The additional mass attached at the end of the beam is modeled with 20 node hex elements (Fig. 50.10). The nodes in this mesh did not naturally align with those in the beam mesh, so the two substructures were connected using the multi-point constraint method. 50.4.2 Predictions and Comparison with Experimental Truth Data Here we shall consider a substructuring problem in which the first 20 free normal modes (6 rigid body modes and 14 elastic modes) up to 970 Hz were extracted from the experimental systemCin Fig. 50.6, consisting of the CBP structure with the foam inside. These 20 free normal modes also included the experimental damping ratio. A FE model of the transmission simulator, i.e. the CBP structure (A in Fig. 50.6), was used to remove the effects of the transmission simulator. From the FE model of the transmission simulator, ten free normal modes (six rigid body modes and the first four elastic modes) up to 805 Hz were retained with an arbitrarily assigned damping ratio of 0.5 %. Subsequently, the dynamics of the modified CBP structure (i.e. with the mass attached, systemDin Fig. 50.6) were added to predict the dynamical behavior of the truth hardware (systemEin Fig. 50.6) and shown on the right in Fig. 50.7. The predictions will then be compared to the results of the test on the truth hardware to evaluate the substructuring methods. Two different substructuring approaches were applied, the traditional transmission simulator method (TS) and the CraigMayes method (CM).
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