71 Expansion of Nonlinear System Response Using Linear Transformation. . . 763 Fig. 71.20 Conical spring used for single beam with single contact test case MODE Modified System Mode Shapes Conical Spring Contact 12345678910 1 2 3 4 5 6 7 8 9 10 Bar Color Min Value Max Value Red 0.9 1 Yellow 0.7 0.9 Magenta 0.5 0.7 Cyan 0.3 0.5 Green 0.2 0.3 Blue 0.1 0.2 Black 0.005 0.1 White 0.0 0.005 Unmodified Beam A Mode Shapes Fig. 71.21 Mode contribution matrix for single beam with conical spring contact Table 71.9 Natural frequencies for single beam with conical spring contact Frequency (Hz) Mode # Unmodified Conical spring contact 1 12:850 41:422 2 84:970 92:352 3 254:270 254:989 4 519:510 519:744 5 817:240 817:297 6 1;234:680 1;234:686 7 1;637:960 1;637:960 8 2;201:360 2;201:365 the analytical model to obtain analytical dynamic response predictions for comparison with the test data. The predicted displacement is compared to the measured displacement using PONTOS [23] (high speed digital photogrammetry software) at DOF 81 and DOF 141 over the first 0.2 s of the response, as shown in Fig. 71.22. To quantify the similarity of the reduced analytical model solution with the experimental results, the MAC and TRAC were computed between the reduced analytical model and the experimental time responses, which are shown in Fig. 71.23. Note that the y-axis scale for the MAC and TRAC plots is 0.0–1.0.
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