1 Practical Techniques for Scaling of Optically Measured Operating Deflection Shapes 11 MAC Scaled ODS UsingDrive Point 1 2 3 4 Freq(Hz) 14.19 88.13 244.63 467.50 EMA Impact Test 1 14.34 1.000 0.014 0.015 0.006 2 89.28 0.016 1.000 0.020 0.004 3 247.07 0.016 0.018 0.999 0.014 4 471.75 0.019 0.016 0.027 0.965 Scaled ODS UsingDrive Point 1 2 3 4 Freq (Hz) 14.19 88.13 244.63 467.50 EMA Impact Test 1 14.34 1.000 0.003 0.007 0.002 2 89.28 0.0074 0.989 0.006 0.003 3 247.07 0.0058 0.0185 0.967 0.007 4 471.75 0.045 -0.003 -0.025 1.043 MAC Orthogonality Orthogonality Check a b Fig. 1.7 Correlation between operating deflections shapes, scaled using drive point measurement, and reference mode shapes. (a) MAC values indicating degree of consistency between scaled operating shapes and reference mode shapes (input–output measurement). (b) Experimental mass weighted orthogonality check between the scaled operating shapes and reference modal vectors Fig. 1.8 Comparison of the natural frequencies of the modified (redbar) and unmodified (blue bar) cantilevered beam estimated using stochastic subspace identification (SSI) 1.4.3 Case B.1: Estimating Mode Shapes of the Modified Structure Using Unscaled Deflection Shapes Structural dynamic modification can be used to find the mode shapes of a modified structure using the modes of the original structure and the mode contribution matrix ([E12]). In order to demonstrate the necessity of scaling ODS, the operating shapes of the unmodified structure in conjunction with unscaled mode contribution matrix ([Eun 12]) were used in the SDM process to estimate the modified ODS (blue lines in Fig. 1.9). The mode contribution matrix extracted using ODS does not represent the real contribution of each original mode shapes in the response of modified structure. Figure 1.9 shows that the unscaled ODS used in the SDM process does not yield the appropriate modes shapes of the modified structure, and the estimated mode shapes do not correlate well to the final mode shapes of the modified structure. The inconsistency between the estimated and experimentally measured modes is more evident when third and fourth modes are compared (see Fig. 1.9). Orthogonality values, shown in Fig. 1.10, indicate the importance of scaling operating shapes before executing structural
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