40 A.W. Phillips and R.J. Allemang 0 500 1000 1500 2000 2500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Consistency Diagram Frequency (Hz) Model Iteration cluster pole & vector pole frequency conjugate non realistic 1/condition Fig. 4.8 C-Plate consistency diagram, real weighting, full frequency range 5 10 15 20 25 5 10 15 20 25 Mode (real) Mode (imag) MAC 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5 10 15 20 25 5 10 15 20 25 Mode (real) Mode (imag) MAC (weighted) 0 0.5 1 1.5 2 2.5 x 10−3 Fig. 4.9 C-Plate, real weighting, riMAC and riwMAC 4.6 Summary and Future Work A relatively simple change to the weighting vectors used in the weighted estimation of the residues for each mode has dramatically improved the results with little to no observable negative effects. For the examples chosen, the use of central vector rotation and real normalization of the modal participation vectors appears to improve the quality and characteristics of the final, scaled modal vectors (residues) significantly. Future work will involve alternative numerical methods for decoupling the contaminated modal vectors and a more rigorous evaluation of the source of contamination derived from the companion matrix solution with the goal of eliminating the contamination earlier in the parameter estimation process. A more complete understanding of why this technique works so well is still needed. Acknowledgements The authors would like to acknowledge the collaboration and assistance from the graduate students and faculty of the Structural Dynamics Research Lab at the University of Cincinnati. In particular, the discussions and collaborations with Dr. David L. Brown have been instrumental in the progress made to this point.
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