26 FEM Calibration with FRF Damping Equalization 269 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m4 1.00% 0.10% 0.01% -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 k9 1.00% 0.10% 0.01% -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m4 5 p½bw 1 p½bw 1/5 p½bw -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 k9 3 p½bw 1 p½bw 1/3 p½bw Fig. 26.1 Normalized deviation metric versus parameter variation from nominal of two parameters, k9 and m4, for (upper) three system damping levels at 0.01, 0.1 and 1 %, and (lower) various frequency sampling rates in number of samples per half-bandwidth (p½bw) The experimental state-space system can be brought to diagonal form by a similarity transformation. Using the mode matrixX, pertinent to the eigenvalue problemAXDX , for transformation we have for the diagonal realization that Pz DAz CX 1Bu (26.12a) y DCXz CDu (26.12b) with ADX 1AXDdiag.œn/ (26.13) forwhichœn are the complex-valued system poles as given by the experimental data. The relative modal damping—n, obtained from these poles are —n D Re.œn/=Im.œn/8Im.œn/>0 (26.14a)
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