762 T. Marinone et al. Table 71.6 Natural frequency and damping estimates for experimental modal data BeamA BeamB Mode # Test frequency (Hz) Test damping (%Crit.) Test frequency (Hz) Test damping (%Crit.) 1 12:850 1.100 23:400 0.440 2 84:970 0.360 144:544 0.100 3 254:270 0.490 405:093 0.090 4 519:510 0.130 797:049 0.060 5 817:240 0.150 1;315:013 0.120 6 1;234:680 0.200 – 7 1;637:960 0.360 – Table 71.7 Beam A correlation results Frequency (Hz) Original test Expanded test Mode # Analytical Test Frequency (% diff.) MAC POC MAC POC 1 12:915 12:850 0:502 0.998 0.854 0.990 0.854 2 84:119 84:970 1.001 0.999 0.969 0.999 0.969 3 252:339 254:270 0.759 1.000 1.084 0.999 1.084 4 519:587 519:510 0:015 0.999 0.949 0.998 0.949 5 806:163 817:240 1.355 0.997 0.957 0.995 0.957 6 1;256:551 1;234:680 1:771 0.986 0.913 0.983 0.913 7 1;682:965 1;637:960 2:748 0.918 0.882 0.927 0.882 Table 71.8 Beam B correlation results Frequency (Hz) Original test Expanded test Mode # Analytical Test Frequency (% diff.) MAC POC MAC POC 1 23.029 23.400 1.585 0.993 0.919 0.910 0.919 2 144.456 144.544 0.061 0.994 0.906 0.972 0.906 3 403.340 405.093 0.433 0.991 0.954 0.863 0.954 4 791.173 797.049 0.737 0.980 0.922 0.889 0.922 5 1,308.790 1,315.013 0.473 0.952 0.910 0.870 0.910 component models were reduced down to retain the 15 tested ADOF for each component. The SEREP reduction scheme was used and therefore, 15 modes for each component were retained in the reduced models in order to formulate a fully ranked transformation matrix. This transformation matrix was then used to expand the test mode shapes out to the full space FEM set of NDOF, which smoothes and completes the measured data. Table 71.7 lists the correlation results for Beam A, while Table 71.8 lists the correlation results for Beam B. Both tables show that high correlation between the analytical and test results were obtained with minimal frequency differences (<2%). Although multiple cases were studied [3], the case studied here is of a single beam with single contact point. A linear conical spring was mounted to a fixed block to closely resemble a translational DOF spring, as shown in Fig. 71.20. In addition, the area that the beam impacts the spring is relatively small and is a reasonable approximation of a single DOF, as shown in the red outlined image of Fig. 71.20. The base of the spring is attached to a block that is bolted to the frame of the test bed and can be assumed to be grounded, as shown in the blue outlined image of Fig. 71.20. A force pulse was applied to the single beam using a modal impact hammer. A gap distance of 0.1715 in. was measured between the conical spring and contact thumper attached to the beam, which is shown in the red outlined image of Fig. 71.20. The conical spring was approximated as a single translational DOF stiffness located at DOF 141 and a full space modified system model was developed with the spring stiffness applied. Figure 71.21 shows the mode contribution matrix where the number of the unmodified component modes needed to form the modified system modes are able to be clearly identified. The various box colors indicate the amount that each unmodified component mode contributes in a particular modified system mode; the actual contribution ranges for each color are shown. The first eight natural frequencies of the modified system as well as for the unmodified component are listed in Table 71.9. Accelerometers and PONTOS [22,23] targets were mounted to the test structure at several locations such that acceleration and displacement time response data could be acquired at collocated points. The system was excited by applying a force pulse into the single beam using a calibrated modal impact hammer. The experimentally measured force pulse was then input to
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