Dynamics of Machines - Part II - IFS.pdf

presented in section 1.6.9, to learn how to deal with experimental data and how to extract
important information. H1(ω) as well as H2(ω) are obtained when an excitation force
is horizontally acting on the platform mass and its value is measured by using a force
transducer, and simultaneously the acceleration response of the platform is measured using
a acceleration sensor. The experimental setup can be seen in figure 36(b). The most
common ways of representing the frequency response functions H1(ω) and H2(ω) are in
the form of amplitude and phase, or real and imaginary. In table 6 such values are presented
in the real and imaginary forms and in figure 37 they are plotted. Please, plot H1(ω) and
H2(ω) in terms of magnitude and phase.
Frequency - H1 - H2 COHERENCE
[Hz] [(m/s 2 )/N] [(m/s 2 )/N]
1.6250 0.0490 - 0.0040i 0.0595 - 0.0049i 0.8236
1.7500 0.0610 - 0.0051i 0.0698 - 0.0058i 0.8745
1.8750 0.0750 - 0.0071i 0.0855 - 0.0080i 0.8776
2.0000 0.0826 - 0.0068i 0.0945 - 0.0078i 0.8744
2.1250 0.0974 - 0.0025i 0.1093 - 0.0028i 0.8907
2.2500 0.1124 + 0.0015i 0.1204 + 0.0016i 0.9335
2.3750 0.1310 - 0.0018i 0.1393 - 0.0019i 0.9403
2.5000 0.1411 - 0.0100i 0.1477 - 0.0105i 0.9555
2.6250 0.1540 - 0.0112i 0.1601 - 0.0116i 0.9621
2.7500 0.1817 - 0.0040i 0.1889 - 0.0041i 0.9619
2.8750 0.2113 - 0.0145i 0.2184 - 0.0150i 0.9677
3.0000 0.2474 - 0.0172i 0.2520 - 0.0176i 0.9819
3.1250 0.2676 - 0.0230i 0.2726 - 0.0234i 0.9817
3.2500 0.3016 - 0.0364i 0.3080 - 0.0371i 0.9792
3.3750 0.3460 - 0.0487i 0.3536 - 0.0497i 0.9787
3.5000 0.4072 - 0.0467i 0.4173 - 0.0479i 0.9758
3.6250 0.4601 - 0.0673i 0.4697 - 0.0687i 0.9795
3.7500 0.5107 - 0.0903i 0.5165 - 0.0914i 0.9887
3.8750 0.5894 - 0.1239i 0.5974 - 0.1256i 0.9866
4.0000 0.6862 - 0.1427i 0.6994 - 0.1454i 0.9812
4.1250 0.8110 - 0.1959i 0.8228 - 0.1987i 0.9857
4.2500 0.9381 - 0.2824i 0.9539 - 0.2872i 0.9834
4.3750 1.1113 - 0.4002i 1.1429 - 0.4116i 0.9723
4.5000 1.3290 - 0.5385i 1.3711 - 0.5556i 0.9693
4.6250 1.5586 - 0.8030i 1.6312 - 0.8405i 0.9555
4.7500 1.8764 - 1.4666i 1.9844 - 1.5509i 0.9456
4.8750 1.8832 - 2.0905i 2.0664 - 2.2938i 0.9114
5.0000 1.2159 - 3.1027i 1.3216 - 3.3723i 0.9201
5.1250 0.2098 - 3.6778i 0.2413 - 4.2301i 0.8694
5.2500 -1.6165 - 3.2734i -1.7564 - 3.5568i 0.9203
5.3750 -2.2154 - 2.3597i -2.3326 - 2.4844i 0.9498
5.5000 -2.1657 - 1.4778i -2.2476 - 1.5337i 0.9635
5.6250 -1.9289 - 1.1157i -1.9659 - 1.1371i 0.9812
5.7500 -1.7058 - 0.8104i -1.7278 - 0.8208i 0.9873
5.8750 -1.5511 - 0.6322i -1.5665 - 0.6384i 0.9902
6.0000 -1.4389 - 0.5016i -1.4438 - 0.5033i 0.9966
6.1250 -1.3520 - 0.4295i -1.3559 - 0.4307i 0.9971
6.2500 -1.2591 - 0.3428i -1.2621 - 0.3436i 0.9976
6.3750 -1.1843 - 0.3000i -1.1866 - 0.3006i 0.9980
6.5000 -1.1241 - 0.2668i -1.1264 - 0.2673i 0.9980
6.6250 -1.0716 - 0.2302i -1.0725 - 0.2304i 0.9991
6.7500 -1.0206 - 0.2121i -1.0216 - 0.2123i 0.9990
6.8750 -0.9715 - 0.1980i -0.9722 - 0.1981i 0.9993
7.0000 -0.9376 - 0.1766i -0.9384 - 0.1767i 0.9992
7.1250 -0.9073 - 0.1613i -0.9077 - 0.1614i 0.9995
7.2500 -0.8793 - 0.1528i -0.8797 - 0.1529i 0.9995
7.3750 -0.8516 - 0.1459i -0.8519 - 0.1459i 0.9996
7.5000 -0.8271 - 0.1377i -0.8273 - 0.1377i 0.9998
7.6250 -0.8107 - 0.1259i -0.8109 - 0.1260i 0.9997
7.7500 -0.7879 - 0.1204i -0.7881 - 0.1204i 0.9997
7.8750 -0.7695 - 0.1170i -0.7696 - 0.1170i 0.9998
8.0000 -0.7513 - 0.1098i -0.7515 - 0.1098i 0.9998
8.1250 -0.7374 - 0.1058i -0.7376 - 0.1059i 0.9998
8.2500 -0.7240 - 0.1038i -0.7242 - 0.1038i 0.9998
8.3750 -0.7122 - 0.0994i -0.7123 - 0.0994i 0.9998
8.5000 -0.6963 - 0.0949i -0.6964 - 0.0950i 0.9998
8.6250 -0.6861 - 0.0930i -0.6862 - 0.0930i 0.9999
8.7500 -0.6792 - 0.0897i -0.6793 - 0.0897i 0.9998
8.8750 -0.6705 - 0.0886i -0.6706 - 0.0886i 0.9998
9.0000 -0.6606 - 0.0847i -0.6607 - 0.0847i 0.9999
9.1250 -0.6544 - 0.0815i -0.6545 - 0.0815i 0.9998
9.2500 -0.6463 - 0.0793i -0.6465 - 0.0794i 0.9997
9.3750 -0.6365 - 0.0765i -0.6367 - 0.0765i 0.9997
9.5000 -0.6287 - 0.0774i -0.6289 - 0.0774i 0.9997
9.6250 -0.6250 - 0.0762i -0.6253 - 0.0762i 0.9996
9.7500 -0.6207 - 0.0722i -0.6209 - 0.0722i 0.9997
9.8750 -0.6160 - 0.0711i -0.6162 - 0.0711i 0.9997
10.0000 -0.6081 - 0.0741i -0.6083 - 0.0741i 0.9998
Table 6: Two experimental frequency response functions H1(ω) and H2(ω) of the test rig.
3. Identification of model parameters – Suppose you have no access to the values of mass
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