Table 2 – FE model characteristics for crankshaft. FEM MoGeSeC EI Mode Freq. [Hz] MACFE/MOG Freq. [Hz] Error [%] MACFE/EI Freq. [Hz] Error [%] 1 314.68 77.3 314,4 0,09 76.4 314.36 0.1 2 447.38 93.5 449,65 -0,51 77.8 450.27 -0.64 3 712.97 93.6 727,36 -1,98 82.2 728.06 -2.07 4 782.98 80.4 832,09 -5,9 79.4 829.38 -5.59 5 811.12 90.3 878,83 -7,7 88.1 878.64 -7.68 6 1030.39 88.0 1111,55 -7,3 89.7 1110.82 -7.24 7 1147.57 83.8 1190,09 -3,57 79.4 1190.37 -3.6 mean 86.7 -3.84 81.8 -3.82 x Mode shapes shown in Figure 11 and 12 demonstrate the comparison between numerical and identified results. It is evident that EI nodes are more concentrated on only a part of the structure, whilst they are more widespread in the MoGeSeC case; the spatial incompleteness introduced through the EI selection criterion is considered one of the main important task that it can be improved. It is highly reduced through MoGeSeC approach. FREQUENCY RESPONSE COMPARISON In Figures 13 and 14 the FRFs comparison is shown. The responses do not come from the analysis of the same excitation and measuring points, because the selected nodes are different with respect to the selection criterion. Modal superposition and proportional identified damping is applied. Eigenfrequencies are easily well identified, as confirmed in Table 2, with both approaches; also modal displacements are estimated in a more than satisfactory manner. Similar good identification are obtained, thus a global balance evaluation is considered. NODE LOCATIONS COMPARISON Figures 15 and 16 depicts the first six nodes selected by MoGeSeC (in blue) and by EI (in red). For both the colours, the lighter the colour of the area, the less the region is suitable for the sensor location, in the same manner, the darker the colour of the area, the more the node location is suitable for depicting model modal behaviour. The darker zone underlines where a node can be selected, so in the selection process the zone changes in lighter colour because it is yet selected. Dividing Figures 15 and 16 in a matrix, the rows represent the selection proceedings of the nodes starting from 1 to 6, the columns represent the two approaches, in particular the first (on the left) represents the geometric weight, the second depicts the modal contribution and the third is the balance of the two previous choices proposed by MoGeSeC. For EI just one images is reported for showing the selection results (fourth column). The third and the fourth columns have coloured dots that depict the nodes previously selected, so in the first row no nodes are shown, because selection process is at the first step. There is a strong relationship between the analysed selection methods, as highlighted by the colour distribution. By observing the colour map, MoGeSeC appears to be very less sensitive to geometrical error in sensor location, in other words, displacements around the best location of sensor (selected by method) do not create a great change in the ill-conditioning of the reduced model. This is in accordance with the experience. EI shows a great sensitivity to the error in sensor location because it presents narrow good area nears worse, i.e. it does not univocally highlight positions that could be selected, in fact the images do not show uniform dark zones as in MoGeSeC results. In particular EI selects nodes without considering the body geometry, so it principally put the nodes on a part of the model, whereas MoGeSeC, considering the geometry, distributes the nodes across the whole external surface of the model, solution that is very easy and useful in experimental modal analysis. 289
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