Figure 8: Overlay of strain response of box-beam at (a) tip and (b) interior location; predicted solution used first 10 modes in expansion process. To study the sensitivity of strain solution in detail, the displacement solution correlation was performed. Figure 9a, b &c shows the MAC for displacement solution between the predicted and reference model responses for time period corresponding to the strain time period (0.2 – 0.25 seconds). The MAC plots are shown for three different mode configurations – using first six, eight and then ten modes in expansion solution. The MAC for all the three mode configurations is very good because they all over-specify the required number of modes for expansion (recall that the forcing pulse excites first four modes primarily). So to show the difference between six, eight and ten mode configuration, the MAC plots are shown from 0.9 -1 indicating that the MAC for that particular time period is better than 90% always. Notice that even though with six-mode configuration, the displacement responses show good correlation (better than 90%), the correlation however improves with eight and ten-mode configuration confirming that greater number of modes used in the solution process will always yield better expansion results. Therefore, as a general rule, more modes will be required especially when considering strain rather than displacement. Figure 9: MAC between displacement response vectors of reference and expansion algorithm solutions with different number of modes used for expansion, (a) using first 6 modes (b) using first 8 modes, (c) using first 10 modes in expansion process; MAC performed for time steps 200-250 and shown for 0.9 – 1. 195
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