Clearly, there is some small contribution of the higher order modes at the very start of the transient. In order to include more modes, additional measurement points would be required. However, this is not possible with the 8 target points selected. In order to understand the effect of using less number of modes for the response, a mode superposition solution was performed using only the first five modes used in the expansion process; this essentially truncates the effects of the higher order modes by using the modal superposition solution scheme. The results after using modal superposition scheme instead of the direct integration approach are shown in Figure 14. The down-sampled results have also been shown at two comparison locations (Location 7, and 8) in Figure 14. At locations 7 and 8, as seen from Figures 14 b and d, there is definite improvement observed in the correlation between the FEA strains and the strains predicted through the proposed approach because the effect of higher order modes is not observed in the FEA solution as only first five modes were used in the mode superposition solution scheme. Location 4 was shown to provide excellent displacement response results as compared to the location 7. Note that the location 4 is nearer to the free edge of the BU structure, while the locations 7 and 8 are very near to the fixed edge of the BU structure. Invariably, higher displacement response and lower strain response will be observed at location 4 as compared to locations 7 and 8. The displacement response at location 7 was contaminated by experimental noise as observed in Case 1. Similarly, there is possibility of the strain response at location 4 to be contaminated by noise hence producing the discrepancies observed. However the locations 7 and 8 provide excellent strain response comparison, which validates the proposed methodology of estimating dynamic stress-strain experimentally. 0.25 0.3 0.35 0.4 -8 -6 -4 -2 0 2 4 6 8 x 10-6 Time (s) Y Normal Strain Strain at Location 7 downsampled FEA Expanded 0.25 0.3 0.35 0.4 -8 -6 -4 -2 0 2 4 6 8 x 10-6 Time (s) Y Normal Strain Modal Strain at Location 7 Modal FEA Expanded 0.25 0.3 0.35 0.4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10-5 Time (s) Y Normal Strain Modal Strain at Location 8 Modal FEA Expanded 0.25 0.3 0.35 0.4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10-5 Time (s) Y Normal Strain Strain at Location 8 downsampled FEA Expanded (a) (b) (c) (d) Figure 14: Comparison of strain response from FEA solution and predicted solution at Location 7 and 8 215
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