12 Development of a Mapping Function for a Low- to High-Amplitude Input 117 Fig. 12.2 Detonator interface pre and post test 12.3 Background The initial test of the MAPP set-up occurred in April 2010 utilizing a pellet sized pyroshock input. These tests demonstrated that it was possible to match portions of a desired figure of merit. However, it led to desiring a better understanding of how the input can be utilized to predict a response. In other words, is there a mapping function between a modal and pyroshock input? To develop this relationship a complete modal study was performed on the MAPP test set-up in December 2011. Tri-axial accelerometers (consisting of 3 PCB 353B17 accelerometers on blocks) were glued to the plate on a 10 10 grid as shown in Fig. 12.3. Figure 12.4 depicts a schematic of the test set-up and the layout of accelerometer locations. The AFRL Tri-axial accelerometer that was placed on the bookshelf is show in Fig. 12.5a. A tri-axial accelerometer created by placing 3 PCB 353B17 accelerometers on a titanium block is shown in Fig. 12.5b, while Fig. 12.5c shows 2 rows of accelerometers used in this test. To perform this analysis a series of five impacts were captured at each accelerometer location. The Frequency Response Functions (FRF) at every location (input and output) was averaged together and the Auto Power Spectra (input location/ output location) and Cross Power Spectra (output location/ output location) were calculated using LMS Test.Lab. This data was saved and will be utilized to develop a mapping function between pyroshock and modal inputs. 12.3.1 Sub-scale Comparison Laboratory Study The results from prior sub-scale laboratory tests show that multiple inputs can significantly affect the desired outputs as described by Wolfson [2]. Figure 12.6 shows the acceleration time histories for the z-axis output (orthogonal with the plate) for two points on the plate [Fig. 12.6a, b], and the simultaneous impacts at both points [Fig. 12.6c]. It can be seen that the individual impacts have a maximum force of less than 40 g’s, however; if they are combined their overall force magnitude is higher at over 60 g’s. This point is further illustrated in the Frequency Response Functions (FRF’s) shown in Fig. 12.7. In this plot, the red line represents the FRF at the output location from an input at one point. The green line represents an input at the second point, and the blue line is the combined input at both points. Figure 12.7 shows that there are some different principal modes in the two individual inputs, but there are many frequencies where they do have similar responses. When the inputs are combined the magnitude of the response at specific frequencies are generally increased, however, in some instances the overall behavior is reduced at that frequency. The final comparison chart, and the one that shows the most significance, is in Fig. 12.7b. It shows the comparison of SRS from the individual and combined inputs. The SRS plots shown in Fig. 12.7b were calculated using LMS Test.Lab. This comparison shows a significant increase in the damage potential at the output point due to the simultaneous impacts. Above 1,000 Hz, there appears to be an order of magnitude increase in the SRS. This initial study has shown the effect that simultaneous impacts can have on the FRF’s and the SRS’s for the aluminum plate.
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