182 C.L. Fisher et al. Fig. 19.7 Experimental set up of test article Table 19.2 Natural frequency shifts due to mass increase of the cantilever arms Arm Freq. w/o Mass (Hz) Freq. w/Mass (Hz) 1 29 17 2 42 24 3 74 42.8 4 115 66.5 Fig. 19.8 Slowed service shock used in experimental testing 0 0.5 1 1.5 2 2.5 −80 −60 −40 −20 0 20 40 60 80 Time (s) Acceleration (g) Least Favorable Response Table 19.3 Temporal moments of synthesized wave compared to service shock Temporal moments Synth. wave Service shock Percent error Root mean energy (g) 24.35 23.60 3.14 Centroid (s) 0.20 0.16 28.32 Duration (s) 0.25 0.27 6.49 Skewness 1.69 1.64 3.42 of the original pyrotechnic shock was far higher than the natural frequency range of the test article requiring its slowing to lower the frequency range to that of the test article. This resulted in the final pyrotechnic shock, Fig. 19.8, having a duration of over 2 s which is longer than typically observed in shock environments. From the pyrotechnic shock seen in Fig. 19.8, a total of four additional shock time histories were generated using the four synthesis methods introduced previously in Sect.19.2, with the resulting time histories provided in Fig. 19.9. These four time histories and the service shock were the five shock environments used in the experimental failure tests. The LFR time history was generated focusing on arm 2 with a frequency response function generated from the random vibration test of the weighted test article. The temporal moments time history was generated by further limiting the decaying sinusoid synthesis method to match the first four temporal moments of the service shock. As seen in Table 19.3, three of the four temporal moments, root mean energy, kurtosis, and skewness, were matched with a reasonable error. However, it was challenging to closely match the centroid of the synthesized wave to the centroid of the service shock, which can be seen with the larger margin of error compared to the other temporal moments matched.
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