Table 4 Percent Differences of Modal Frequencies for Varying Impact Amplitudes Modal Frequency: 1,000N Bolt Preload Level Mode Shape Low Amplitude High Amplitude % Difference A 498 498 0.00 B 655 654 0.15 C 1036 1013 2.24 D 1147 1146 0.09 E 1973 1973 0.00 F 2193 2152 1.89 Modal Frequency: 20,000N Bolt Preload Level Mode Shape Low Amplitude High Amplitude % Difference A 511 511 0.00 B 678 678 0.00 C 1195 1194 0.08 D 1149 1148 0.09 E 1975 1973 0.10 F 2289 2286 0.13 Since the modal frequencies were a poor indicator of nonlinearity in this frequency range, another analysis method was needed to quantify a change in nonlinearity. In this case, a simple comparison of frequency response functions was the clearest indicator of nonlinearity. In the problem being modeled, the load path enters through the rim of the circular plate and moves though the bolts into the square plate. To simulate this transmission of force, frequency response functions were measured between an impact point near the outer edge of the circular plate and the acceleration response on the square plate for both preload levels and both impact amplitude levels. These frequency response functions for both impact levels and the 1000N preload level are shown in Fig. 5. The same data for the 20000N preload level is shown in Fig. 6. The two responses vary substantially for impacts of different amplitude when the preload is low. This difference indicates significant system nonlinearity due to impact amplitude. The two responses are nearly identical, however, for the case where the preload is high. This result indicates that the nonlinearity due to impact amplitude decreases for higher preloads. This result was expected since the system behaves more as a single body, with little relative motion between the two plates. This decrease in nonlinearity will lead to an improved ability to estimate forces from a response measured across the boundary. Fig. 5 Frequency Response Functions for 1000N Preload Level 0 500 1000 1500 2000 2500 3000 3500 4000 10-4 10-3 10-2 10-1 10 0 10 1 10 2 10 3 FRFs for Impacts of Different Amplitude Measured on Circular Plate for 1000N Preload Test Frequency (Hz) |FRF| 10-20 lbf Impact 200-300 lbf Impact 0 500 1000 1500 2000 2500 3000 3500 4000 10-4 10-3 10-2 10-1 10 0 10 1 10 2 10 3 FRFs for Impacts of Different Amplitude Measured on Square Plate for 1000N Preload Test Frequency (Hz) |FRF| 10-20 lbf Impact 200-300 lbf Impact 572
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