264 S. B. Cooper et al. 50 100 150 200 250 Frequency (Hz) 10-5 10-4 10-3 10-2 10-1 H1 (mms-2/N) 300 350 400 450 500 Frequency (Hz) 10-4 10-3 10-2 10-1 H1 (mms-2/N) 50 100 150 200 250 Frequency (Hz) 10-5 10-4 10-3 10-2 10-1 H1 (mms-2/N) 300 350 400 450 500 Frequency (Hz) 10-4 10-3 10-2 10-1 100 H1 (mms-2/N) a b d c Fig. 27.3 Acceleration response function obtained from low-level broadband excitation performed on the nonlinear assembly. (a, b) (Bottom centre of the first cylinder) (c, d) (Drive point) Table 27.1 Estimated Linear resonance frequencies and damping ratios based on low-level random data Mode number Natural frequency (Hz) Damping ratio (%) Mode number Natural frequency (Hz) Damping ratio (%) 1 82.17 0.29 7 169.98 0.46 2 84.34 0.19 8 172.05 0.46 3 87.17 0.09 9 179.68 0.19 4 158.42 0.13 10 237.51 0.34 5 163.41 0.39 11 238.68 0.12 6 167.29 0.57 12 243.45 0.28 three modes of the assembly ranging from the lowest (10 N) to a highest (120 N) input levels of excitation. These steppedsine FRFs only consider the first harmonic and neglect all other higher-order harmonic components in both input and output. In Fig. 27.4a, a clear symptom of nonlinearity is observed based on the shift in frequency and maximum amplitude, most especially for the first mode around 82 Hz. The corresponding phase plot in Fig. 27.4b also shows the presence of nonlinear behaviour through the reduction observed in the phase plot as the excitation increases. Sine-sweep test was also conducted on the plate casing assembly at multiple excitation levels to gain some insight into the time series data, the sine-sweep test was conducted to cover a frequency bandwidth of 70–93 Hz. Accelerations at selected
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