516 T. Rogers et al. Fig. 45.11 Effect on the FRF of a single cubic spring with coefficient k3 D 10 4 Nm 3, positioned between masses 22 and 26, for varying magnitude of Gaussian white noise forcing Fig. 45.12 FRF of response at mass 1 for Gaussian random forcing of 100 N on a 30 DoF linear chain system with 30 cubic nonlinearities randomly located in the system. The value of k3 is increased and the modal structure of the system is clearly removed as the effect of the nonlinearity increases Considering Fig. 45.12, there is a clear modal structure at low values of k3. This structure closely resembles that of the underlying linear system seen in Fig. 45.3; it may be inferred that the presence of the nonlinearities in the system are having little effect on the modal behaviour. With increasing coefficient size, distortion to the linear modal structure becomes apparent by k3 D10 8 Nm 3; the effect is a complete disruption of the linear modal structure by k 3 D10 9 Nm 3 and by k3 D10 10 Nm 3 it has become almost impossible to distinguish more than two ‘resonance’ peaks: one at low frequency and one at high.
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