45 On the Behaviour of Structures with Many Nonlinear Elements 517 Fig. 45.13 FRF of response at mass 1 for a Gaussian random forcing of 100 N on a 30 DoF linear chain system with 50 cubic nonlinearities randomly located in the system. The value of k3 is steadily increased as before Fig. 45.14 FRF of response at mass 1 for a Gaussian random forcing of 100 N on a 30 DoF linear chain system with 100 cubic nonlinearities randomly located in the system. The value of k3 is steadily increased as before It is therefore seen that, as the nonlinear effects in the system increase, the linear modal structure is washed out, with the FRF tending towards only two identifiable peaks. A significant low frequency peak is seen close to the first natural frequency of the linear system and another peak is seen at frequencies significantly above the highest natural frequency of the underlying linear system. It appears that the action of the nonlinearities is to channel energy up and down the spectrum, washing out the linear modal structure, it is this washing out that may allow parallels to be drawn with SEA and opens up the possibility of using average energies to understand response across all frequency ranges.
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