Methods are presented for calculating the response spectrum of a nonlinear oscillator with broadband random excitation. A perturbation approach is used for oscillators with slightly nonlinear spring elements to show that the effect of the nonlinearity is a slight shift in the spectrum peak. A new heuristic approach is used for oscillators with large nonlinearities and small damping to show that in addition to a shift in the peak an increase in spectral bandwidth also occurs. The Duffing oscillator is studied as a specific example.

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