Narrowband random third order superharmonic and one third order subharmonic response of a Duffing oscillator is discussed. A multiple time scale approach is used. The work is a more rigorous approach than that already published on random superharmonic response by the authors, and the results obtained corroborate the previous ones. In particular, random jumps in amplitude can occur, but are less likely to occur as the bandwidth of the excitation is increased. The results are further corroborated by comparison with digital simulation. In addition, new results on random subharmonic response are also presented, obtained by using the same approach.

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Journal Journal of Sound and Vibration
Davies, H.G. (H. G.), & Rajan, S. (1988). Random superharmonic and subharmonic response: Multiple time scaling of a duffing oscillator. Journal of Sound and Vibration, 126(2), 195–208. doi:10.1016/0022-460X(88)90235-0