The third order superharmonic response of a Duffing oscillator to narrow band random excitation is analyzed. The analysis shows the effect of excitation bandwidth on the response and stability of the non-linear oscillator. In particular the analysis shows that multivalued superharmonic response can occur only when the excitation bandwidth is small. Stability of the response is examined by constructing a mean square phase plane from a time dependent Fokker-Planck equation and also by perturbing the stationary solutions.
Topics in Catalysis
Department of Systems and Computer Engineering

Davies, H.G. (H. G.), & Rajan, S. (1986). Random superharmonic response of a Duffing oscillator. Topics in Catalysis, 111(1), 61–70. doi:10.1016/S0022-460X(86)81423-7